Publications Peter ZOLLER

2024

Articles

• R. Ott, T. Zache, M. Prüfer, S. Erne, M. Tajik, H. Pichler, J. Schmiedmayer, P. Zoller Hamiltonian Learning in Quantum Field Theories, Phys. Rev. Research 6 43284 (2024-12-16), http://dx.doi.org/10.1103/PhysRevResearch.6.043284 doi:10.1103/PhysRevResearch.6.043284 (ID: 721175) Toggle Abstract
  We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for varying spatial measurement resolutions gives access to field theories at different energy scales, and allows to learn a flow of Hamiltonians reminiscent of the renormalization group. Our method, which we demonstrate in both theoretical studies and available data from a quantum gas experiment, promises new ways of addressing the emergence of quantum field theories in quantum simulation experiments.
• H. Kamal, J. Kemp, Y. He, Y. Fuji, M. Aidelsburger, P. Zoller, N. Y. Yao Floquet Flux Attachment in Cold Atomic Systems, Phys. Rev. Lett. 133 163403 (2024-10-17), http://dx.doi.org/10.1103/PhysRevLett.133.163403 doi:10.1103/PhysRevLett.133.163403 (ID: 721233) Toggle Abstract
  Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably the fractional quantum Hall effect. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically-driven (Floquet) system of either spins or hard-core bosons. We demonstrate that such a system naturally realizes correlated hopping interactions and provides a sharp connection between such interactions and flux attachment. Starting with a simple, nearest-neighbor, free boson model, we find evidence -- from both a coupled wire analysis and large-scale density matrix renormalization group simulations -- that Floquet flux attachment stabilizes the bosonic integer quantum Hall state at 1/4 filling (on a square lattice), and the Halperin-221 fractional quantum Hall state at 1/6 filling (on a honeycomb lattice). At 1/2 filling on the square lattice, time-reversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an optical-lattice-based implementation of our model on a square lattice and discuss prospects for adiabatic preparation as well as effects of Floquet heating.
• B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, L. Piroli Many-body entropies and entanglement from polynomially-many local measurements, Phys. Rev. X 14 31035 (2024-08-26), http://dx.doi.org/10.1103/PhysRevX.14.031035 doi:10.1103/PhysRevX.14.031035 (ID: 721143) Toggle Abstract
  Randomized measurements (RMs) provide a practical scheme to probe complex many-body quantum systems. While they are a very powerful tool to extract local information, global properties such as entropy or bipartite entanglement remain hard to probe, requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. Combined with the RM toolbox, this yields a simple strategy for entropy and entanglement estimation which is provably accurate assuming that the state to be measured satisfies the AFCs, and which only requires polynomially-many measurements and post-processing operations. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.
• L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, M. K. Joshi Observing the quantum Mpemba effect in quantum simulations, PRL 133 10402 (2024-07-01), http://dx.doi.org/10.1103/PhysRevLett.133.010402 doi:10.1103/PhysRevLett.133.010402 (ID: 721174) Toggle Abstract
  The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena— the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and post-processed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.
• J. Ye, P. Zoller Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics, Phys. Rev. Lett. 132 190001 (2024-05-07), http://dx.doi.org/10.1103/PhysRevLett.132.190001 doi:10.1103/PhysRevLett.132.190001 (ID: 721252) Toggle Abstract
  Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today’s realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier.
• R. Stricker, J. Carrasco, M. Ringbauer, L. Postler, M. Meth, C. Edmunds, P. Schindler, R. Blatt, P. Zoller, B. Kraus, T. Monz Towards experimental classical verification of quantum computation, Quantum Sci. Technol. 9 (2024-02-26), http://dx.doi.org/10.1088/2058-9565/ad2986 doi:10.1088/2058-9565/ad2986 (ID: 720821) Toggle Abstract
  With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers [4,5]. In a recent breakthrough in computer science [6-8], a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proof-of-principle experiment a verification protocol using only classical means on a small trapped-ion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gate-level benchmarking [9], or additional quantum resources in case we do not have access to or trust in the device to be tested [5]. While our experimental demonstration uses a simplified version [10] of Mahadev's protocol [6] we demonstrate the necessary steps for verifying fully untrusted devices. A scaled-up version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on post-quantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaled-up version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage [8], generating [12] and certifying quantum randomness [7], or composable remote state preparation [13].
• J. Carrasco, M. Votto, V. Vitale, C. Kokail, A. Neven, P. Zoller, B. Vermersch, B. Kraus Entanglement phase diagrams from partial transpose moments, Phys. Rev. A 109 12422 (2024-01-18), http://dx.doi.org/10.1103/PhysRevA.109.012422 doi:10.1103/PhysRevA.109.012422 (ID: 720958) Toggle Abstract
  We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a tripartite pure state. We introduce a ratio of simple polynomials of low-order moments of the partially transposed reduced density matrix and show that this ratio takes well-defined values in the thermodynamic limit for various families of entangled states. This allows to sharply distinguish entanglement phases, in a way that can be understood from a quantum information perspective based on the spectrum of the partially transposed density matrix. We analyze in particular the entanglement phase diagram of Haar random states, states resulting form the evolution of chaotic Hamiltonians, stabilizer states, which are outputs of Clifford circuits, Matrix Product States, and fermionic Gaussian states. We show that for Haar random states the resulting phase diagram resembles the one obtained via the negativity and that for all the cases mentioned above a very distinctive behaviour is observed. Our results can be used to experimentally test necessary conditions for different types of mixed-state randomness, in quantum states formed in quantum computers and programmable quantum simulators.

Preprints

• D. Gonzalez Cuadra, M. Hamdan, T. Zache, B. Braverman, M. Kornjaca, A. Lukin, S. H. Cantu, F. Liu, S. Wang, A. Keesling, M. Lukin, P. Zoller, A. Bylinskii Observation of string breaking on a (2 + 1)D Rydberg quantum simulator, (2024-10-21), arXiv:2410.16558v1 arXiv:2410.16558v1 (ID: 721288) Toggle Abstract
  Lattice gauge theories (LGTs) describe a broad range of phenomena in condensed matter and particle physics. A prominent example is confinement, responsible for bounding quarks inside hadrons such as protons or neutrons. When quark-antiquark pairs are separated, the energy stored in the string of gluon fields connecting them grows linearly with their distance, until there is enough energy to create new pairs from the vacuum and break the string. While such phenomena are ubiquitous in LGTs, simulating the resulting dynamics is a challenging task. Here, we report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator based on neutral atom arrays. We show that a (2+1)D LGT with dynamical matter can be efficiently implemented when the atoms are placed on a Kagome geometry, with a local U(1) symmetry emerging from the Rydberg blockade, while long-range Rydberg interactions naturally give rise to a linear confining potential for a pair of charges, allowing us to tune both their masses as well as the string tension. We experimentally map out the corresponding phase diagram by adiabatically preparing the ground state of the atom array in the presence of defects, and observe substructure of the confined phase, distinguishing regions dominated by fluctuating strings or by broken string configurations. Finally, by harnessing local control over the atomic detuning, we quench string states and observe string breaking dynamics exhibiting a many-body resonance phenomenon. Our work paves a way to explore phenomena in high-energy physics using programmable quantum simulators.
• R. Ott, T. Zache, N. Maskara, M. Lukin, P. Zoller, H. Pichler Probing topological entanglement on large scales, (2024-08-22), arXiv:2408.12645 arXiv:2408.12645 (ID: 721272) Toggle Abstract
  Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. However, measuring such entropies, which can be used to certify topological order, on large partitions is challenging and becomes practically unfeasible for large systems. We propose a protocol based on local adiabatic deformations of the Hamiltonian which extracts the universal features of long-range topological entanglement from measurements on small subsystems of finite size, trading an exponential number of measurements against a polynomial-time evolution. Our protocol is general and readily applicable to various quantum simulation architectures. We apply our method to various string-net models representing both abelian and non-abelian topologically ordered phases, and illustrate its application to neutral atom tweezer arrays with numerical simulations.
• A. Kruckenhauser, M. Yuan, H. Zheng, M. Mamaev, P. Zeng, X. M. Mao, Q. Xu, T. Zache, L. Jiang, R. van Bijnen, P. Zoller Dark spin-cats as biased qubits, (2024-08-08), arXiv:2408.04421v1 arXiv:2408.04421v1 (ID: 721274) Toggle Abstract
  We present a biased atomic qubit, universally implementable across all atomic platforms, encoded as a `spin-cat' within ground state Zeeman levels. The key characteristic of our configuration is the coupling of the ground state spin manifold of size Fg≫1 to an excited Zeeman spin manifold of size Fe=Fg−1 using light. This coupling results in eigenstates of the driven atom that include exactly two dark states in the ground state manifold, which are decoupled from light and immune to spontaneous emission from the excited states. These dark states constitute the `spin-cat', leading to the designation `dark spin-cat'. We demonstrate that under strong Rabi drive and for large Fg, the `dark spin-cat' is autonomously stabilized against common noise sources and encodes a qubit with significantly biased noise. Specifically, the bit-flip error rate decreases exponentially with Fg relative to the dephasing rate. We provide an analysis of dark spin-cats, their robustness to noise, and discuss bias-preserving single qubit and entangling gates, exemplified on a Rydberg tweezer platform.
• A. Chu, V. Martinez-Lahuerta, M. Miklos, K. Kim, P. Zoller, K. Hammerer, J. Ye, A. M. Rey Exploring the interplay between mass-energy equivalence, interactions and entanglement in an optical lattice clock, (2024-06-06), arXiv:2406.03804v1 arXiv:2406.03804v1 (ID: 721260) Toggle Abstract
  We propose protocols that probe manifestations of the mass-energy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the mass-energy equivalence effects (gravitational redshift and second order Doppler shift) in such setting, we devise a dressing protocol using an additional nuclear spin state. We then analyze the interplay between photon-mediated interactions and gravitational redshift and show that such interplay can lead to entanglement generation and frequency synchronization. In the regime where all atomic spins synchronize, we show the synchronization time depends on the initial entanglement of the state and can be used as a proxy of its metrological gain compared to a classical state. Our work opens new possibilities for exploring the effects of general relativity on quantum coherence and entanglement in OLC experiments.
• T. Olsacher, T. Kraft, C. Kokail, B. Kraus, P. Zoller Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems, (2024-05-10), arXiv:2405.06768 arXiv:2405.06768 (ID: 721275) Toggle Abstract
  We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present various strategies to learn the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare different ansätze based on an experimentally accessible "learning error" which we consider as a function of the number of runs of the experiment. Initially, the learning error decreasing with the inverse square root of the number of runs, as the error in the reconstructed parameters is dominated by shot noise. Eventually the learning error remains constant, allowing us to recognize missing ansatz terms. A central aspect of our approach is to (re-)parametrize ansätze by introducing and varying the dependencies between parameters. This allows us to identify the relevant parameters of the system, thereby reducing the complexity of the learning task. Importantly, this (re-)parametrization relies solely on classical post-processing, which is compelling given the finite amount of data available from experiments. A distinguishing feature of our approach is the possibility to learn the Hamiltonian, without the necessity of learning the complete Liouvillian, thus further reducing the complexity of the learning task. We illustrate our method with two, experimentally relevant, spin models.
• D. Vasilyev, A. Shankar, C. R. Kaubrügger, P. Zoller Optimal Multiparameter Metrology: The Quantum Compass Solution, (2024-04-22), arXiv:2404.14194 arXiv:2404.14194 (ID: 721276) Toggle Abstract
  We study optimal quantum sensing of multiple physical parameters using repeated measurements. In this scenario, the Fisher information framework sets the fundamental limits on sensing performance, yet the optimal states and corresponding measurements that attain these limits remain to be discovered. To address this, we extend the Fisher information approach with a second optimality requirement for a sensor to provide unambiguous estimation of unknown parameters. We propose a systematic method integrating Fisher information and Bayesian approaches to quantum metrology to identify the combination of input states and measurements that satisfies both optimality criteria. Specifically, we frame the optimal sensing problem as an optimization of an asymptotic Bayesian cost function that can be efficiently solved numerically and, in many cases, analytically. We refer to the resulting optimal sensor as a `quantum compass' solution, which serves as a direct multiparameter counterpart to the Greenberger-Horne-Zeilinger state-based interferometer, renowned for achieving the Heisenberg limit in single-parameter metrology. We provide exact quantum compass solutions for paradigmatic multiparameter problem of sensing two and three parameters using an SU(2) sensor. Our metrological cost function opens avenues for quantum variational techniques to design low-depth quantum circuits approaching the optimal sensing performance in the many-repetition scenario. We demonstrate this by constructing simple quantum circuits that achieve the Heisenberg limit for vector field and 3D rotations estimation using a limited set of gates available on a trapped-ion platform. Our work introduces and optimizes sensors for a practical notion of optimality, keeping in mind the ultimate goal of quantum sensors to precisely estimate unknown parameters.

2023

Articles

• M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring Large-Scale Entanglement in Quantum Simulation, Nature 624 539 (2023-11-29), http://dx.doi.org/10.1038/s41586-023-06768-0 doi:10.1038/s41586-023-06768-0 (ID: 721080) Toggle Abstract
  Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian, as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a 1D XXZ Heisenberg chain on a 51-ion programmable quantum simulator and perform sample-efficient `learning' of the entanglement Hamiltonian for subsystems of up to 20 lattice sites. Our experiments provide compelling evidence for a local structure of the entanglement Hamiltonian. This observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially-varying temperature profile as a signature of entanglement. Our results also show the transition from area to volume-law scaling of Von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.
• T. Zache, D. Gonzalez Cuadra, P. Zoller Quantum and classical spin network algorithms for q-deformed Kogut-Susskind gauge theories, Phys. Rev. Lett. 131 171902 (2023-10-24), http://dx.doi.org/10.1103/PhysRevLett.131.171902 doi:10.1103/PhysRevLett.131.171902 (ID: 721075) Toggle Abstract
  Treating the infinite-dimensional Hilbert space of non-abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical Spin Network Algorithms for q-deformed gauge theories (SNAQs). To be explicit, we focus on SU(2)k gauge theories, that are controlled by the deformation parameter k and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)k plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-abelian gauge theories far from equilibrium where no other methods are currently available.
• T. Zache, D. González-Cuadra, P. Zoller Fermion-qudit quantum processors for simulating lattice gauge theories with matter, Quantum 7 1140 (2023-10-16), http://dx.doi.org/10.22331/q-2023-10-16-1140 doi:10.22331/q-2023-10-16-1140 (ID: 721067) Toggle Abstract
  Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this work, we present a complete Rydberg-based architecture, co-designed to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardware-efficient manner. Ref. [1] showed how a qudit processor, where non-abelian gauge fields are locally encoded and time-evolved, considerably reduces the required simulation resources compared to standard qubit-based quantum computers. Here we integrate the latter with a recently introduced fermionic quantum processor [2], where fermionic statistics are accounted for at the hardware level, allowing us to construct quantum circuits that preserve the locality of the gauge-matter interactions. We exemplify the flexibility of such a fermion-qudit processor by focusing on two paradigmatic high-energy phenomena. First, we present a resource-efficient protocol to simulate the Abelian-Higgs model, where the dynamics of confinement and string breaking can be investigated. Then, we show how to prepare hadrons made up of fermionic matter constituents bound by non-abelian gauge fields, and show how to extract the corresponding hadronic tensor. In both cases, we estimate the required resources, showing how quantum devices can be used to calculate experimentally-relevant quantities in particle physics.
• D. González-Cuadra, D. Bluvstein, M. Kalinowski, C. R. Kaubrügger, N. Maskara, P. Naldesi, T. Zache, A. Kaufman, M. Lukin, H. Pichler, B. Vermersch, J. Ye, P. Zoller Fermionic quantum processing with programmable neutral atom arrays, PNAS 120 e2304294120 (2023-08-22), http://dx.doi.org/10.1073/pnas.2304294120 doi:10.1073/pnas.2304294120 (ID: 721066) Toggle Abstract
  Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding non-local fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement non-local tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation, as well as to simulate lattice gauge theory dynamics.
• P. Naldesi, A. Elben, A. Minguzzi, D. Clement, P. Zoller, B. Vermersch Fermionic correlation functions from randomized measurements in programmable atomic quantum devices, Phys. Rev. Lett. 131 60601 (2023-08-07), http://dx.doi.org/10.1103/PhysRevLett.131.060601 doi:10.1103/PhysRevLett.131.060601 (ID: 720886) Toggle Abstract
  We provide a measurement protocol to estimate 2- and 4-point fermionic correlations in ultra-cold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.
• Q. Xu, G. Zheng, Y. Wang, P. Zoller, A. A. Clerk, L. Jiang Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits, npj Quantum Information 9 (2023-08-03), http://dx.doi.org/10.1038/s41534-023-00746-0 doi:10.1038/s41534-023-00746-0 (ID: 720895) Toggle Abstract
  We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ1 and the engineered dissipation rate κ2. Under a practical noise ratio κ1/κ2=10−3, the repetition-SC scheme can reach a 10−15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.
• C. R. Kaubrügger, A. Shankar, D. Vasilyev, P. Zoller Optimal and Variational Multi-Parameter Quantum Metrology and Vector Field Sensing, PRX Quantum 4 20333 (2023-06-01), http://dx.doi.org/10.1103/PRXQuantum.4.020333 doi:10.1103/PRXQuantum.4.020333 (ID: 721056) Toggle Abstract
  We study multi-parameter sensing of 2D and 3D vector fields within the Bayesian framework for SU(2) quantum interferometry. We establish a method to determine the optimal quantum sensor, which establishes the fundamental limit on the precision of simultaneously estimating multiple parameters with an N-atom sensor. Keeping current experimental platforms in mind, we present sensors that have limited entanglement capabilities, and yet, significantly outperform sensors that operate without entanglement and approach the optimal quantum sensor in terms of performance. Furthermore, we show how these sensors can be implemented on current programmable quantum sensors with variational quantum circuits by minimizing a metrological cost function. The resulting circuits prepare tailored entangled states and perform measurements in an appropriate entangled basis to realize the best possible quantum sensor given the native entangling resources available on a given sensor platform. Notable examples include a 2D and 3D quantum ``compass'' and a 2D sensor that provides a scalable improvement over unentangled sensors. Our results on optimal and variational multi-parameter quantum metrology are useful for advancing precision measurements in fundamental science and ensuring the stability of quantum computers, which can be achieved through the incorporation of optimal quantum sensors in a quantum feedback loop.

Book

• D. Gross, A. Sevrin, P. Zoller The Physics of Quantum Information, Proceedings of the 28th Solvay Conference on Physics, (2023-05-01), http://dx.doi.org/10.1142/13369 doi:10.1142/13369 (ID: 721068)

Preprint

• M. Meth, J. Haase, J. Zhang, C. Edmunds, L. Postler, A. Steiner, A. Jena, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. A. Muschik, M. Ringbauer Simulating 2D lattice gauge theories on a qudit quantum computer, (2023-10-18), arXiv:2310.12110 arXiv:2310.12110 (ID: 721176) Toggle Abstract
  Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in d different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

2022

Articles

• A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation, Quantum Sci. Technol. 8 (2022-12-19), http://dx.doi.org/10.1088/2058-9565/aca996 doi:10.1088/2058-9565/aca996 (ID: 720885) Toggle Abstract
  We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the well-structured manifolds of states with principal quantum number n. This enables us to construct generalized large-spin Heisenberg models for which we develop state-preparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sine-Gordon and massive Schwinger models. Moreover, these high-dimensional manifolds also offer the opportunity to perform quantum information processing operations for qudit-based quantum computing, which we exemplify with an entangling gate and a state-transfer protocol for the states in the neighborhood of the circular Rydberg level.
• A. Elben, S. Flammia, Hsin Y. Huang, R. Kueng, J. Preskill, B. Vermersch, Peter Zoller The randomized measurement toolbox, Nat. Rev. Phys. s42254 (2022-12-02), http://dx.doi.org/10.1038/s42254-022-00535-2 doi:10.1038/s42254-022-00535-2 (ID: 720824) Toggle Abstract
  Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages; for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.
• Athreya Shankar, E. A. Yuzbashyan, V. Gurarie, Peter Zoller, J. J. Bollinger, A M. Rey Simulating dynamical phases of chiral p+ip superconductors with a trapped ion magnet, PRX Quantum 3 40324 (2022-11-30), http://dx.doi.org/10.1103/PRXQuantum.3.040324 doi:10.1103/PRXQuantum.3.040324 (ID: 720833) Toggle Abstract
  Two-dimensional p+ip superconductors and superfluids are systems that feature chiral behavior emerging from the Cooper pairing of electrons or neutral fermionic atoms with non-zero angular momentum. Their realization has been a longstanding goal because they offer great potential utility for quantum computation and memory. However, they have so far eluded experimental observation both in solid state systems as well as in ultracold quantum gases. Here, we propose to leverage the tremendous control offered by rotating two-dimensional trapped-ion crystals in a Penning trap to simulate the dynamical phases of two-dimensional p+ip superfluids. This is accomplished by mapping the presence or absence of a Cooper pair into an effective spin-1/2 system encoded in the ions' electronic levels. We show how to infer the topological properties of the dynamical phases, and discuss the role of beyond mean-field corrections. More broadly, our work opens the door to use trapped ion systems to explore exotic models of topological superconductivity and also paves the way to generate and manipulate skyrmionic spin textures in these platforms.
• Daniel González-Cuadra , T. Zache, J. Carrasco, Barbara Kraus, Peter Zoller Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms, Phys. Rev. Lett. 129 160501 (2022-10-13), http://dx.doi.org/10.1103/PhysRevLett.129.160501 doi:10.1103/PhysRevLett.129.160501 (ID: 720827)
• S. Flannigan, N. Pearson, G. H. Low, A. Buyskikh, I. Bloch, Peter Zoller, M. Troyer, A. J. Daley Propagation of errors and quantitative quantum simulation with quantum advantage, Quantum Sci. Technol. 7 45025 (2022-08-30), http://dx.doi.org/10.1088/2058-9565/ac88f5 doi:10.1088/2058-9565/ac88f5 (ID: 720858) Toggle Abstract
  The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.
• T. Olsacher, L. Pastori, C. Kokail, L. Sieberer, Peter Zoller Digital quantum simulation, learning of the Floquet Hamiltonian, and quantum chaos of the kicked top, J. Phys. A: Math. Gen. 55 (2022-08-19), http://dx.doi.org/10.1088/1751-8121/ac8087 doi:10.1088/1751-8121/ac8087 (ID: 720859) Toggle Abstract
  The kicked top is one of the paradigmatic models in the study of quantum chaos (Haake et al 2018 Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)). Recently it has been shown that the onset of quantum chaos in the kicked top can be related to the proliferation of Trotter errors in digital quantum simulation (DQS) of collective spin systems. Specifically, the proliferation of Trotter errors becomes manifest in expectation values of few-body observables strongly deviating from the target dynamics above a critical Trotter step, where the spectral statistics of the Floquet operator of the kicked top can be predicted by random matrix theory. In this work, we study these phenomena in the framework of Hamiltonian learning (HL). We show how a recently developed HL protocol can be employed to reconstruct the generator of the stroboscopic dynamics, i.e., the Floquet Hamiltonian, of the kicked top. We further show how the proliferation of Trotter errors is revealed by HL as the transition to a regime in which the dynamics cannot be approximately described by a low-order truncation of the Floquet–Magnus expansion. This opens up new experimental possibilities for the analysis of Trotter errors on the level of the generator of the implemented dynamics, that can be generalized to the DQS of quantum many-body systems in a scalable way. This paper is in memory of our colleague and friend Fritz Haake.
• L. Pastori, T. Olsacher, C. Kokail, Peter Zoller Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning, PRX Quantum 3 30324 (2022-08-18), http://dx.doi.org/10.1103/PRXQuantum.3.030324 doi:10.1103/PRXQuantum.3.030324 (ID: 720828) Toggle Abstract
  The goal of digital quantum simulation is to approximate the dynamics of a given target Hamiltonian via a sequence of quantum gates, a procedure known as Trotterization. The quality of this approximation can be controlled by the so called Trotter step, that governs the number of required quantum gates per unit simulation time, and is intimately related to the existence of a time-independent, quasilocal Hamiltonian that governs the stroboscopic dynamics, refered to as the Floquet Hamiltonian of the Trotterization. In this work, we propose a Hamiltonian learning scheme to reconstruct the implemented Floquet Hamiltonian order-by-order in the Trotter step: this procedure is efficient, i.e., it requires a number of measurements that scales polynomially in the system size, and can be readily implemented in state-of-the-art experiments. With numerical examples, we propose several applications of our method in the context of verification of quantum devices, from the characterization of the distinct sources of errors in digital quantum simulators to the design of new types of quantum gates. Furthermore, we show how our approach can be extended to the case of non-unitary dynamics and used to learn Floquet Liouvillians, thereby offering a way of characterizing the dissipative processes present in NISQ quantum devices.
• A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, Peter Zoller Practical quantum advantage in quantum simulation, Nature 607 676 (2022-07-27), http://dx.doi.org/10.1038/s41586-022-04940-6 doi:10.1038/s41586-022-04940-6 (ID: 720857) Toggle Abstract
  The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as ‘quantum advantage’. As a next step along the development of this technology, it is now important to discuss ‘practical quantum advantage’, the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital–analogue devices that exist today already promise substantial flexibility in near-term applications.
• M. Di Liberto, A. Kruckenhauser, P. Zoller, M. Baranov Topological phonons in arrays of ultracold dipolar particles, Quantum 6 731 (2022-05-31), http://dx.doi.org/10.22331/q-2022-06-07-731 doi:10.22331/q-2022-06-07-731 (ID: 720680) Toggle Abstract
  The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for developing new fault-tolerant applications. We discuss how to design and study a large variety of topology-related phenomena for phonon-like collective modes in arrays of ultracold polarized dipolar particles. These modes are coherently propagating vibrational excitations, corresponding to oscillations of particles around their equilibrium positions, which exist in the regime where long-range interactions dominate over single-particle motion. We demonstrate that such systems offer a distinct and versatile tool to investigate topological effects that can be accessed by choosing the underlying crystal structure and by controlling the anisotropy of the interactions. Our results show that arrays of dipolar particles provide a promising unifying platform to investigate topological phenomena with phononic modes.
• T. Zache, C. Kokail, B. Sundar, P. Zoller Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter, Quantum 6 702 (2022-04-27), http://dx.doi.org/10.22331/q-2022-04-27-702 doi:10.22331/q-2022-04-27-702 (ID: 720692) Toggle Abstract
  Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian to probe this relationship experimentally. This is made possible by exploiting the quasi-local structure of Entanglement Hamiltonians. The feasibility of this proposal is illustrated for two paradigmatic examples realizable with current technology, an integer quantum Hall state of non-interacting fermions on a 2D lattice and a symmetry protected topological state of interacting fermions on a 1D chain. Our results pave the road towards an experimental identification of topological order in strongly correlated quantum many-body systems.
• V. Kuzmin, T. Zache, L. Pastori, A. Celi, M. Baranov, P. Zoller Probing infinite many-body quantum systems with finite size quantum simulators, PRX Quantum 3 20304 (2022-04-06), http://dx.doi.org/10.1103/PRXQuantum.3.020304 doi:10.1103/PRXQuantum.3.020304 (ID: 720681) Toggle Abstract
  Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators, which limits their reliability for strongly correlated systems, for instance in the vicinity of a quantum phase transition (QPT). Here, we propose a protocol that makes optimal use of a given finite system size by directly preparing, via coherent evolution with a local deformation of the system Hamiltonian, a part of the translation-invariant infinite-sized system as a mixed state representing the reduced density operator. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasi-particle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a non-integrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs.
• V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, Barbara Kraus, Peter Zoller, P. Calabrese, B. Vermersch, M. Dalmonte Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12 106 (2022-03-25), http://dx.doi.org/10.21468/SciPostPhys.12.3.106 doi:10.21468/SciPostPhys.12.3.106 (ID: 720887) Toggle Abstract
  Abstract<br /> <br /> When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of (quantum) information throughout the system. Here, we show that, in the presence of continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics: in given quantum number sectors, entropy decreases as a function of time, signalling dynamical purification. Such dynamical purification bridges between two distinct short and intermediate time regimes, characterized by a log-volume and log-area entropy law, respectively. It is generic to symmetric quantum evolution, and as such occurs for different partition geometry and topology, and classes of (local) Liouville dynamics. We then develop a protocol to measure symmetry-resolved entropies and negativities in synthetic quantum systems based on the random unitary toolbox, and demonstrate the generality of dynamical purification using experimental data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems, and, in particular, in noisy-intermediate scale quantum devices.
• C. Marciniak, T. Feldker, I. Pogorelov, C. R. Kaubrügger, D. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, T. Monz Optimal metrology with variational quantum circuits on trapped ions, Nature 603 604 (2022-03-23), http://dx.doi.org/10.1038/s41586-022-04435-4 doi:10.1038/s41586-022-04435-4 (ID: 720667) Toggle Abstract
  Cold atoms and ions exhibit unparalleled performance in frequency metrology epitomized in the atomic clock. More recently, such atomic systems have been used to implement programmable quantum computers and simulators with highest reported operational fidelities across platforms. Their strength in metrology and quantum information processing offers the opportunity to utilize tailored, programmable entanglement generation to approach the `optimal quantum sensor' compatible with quantum mechanics. Here we report quantum enhancement in metrology beyond squeezing through low-depth, variational quantum circuits searching for optimal input states and measurement operators in a trapped ion platform. We perform entanglement-enhanced Ramsey interferometry finding optimal parameters for variational quantum circuits using a Bayesian approach to stochastic phase estimation tailored to the sensor platform capabilities and finite dynamic range of the interferometer. We verify the performance by both directly using theory predictions of optimal parameters, and performing online quantum-classical feedback optimization to `self-calibrate' the variational parameters. In both cases we find that variational circuits outperform classical and direct spin squeezing strategies under realistic noise and imperfections. With 26 ions we achieve 2.02(8) dB of metrological gain over classical interferometers.
• L. K. Joshi, A. Elben, A. Vikram, B. Vermersch, V. Galitski, P. Zoller Probing many-body quantum chaos with quantum simulators, Phys. Rev. X (2022-01-27), http://dx.doi.org/10.1103/PhysRevX.12.011018 doi:10.1103/PhysRevX.12.011018 (ID: 720665) Toggle Abstract
  The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (pSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol which allows the measurement of SFF and pSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with simulations for Hamiltonian and Floquet many-body spin-systems.

2021

Articles

• C. R. Kaubrügger, D. Vasilyev, T. Schulte, K. Hammerer, P. Zoller Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks, Phys. Rev. X 11 41045 (2021-12-06), http://dx.doi.org/10.1103/PhysRevX.11.041045 doi:10.1103/PhysRevX.11.041045 (ID: 720629) Toggle Abstract
  We discuss quantum variational optimization of Ramsey interferometry with ensembles of N entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean square error of the estimated phase for a given prior distribution, i.e. we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.
• A. Rath, R. van Bijnen, A. Elben, P. Zoller, B. Vermersch Importance sampling of randomized measurements for probing entanglement, Phys. Rev. Lett. 127 (2021-11-11), http://dx.doi.org/10.1103/PhysRevLett.127.200503 doi:10.1103/PhysRevLett.127.200503 (ID: 720632) Toggle Abstract
  We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the required number of measurements to estimate the purity of product states and GHZ states.
• C. Kokail, B. Sundar, T. Zache, A. Elben, B. Vermersch, M. Dalmonte, R. van Bijnen, P. Zoller Quantum Variational Learning of the Entanglement Hamiltonian, Phys. Rev. Lett. 127 170501 (2021-10-22), http://dx.doi.org/10.1103/PhysRevLett.127.170501 doi:10.1103/PhysRevLett.127.170501 (ID: 720649) Toggle Abstract
  Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
• A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng, B. Kraus Symmetry-resolved entanglement detection using partial transpose moments, npj Quantum Information 7 (2021-10-20), http://dx.doi.org/10.1038/s41534-021-00487-y doi:10.1038/s41534-021-00487-y (ID: 720635) Toggle Abstract
  We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.
• D. Paulson, L. Dellantonio, J. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, C. A. Muschik Simulating 2D effects in lattice gauge theories on a quantum computer, PRX Quantum 2 30334 (2021-08-25), http://dx.doi.org/10.1103/PRXQuantum.2.030334 doi:10.1103/PRXQuantum.2.030334 (ID: 720526) Toggle Abstract
  Quantum computing is in its greatest upswing, with so-called noisy-intermediate-scale-quantum devices heralding the computational power to be expected in the near future. While the field is progressing toward quantum advantage, quantum computers already have the potential to tackle classically intractable problems. Here, we consider gauge theories describing fundamental-particle interactions. On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study ground-state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low-energy observable quantities, e.g., the hadron spectrum, in the continuum theory. By including both dynamical matter and a nonminimal gauge-field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two variational-quantum-eigensolver- (VQE) based protocols for the study of magnetic field effects and for taking an important first step toward computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations.
• C. Kokail, R. van Bijnen, A. Elben, B. Vermersch, P. Zoller Entanglement Hamiltonian Tomography in Quantum Simulation, Nature Phys. (2021-06-24), http://dx.doi.org/10.1038/s41567-021-01260-w doi:10.1038/s41567-021-01260-w (ID: 720530) Toggle Abstract
  Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum devices. Here we discuss an efficient tomographic protocol for reconstructing reduced density matrices and entanglement spectra for spin systems. The key step is a parametrization of the reduced density matrix in terms of an entanglement Hamiltonian involving only quasi local few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomised measurements. The ansatz is suggested by Conformal Field Theory in quench dynamics, and via the Bisognano-Wichmann theorem for ground states. Not only does the protocol provide a testbed for these theories in quantum simulators, it is also applicable outside these regimes. We show the validity and efficiency of the protocol for a long-range Ising model in 1D using numerical simulations. Furthermore, by analyzing data from 10 and 20 ion quantum simulators [Brydges \textit{et al.}, Science, 2019], we demonstrate measurement of the evolution of the entanglement spectrum in quench dynamics.
• V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, M. Dalmonte Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12 (2021-03-25), http://dx.doi.org/10.21468/SciPostPhys.12.3.106 doi:10.21468/SciPostPhys.12.3.106 (ID: 720620)
• J. Carrasco, A. Elben, C. Kokail, B. Kraus, P. Zoller Theoretical and Experimental Perspectives of Quantum Verification, PRX Quantum 2 10102 (2021-03-03), http://dx.doi.org/10.1103/PRXQuantum.2.010102 doi:10.1103/PRXQuantum.2.010102 (ID: 720626) Toggle Abstract
  In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input Hamiltonian as design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses cross-device verification on the quantum level, i.e. by comparing quantum states prepared on different quantum devices. We focus in particular on protocols using randomized measurements, and we propose establishing a central data repository, where existing experimental devices and platforms can be compared. In our final example, we address verification of the output of a quantum device from a computer science perspective, addressing the question of how a user of a quantum processor can be certain about the correctness of its output, and propose minimal demonstrations on present day devices.
• Z. Cian, H. Dehghani, A. Elben, B. Vermersch, G. Zhu, M. Barkeshli, P. Zoller, M. Hafezi Many-body Chern number from statistical correlations of randomized measurements, Phys. Rev. Lett. 126 50501 (2021-02-01), http://dx.doi.org/10.1103/PhysRevLett.126.050501 doi:10.1103/PhysRevLett.126.050501 (ID: 720496) Toggle Abstract
  One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Remarkably, our results apply to disk-like geometries that are more amenable to current quantum simulator architectures.

Preprint

• C. Kargi, J. P. Dehollain, F. Henriques, L. Sieberer, T. Olsacher, P. Hauke, M. Heyl, P. Zoller, N. Langford Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations, (2021-10-21), arXiv:2110.11113 arXiv:2110.11113 (ID: 720694) Toggle Abstract
  Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art DQS resource scaling. Moreover, recent theoretical studies of Trotterised Ising models suggest it also offers feasible performance for unexpectedly large step sizes up to a sharp breakdown threshold, but demonstrations and characterisation have been limited, and the question of whether this behaviour applies as a general principle has remained open. Here, we study a set of paradigmatic and experimentally realisable DQS models, and show that a range of Trotterisation performance behaviours, including the existence of a sharp threshold, are remarkably universal. Carrying out a detailed characterisation of a range of performance signatures, we demonstrate that it is the onset of digitisation-induced quantum chaos at this threshold that underlies the breakdown of Trotterisation. Specifically, combining analysis of detailed dynamics with conclusive, global static signatures based on random matrix theory, we observe clear signatures of regular behaviour pre-threshold, and conclusive, initial-state-independent evidence for the onset of quantum chaotic dynamics beyond the threshold. We also show how this behaviour consistently emerges as a function of system size for sizes and times already relevant for current experimental DQS platforms. The advances in this work open up many important questions about the algorithm performance and general shared features of sufficiently complex Trotterisation-based DQS. Answering these will be crucial for extracting the maximum simulation power from future quantum processors.

2020

Articles

• A. Elben, R. Kueng, H. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, B. Vermersch Mixed-state entanglement from local randomized measurements, Phys. Rev. Lett. 125 (2020-11-11), http://dx.doi.org/10.1103/PhysRevLett.125.200501 doi:10.1103/PhysRevLett.125.200501 (ID: 720525) Toggle Abstract
  We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by post-processing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al, Science 364, 260 (2019)].
• X. Qiu, P. Zoller, X. Li Programmable Quantum Annealing Architectures with Ising Quantum Wires, PRX Quantum 1 20311 (2020-11-06), http://dx.doi.org/10.1103/PRXQuantum.1.020311 doi:10.1103/PRXQuantum.1.020311 (ID: 720652) Toggle Abstract
  Quantum annealing aims at solving optimization problems efficiently by preparing the ground state of an Ising spin-Hamiltonian quantum mechanically. A prerequisite of building a quantum annealer is the implementation of programmable long-range two-, three-, or multispin Ising interactions. We discuss an architecture, where the required spin interactions are implemented via two-port or in general multiport quantum Ising wires connecting the spins of interest. This quantum annealing architecture of spins connected by Ising quantum wires can be realized by exploiting the three-dimensional (3D) character of atomic platforms, including atoms in optical lattices and Rydberg tweezer arrays. The realization only requires engineering on-site terms and two-body interactions between nearest neighboring qubits. The locally coupled spin model on a 3D cubic lattice is sufficient to effectively produce arbitrary all-to-all coupled Ising Hamiltonians. We illustrate the approach for few-spin devices solving Max-Cut and prime factorization problems, and discuss the potential scaling to large atom-based systems.
• J. Argüello-Luengo, . González-Tudela, T. Shi, P. Zoller, J. I. Cirac Quantum Simulation of 2D Quantum Chemistry in Optical Lattices, Phys. Rev. Research 2 (2020-10-16), http://dx.doi.org/10.1103/PhysRevResearch.2.042013 doi:10.1103/PhysRevResearch.2.042013 (ID: 720479) Toggle Abstract
  Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H+2, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions. We extend this approach to larger systems by introducing as many mediating atoms as fermions, and derive the effective repulsion law. In all cases, we analyze how the continuous limit is approached for increasing optical lattice sizes.
• D. Vasilyev, A. Grankin, M. Baranov, L. Sieberer, P. Zoller Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits, PRX Quantum 1 (2020-10-09), http://dx.doi.org/10.1103/PRXQuantum.1.020302 doi:10.1103/PRXQuantum.1.020302 (ID: 720493) Toggle Abstract
  We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic vs. non-ergodic dynamics, which we illustrate for disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies, and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.
• T. Olsacher, L. Postler, P. Schindler, T. Monz, P. Zoller, L. Sieberer Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings, PRX Quantum 1 20316 (2020-08-26), http://dx.doi.org/10.1103/PRXQuantum.1.020316 doi:10.1103/PRXQuantum.1.020316 (ID: 720527) Toggle Abstract
  Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel. We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions. Furthermore, we show that combining our methods with optimal coherent control techniques allows to realize maximally dense universal parallelized quantum circuits.
• A. Kruckenhauser, L. Sieberer, W. G. Tobias, K. Matsuda, L. De Marco, J. Li, G. Valtolina, A. M. Rey, J. Ye, M. Baranov, P. Zoller Quantum many-body physics with ultracold polar molecules: Nanostructured potential barriers and interactions, Phys. Rev. A 102 23320 (2020-08-19), http://dx.doi.org/10.1103/PhysRevA.102.023320 doi:10.1103/PhysRevA.102.023320 (ID: 720474) Toggle Abstract
  We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing-wave optical light fields exploiting optical nonlinearities. In the second, static electric-field gradients in combination with microwave dressing are used to write nanostructured spatial patterns on the induced electric dipole moments, and thus dipolar interactions. We study the formation of interlayer and interface bound states of molecules in these configurations, and provide detailed estimates for binding energies and expected losses for present experimental setups.
• M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico Ortega, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U. Wiese, M. Wingate, J. Zakrzewski, P. Zo Simulating Lattice Gauge Theories within Quantum Technologies, The European Physical Journal D 74 165 (2020-08-04), http://dx.doi.org/10.1140/epjd/e2020-100571-8 doi:10.1140/epjd/e2020-100571-8 (ID: 720395) Toggle Abstract
  Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.
• A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. Lukin, P. Zoller Emerging 2D Gauge theories in Rydberg configurable arrays, Phys. Rev. X 10 (2020-06-16), http://dx.doi.org/10.1103/PhysRevX.10.021057 doi:10.1103/PhysRevX.10.021057 (ID: 720355) Toggle Abstract
  Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian --a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically, and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.
• A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, B. Vermersch Many-body topological invariants from randomized measurements, Sci. Adv. 6 (2020-04-10), http://dx.doi.org/10.1126/sciadv.aaz3666 doi:10.1126/sciadv.aaz3666 (ID: 720289) Toggle Abstract
  The classification of symmetry-protected topological (SPT) phases in one dimension has been recently achieved, and had a fundamental impact in our understanding of quantum phases in condensed matter physics. In this framework, SPT phases can be identified by many-body topological invariants, which are quantized non-local correlators for the many-body wavefunction. While SPT phases can now be realized in interacting synthethic quantum systems, the direct measurement of quantized many-body topological invariants has remained so far elusive. Here, we propose measurement protocols for many-body topological invariants for all types of protecting symmetries of one-dimensional interacting bosonic systems. Our approach relies on randomized measurements implemented with local random unitaries, and can be applied to any spin system with single-site addressability and readout. Our scheme thus provides a versatile toolbox to experimentally classify interacting SPT phases.
• P. Guimond, B. Vermersch, M. L. Juan, A. Sharafiev, G. Kirchmair, P. Zoller A Unidirectional On-Chip Photonic Interface for Superconducting Circuits, npj Quantum Information 6 (2020-03-27), http://dx.doi.org/10.1038/s41534-020-0261-9 doi:10.1038/s41534-020-0261-9 (ID: 720478) Toggle Abstract
  We propose and analyze a passive architecture for realizing on-chip, scalable cascaded quantum devices. In contrast to standard approaches, our scheme does not rely on breaking Lorentz reciprocity. Rather, we engineer the interplay between pairs of superconducting transmon qubits and a microwave transmission line, in such a way that two delocalized orthogonal excitations emit (and absorb) photons propagating in opposite directions. We show how such cascaded quantum devices can be exploited to passively probe and measure complex many-body operators on quantum registers of stationary qubits, thus enabling the heralded transfer of quantum states between distant qubits, as well as the generation and manipulation of stabilizer codes for quantum error correction.
• D. Yang, A. Grankin, L. Sieberer, D. Vasilyev, P. Zoller Quantum Non-demolition Measurement of a Many-Body Hamiltonian, Nat. Commun. 11 (2020-02-07), http://dx.doi.org/10.1038/s41467-020-14489-5 doi:10.1038/s41467-020-14489-5 (ID: 720277) Toggle Abstract
  An ideal quantum measurement collapses the wave function of a quantum system to an eigenstate of the measured observable, with the corresponding eigenvalue determining the measurement outcome. For a quantum non-demolition (QND) observable, i.e., one that commutes with the Hamiltonian generating the system's time evolution, repeated measurements yield the same result, corresponding to measurements with minimal disturbance. This concept applies universally to single quantum particles as well as to complex many-body systems. However, while QND measurements of systems with few degrees of freedom has been achieved in seminal quantum optics experiments, it is an open challenge to devise QND measurement of a complex many-body observable. Here, we describe how a QND measurement of the Hamiltonian of an interacting many-body system can be implemented in a trapped-ion analog quantum simulator. Through a single shot measurement, the many-body system is prepared in a narrow energy band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a novel framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis (ETH) and quantum fluctuation relations.
• M. K. Joshi, A. Elben, B. Vermersch, T. Brydges, C. Maier, P. Zoller, R. Blatt, C. F. Roos Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions, Phys. Rev. Lett. 124 240505 (2020-01-07), http://dx.doi.org/10.1103/PhysRevLett.124.240505 doi:10.1103/PhysRevLett.124.240505 (ID: 720436) Toggle Abstract
  In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.
• A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Brydges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, P. Zoller Cross-Platform Verification of Intermediate Scale Quantum Devices, Phys. Rev. Lett. 124 10504 (2020-01-06), http://dx.doi.org/10.1103/PhysRevLett.124.010504 doi:10.1103/PhysRevLett.124.010504 (ID: 720357) Toggle Abstract
  We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[ρ1ρ2] and the purities Tr[ρ21,2], and thus a (mixed-state) fidelity, of two quantum states ρ1 and ρ2 prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof-of-principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.
• S. Barbarino, J. Yu, P. Zoller, J. Budich Preparing Atomic Topological Quantum Matter by Adiabatic Non-Unitary Dynamics, Phys. Rev. Lett. 124 10401 (2020-01-02), http://dx.doi.org/10.1103/PhysRevLett.124.010401 doi:10.1103/PhysRevLett.124.010401 (ID: 720390) Toggle Abstract
  Motivated by the outstanding challenge of realizing low-temperature states of quantum matter in synthetic materials, we propose and study an experimentally feasible protocol for preparing topological states such as Chern insulators. By definition, such (non-symmetry protected) topological phases cannot be attained without going through a phase transition in a closed system, largely preventing their preparation in coherent dynamics. To overcome this fundamental caveat, we propose to couple the target system to a conjugate system, so as to prepare a symmetry protected topological phase in an extended system by intermittently breaking the protecting symmetry. Finally, the decoupled conjugate system is discarded, thus projecting onto the desired topological state in the target system. By construction, this protocol may be immediately generalized to the class of invertible topological phases, characterized by the existence of an inverse topological order. We illustrate our findings with microscopic simulations on an experimentally realistic Chern insulator model of ultracold fermionic atoms in a driven spin-dependent hexagonal optical lattice.

Report

• J. Ye, N. MAVALVALA, R. Beausoleil, P. Dehmer, L. Dimauro, M. Gaarde, S. M. Girvin, C. Greene, T. Ha, M. Kasevich, M. Lipson, M. Lukin, A. M. Lyyra, P. J. Reynolds, M. Safronova, P. Zoller Manipulating Quantum Systems. An Assessment of Atomic, Molecular, and Optical Physics in the United States, (2020-01-01), http://dx.doi.org/10.17226/25613 doi:10.17226/25613 (ID: 720546) Toggle Abstract
  The field of atomic, molecular, and optical (AMO) science underpins many technologies and continues to progress at an exciting pace for both scientific discoveries and technological innovations. AMO physics studies the fundamental building blocks of functioning matter to help advance the understanding of the universe. It is a foundational discipline within the physical sciences, relating to atoms and their constituents, to molecules, and to light at the quantum level. AMO physics combines fundamental research with practical application, coupling fundamental scientific discovery to rapidly evolving technological advances, innovation and commercialization. Due to the wide-reaching intellectual, societal, and economical impact of AMO, it is important to review recent advances and future opportunities in AMO physics.

2019

Articles

• R. Belyansky, J. Young, P. Bienias, Z. Eldredge, A. Kaufman, P. Zoller, A. V. Gorshkov Nondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions, Phys. Rev. Lett. 123 213603 (2019-11-20), http://dx.doi.org/10.1103/PhysRevLett.123.213603 doi:10.1103/PhysRevLett.123.213603 (ID: 720326) Toggle Abstract
  We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model.
• J. Argüello-Luengo, A. Gonzalez-Tudela, T. Shi, P. Zoller, J. I. Cirac Analog quantum chemistry simulation, Nature 574 218 (2019-10-09), http://dx.doi.org/10.1038/s41586-019-1614-4 doi:10.1038/s41586-019-1614-4 (ID: 720043) Toggle Abstract
  Quantum computers hold the promise to provide outstanding computational speed ups in chemical problems, like the determination of the electronic ground state energy of molecules. Here, we demonstrate that the same goal can be achieved with an analog quantum simulator which combines two well-established technologies, namely, ultra-cold atoms in optical lattices and cavity QED. In the proposed simulator, fermionic atoms hopping in an optical potential play the role of electrons, additional optical potentials provide the nuclear attraction, while a single spin excitation over a Mott insulator mediates the electronic Coulomb repulsion. We analyze the impact of discretization and finite size effects of the lattice, and provide the working conditions required for the precise determination of the electronic energy of simple molecules.
• L. Sieberer, T. Olsacher, A. Elben, M. Heyl, P. Hauke, F. Haake, P. Zoller Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top, npj Quantum Information 5 (2019-09-20), http://dx.doi.org/10.1038/s41534-019-0192-5 doi:10.1038/s41534-019-0192-5 (ID: 720105) Toggle Abstract
  This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.
• M. Lacki, P. Zoller, M. Baranov Stroboscopic painting of optical potentials for atoms with subwavelength resolution, Phys. Rev. A 100 (2019-09-11), http://dx.doi.org/10.1103/PhysRevA.100.033610 doi:10.1103/PhysRevA.100.033610 (ID: 720290) Toggle Abstract
  We propose and discuss a method to engineer stroboscopically arbitrary one-dimensional optical potentials with subwavelength resolution. Our approach is based on subwavelength optical potential barriers for atoms in the dark state in an optical \Lambda system, which we use as a stroboscopic drawing tool by controlling their amplitude and position by changing the amplitude and the phase of the control Rabi frequency in the \Lambda system. We demonstrate the ability of the method to engineer both smooth and comb-like periodic potentials for atoms in the dark state, and establish the range of stroboscopic frequencies when the quasienergies of the stroboscopic Floquet system reproduce the band structure of the time-averaged potentials. In contrast to usual stroboscopic engineering which becomes increasingly accurate with increasing the stroboscopic frequency, the presence of the bright states of the \Lambda-system results in the upper bound on the frequency, above which the dynamics strongly mixes the dark and the bright channels, and the description in terms of a time-averaged potential fails. For frequencies below this bound, the lowest Bloch band of quasienergies contains several avoided-crossing coming from the coupling to high energy states, with widths decreasing with increasing stroboscopic frequency. We analyze the influence of these avoided crossings on the dynamics in the lowest band using Bloch oscillations as an example, and establish the parameter regimes when the population transfer from the lowest band into high bands is negligible. We also present protocols for loading atoms into the lowest band of the painted potentials starting from atoms in the lowest band of a standard optical lattice.
• C. R. Kaubrügger, P. Silvi, C. Kokail, R. van Bijnen, A. M. Rey, J. Ye, A. Kaufman, P. Zoller Variational spin-squeezing algorithms on programmable quantum sensors, Phys. Rev. Lett. 123 260505 (2019-08-22), http://dx.doi.org/10.1103/PhysRevLett.123.260505 doi:10.1103/PhysRevLett.123.260505 (ID: 720356) Toggle Abstract
  Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on-demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to generate spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
• B. Vermersch, A. Elben, L. Sieberer, N. Y. Yao, P. Zoller Probing scrambling using statistical correlations between randomized measurements, Phys. Rev. X 9 21061 (2019-06-27), http://dx.doi.org/10.1103/PhysRevX.9.021061 doi:10.1103/PhysRevX.9.021061 (ID: 720042) Toggle Abstract
  We present a protocol to study scrambling using statistical correlations between measurements, performed after evolving a quantum system from random initial states. We show that the resulting statistical correlations are directly related to OTOCs and can be used to probe scrambling in many-body systems. Our protocol, which does not require reversing time evolution or auxiliary degrees of freedom, can be realized in state-of-the-art quantum simulation experiments.
• M. Schütz, B. Vermersch, G. Kirchmair, L. Vandersypen, J. I. Cirac, M. Lukin, P. Zoller Quantum Simulation and Optimization in Hot Quantum Networks, Phys. Rev. B 99 241302 (2019-06-27), http://dx.doi.org/10.1103/PhysRevB.99.241302 doi:10.1103/PhysRevB.99.241302 (ID: 720058) Toggle Abstract
  We propose and analyze a setup based on (solid-state) qubits coupled to a common multi-mode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling requirements for the data bus. Our approach allows for the realization of fast deterministic quantum gates between distant qubits, the simulation of quantum spin models with engineered (long-range) interactions, and provides a flexible architecture for the implementation of quantum approximate optimization algorithms.
• C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, P. Zoller Self-verifying variational quantum simulation of lattice models, Nature 569 360 (2019-05-15), http://dx.doi.org/10.1038/s41586-019-1177-4 doi:10.1038/s41586-019-1177-4 (ID: 720076) Toggle Abstract
  Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments demonstrating self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the long-standing challenge of verifying quantum simulation.
• A. Elben, B. Vermersch, C. F. Roos, P. Zoller Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states, Phys. Rev. A 99 52323 (2019-05-15), http://dx.doi.org/10.1103/PhysRevA.99.052323 doi:10.1103/PhysRevA.99.052323 (ID: 720100) Toggle Abstract
  We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to 10 qubits in a trapped-ion quantum simulator [Brydges et al., arXiv:1806.05747]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
• T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, C. F. Roos Probing Renyi entanglement entropy via randomized measurements, Science 364 260 (2019-04-19), http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034) Toggle Abstract
  Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts - both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.
• M. Heyl, P. Hauke, P. Zoller Quantum localization bounds Trotter errors in digital quantum simulation, Sci. Adv. 5 (2019-04-12), http://dx.doi.org/10.1126/sciadv.aau8342 doi:10.1126/sciadv.aau8342 (ID: 720038) Toggle Abstract
  A fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables. Consequently, for generic quantum many-body Hamiltonians, Trotter errors can become independent of system size and total simulation time. For local observables, DQS is thus intrinsically much more robust than what one might expect from known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size. The threshold separates a regular region with controllable Trotter errors, where the system exhibits localization in the space of eigenstates of the time-evolution operator, from a quantum chaotic regime where the trajectory is quickly scrambled throughout the entire Hilbert space. Our findings show that DQS with comparatively large Trotter steps can retain controlled Trotter errors for local observables. It is thus possible to reduce the number of quantum gate operations required to represent the desired time evolution faithfully, thereby mitigating the effects of imperfect individual gate operations
• A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletic, M. Lukin Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature 568 211 (2019-04-01), http://dx.doi.org/10.1038/s41586-019-1070-1 doi:10.1038/s41586-019-1070-1 (ID: 720062) Toggle Abstract
  Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.
• P. Guimond, A. Grankin, D. Vasilyev, B. Vermersch, P. Zoller Subradiant Bell States in Distant Atomic Arrays, Phys. Rev. Lett. 122 93601 (2019-03-05), http://dx.doi.org/10.1103/PhysRevLett.122.093601 doi:10.1103/PhysRevLett.122.093601 (ID: 720126) Toggle Abstract
  We study collective “free-space” radiation properties of two distant single-layer arrays of quantum emitters as two-level atoms. We show that this system can support a long-lived Bell superposition state of atomic excitations exhibiting strong subradiance, which corresponds to a nonlocal excitation of the two arrays. We describe the preparation of these states and their application in quantum information as a resource of nonlocal entanglement, including deterministic quantum state transfer with high fidelity between the arrays representing quantum memories. We discuss experimental realizations using cold atoms in optical trap arrays with subwavelength spacing, and analyze the role of imperfections.
• M. Riedel, M. Kovacs, P. Zoller, J. Mlynek, T. Calarco Europe's Quantum Flagship initiative, Quantum Sci. Technol. 4 (2019-02-22), http://dx.doi.org/10.1088/2058-9565/ab042d doi:10.1088/2058-9565/ab042d (ID: 720172) Toggle Abstract
  As the first applications leap out of research laboratories toward commercialization, the global race for dominance in the maturing field of quantum technologies is becoming ever fiercer. To retain its historical lead and kick-start a continent-wide quantum-driven industry and accelerate market take-up, Europe has launched the Quantum Flagship, an ambitious €1 billion, 10 year endeavor. This article provides an overview of the underlying considerations and the current state of the initiative. Furthermore, it briefly presents the 20 projects selected to be at the core of the ramp-up phase of the initiative, which will address core applications of quantum technologies such as communications, computing, simulation, as well as sensing and metrology, all of which are supported by basic science. Finally, we present the broader ecosystem of European funding instruments and institutions which aim to create the next generation of disruptive technologies within quantum sciences, placing Europe as a worldwide knowledge-based industrial and technological leader in this innovative field.

2018

Articles

• A. Grankin, D. Vasilyev, P. Guimond, B. Vermersch, P. Zoller Free-space photonic quantum link and chiral quantum optics, Phys. Rev. A 98 3825 (2018-10-12), http://dx.doi.org/10.1103/PhysRevA.98.043825 doi:10.1103/PhysRevA.98.043825 (ID: 719980) Toggle Abstract
  We present the design of a chiral photonic quantum link, where distant atoms interact by exchanging photons propagating in a single direction in free space. This is achieved by coupling each atom in a laser-assisted process to an atomic array acting as a quantum phased-array antenna. This provides a basic building block for quantum networks in free space, i.e., without requiring cavities or nanostructures, which we illustrate with high-fidelity quantum state transfer protocols. Our setup can be implemented with neutral atoms using Rydberg-dressed interactions.
• D. Yang, D. Vasilyev, C. Laflamme, M. Baranov, P. Zoller Quantum Scanning Microscope for Cold Atoms, Phys. Rev. A 98 23852 (2018-08-27), http://dx.doi.org/10.1103/PhysRevA.98.023852 doi:10.1103/PhysRevA.98.023852 (ID: 720027) Toggle Abstract
  We present a detailed theoretical description of an atomic scanning microscope in a cavity QED setup proposed in Phys. Rev. Lett. 120, 133601 (2018). The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The super-resolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a ground level dispersively coupled to the cavity field. Thus, the atomic position encoded in the internal state is revealed as a phase shift of the light reflected from the cavity in a homodyne experiment. Our theoretical description of the microscope operation is based on the stochastic master equation describing the conditional time evolution of the atomic system under continuous observation as a competition between dynamics induced by the Hamiltonian of the system, decoherence effects due to atomic spontaneous decay, and the measurement backaction. Within our approach we relate the observed homodyne current with a local atomic density, and discuss the emergence of a quantum nondemolition measurement regime allowing continuous observation of spatial densities of quantum motional eigenstates without measurement backaction in a single experimental run.
• M. Dalmonte, B. Vermersch, P. Zoller Quantum simulation and spectroscopy of entanglement Hamiltonians, Nature Phys. 14 151 (2018-05-21), http://dx.doi.org/10.1038/s41567-018-0151-7 doi:10.1038/s41567-018-0151-7 (ID: 720028) Toggle Abstract
  The properties of a strongly correlated many-body quantum system, from the presence of topological order to the onset of quantum criticality, leave a footprint in its entanglement spectrum. The entanglement spectrum is composed by the eigenvalues of the density matrix representing a subsystem of the whole original system, but its direct measurement has remained elusive due to the lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible via the quantum simulation and spectroscopy of a suitably constructed entanglement Hamiltonian, building on the Bisognano–Wichmann theorem of axiomatic quantum field theory. This theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as the Hamiltonian of the many-body system of interest with spatially varying couplings. On this basis, we propose a scalable recipe for the measurement of a system’s entanglement spectrum via spectroscopy of the corresponding Bisognano–Wichmann Hamiltonian realized in synthetic quantum systems, including atoms in optical lattices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order and quantum phase transitions.
• E. Rico Ortega, M. Dalmonte, P. Zoller, D. Banerjee, M. Bögli, P. Stebler, U. Wiese SO(3) "Nuclear Physics" with ultracold Gases, Ann. Phys. 393 483 (2018-04-05), http://dx.doi.org/10.1016/j.aop.2018.03.020 doi:10.1016/j.aop.2018.03.020 (ID: 719977) Toggle Abstract
  An ab initio calculation of nuclear physics from Quantum Chromodynamics (QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an outstanding challenge. Here, we discuss the emergence of key elements of nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We show that this model is accessible to state-of-the-art quantum simulation experiments with ultracold atoms in an optical lattice. First, we demonstrate that our model shares characteristic many-body features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of few-body bound states. Then we show that in the one-dimensional case, the dynamics in the gauge invariant sector can be encoded as a spin S=3/2 Heisenberg model, i.e., as quantum magnetism, which has a natural realization with bosonic mixtures in optical lattices, and thus sheds light on the connection between non-Abelian gauge theories and quantum magnetism.
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• D. Yang, C. Laflamme, D. Vasilyev, M. Baranov, P. Zoller Theory of a Quantum Scanning Microscope for Cold Atoms, Phys. Rev. Lett. 120 133601 (2018-03-30), http://dx.doi.org/10.1103/PhysRevLett.120.133601 doi:10.1103/PhysRevLett.120.133601 (ID: 720010) Toggle Abstract
  We propose and analyze a scanning microscope to monitor “live” the quantum dynamics of cold atoms in a cavity QED setup. The microscope measures the atomic density with subwavelength resolution via dispersive couplings to a cavity and homodyne detection within the framework of continuous measurement theory. We analyze two modes of operation. First, for a fixed focal point the microscope records the wave packet dynamics of atoms with time resolution set by the cavity lifetime. Second, a spatial scan of the microscope acts to map out the spatial density of stationary quantum states. Remarkably, in the latter case, for a good cavity limit, the microscope becomes an effective quantum nondemolition device, such that the spatial distribution of motional eigenstates can be measured backaction free in single scans, as an emergent quantum nondemolition measurement.
• Y. Wang, S. Subhankar, P. Bienias, M. Łącki, T. Tsui, M. Baranov, A. V. Gorshkov, P. Zoller, J. V. Porto, S. L. Rolston Dark state optical lattice with sub-wavelength spatial structure, Phys. Rev. Lett. 120 83601 (2018-02-20), http://dx.doi.org/10.1103/PhysRevLett.120.083601 doi:10.1103/PhysRevLett.120.083601 (ID: 719917) Toggle Abstract
  We report on the experimental realization of a conservative optical lattice for cold atoms with sub-wavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a 1D array of ultra-narrow barriers with widths less than 10~nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice, and find good agreement with theoretical predictions. The observed lifetimes of atoms trapped in the lattice are as long as 60 ms, nearly 105 times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimension and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with sub-wavelength spacings.
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• A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, P. Zoller Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models, Phys. Rev. Lett. 120 50406 (2018-02-02), http://dx.doi.org/10.1103/PhysRevLett.120.050406 doi:10.1103/PhysRevLett.120.050406 (ID: 719876) Toggle Abstract
  We present a scheme for measuring Rényi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO quantum simulators, and used to measure for instance area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.
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• B. Vermersch, A. Elben, M. Dalmonte, J. I. Cirac, P. Zoller Unitary n-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies, Phys. Rev. A 97 23604 (2018-02-02), http://dx.doi.org/10.1103/PhysRevA.97.023604 doi:10.1103/PhysRevA.97.023604 (ID: 719928) Toggle Abstract
  We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary n-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.
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2017

Articles

• J. Perczel, J. Borregaard, D. Chang, H. Pichler, S. F. Yelin, P. Zoller, M. Lukin Photonic band structure of two-dimensional atomic lattices, Phys. Rev. A 96 63801 (2017-12-04), http://dx.doi.org/10.1103/PhysRevA.96.063801 doi:10.1103/PhysRevA.96.063801 (ID: 719916) Toggle Abstract
  Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation, and long-lived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including long-range interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such long-range interactions for arbitrary two-dimensional atomic lattices. As applications of our method, we investigate the topological properties of atomic lattices both in free space and near plasmonic surfaces.
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• F. Reiter, A. Sorensen, P. Zoller, C. A. Muschik Autonomous Quantum Error Correction and Application to Quantum Sensing with Trapped Ions, Nat. Commun. 8 (2017-11-28), http://dx.doi.org/10.1038/s41467-017-01895-5 doi:10.1038/s41467-017-01895-5 (ID: 719766) Toggle Abstract
  Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin- or phase flips. Our dissipative error correction scheme operates in a fully autonomous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
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• C. A. Muschik, M. Heyl, E. A. Martínez, T. Monz, P. Schindler, B. Vogell, M. Dalmonte, P. Hauke, R. Blatt, P. Zoller U(1) Wilson lattice gauge theories in digital quantum simulators, New J. Phys. 19 103020 (2017-10-20), http://dx.doi.org/10.1088/1367-2630/aa89ab doi:10.1088/1367-2630/aa89ab (ID: 719936) Toggle Abstract
  Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication (Martinez et al 2016 Nature 534 516), we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle–antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.
• H. Pichler, S. Choi, P. Zoller, M. Lukin Universal photonic quantum computation via time-delayed feedback, PNAS 114 (2017-10-17), http://dx.doi.org/10.1073/pnas.1711003114 doi:10.1073/pnas.1711003114 (ID: 720008) Toggle Abstract
  We propose and analyze a deterministic protocol to generate two-dimensional photonic cluster states using a single quantum emitter via time-delayed quantum feedback. As a physical implementation, we consider a single atom or atom-like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits, while the mirror allows the implementation of feedback. We identify the class of many-body quantum states that can be produced using this approach and characterize them in terms of 2D tensor network states.
• H. Pichler, S. Choi, P. Zoller, M. Lukin Photonic tensor networks produced by a single quantum emitter, PNAS 114 11362 (2017-10-10), http://dx.doi.org/10.1073/pnas.1711003114 doi:10.1073/pnas.1711003114 (ID: 719751) Toggle Abstract
  We propose and analyze a protocol to generate two dimensional tensor network states using a single quantum system that sequentially interacts with a 1D string of qubits. This is accomplished by using parts of the string itself as a quantum queue memory. As a physical implementation, we consider a single atom or atom like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits while the mirror allows the implementation of the queue memory. We identify the class of many-body quantum states that can be produced using this approach. These include universal resources for measurement based quantum computation and states associated with topologically ordered phases. We discuss an explicit protocol to deterministically create a 2D cluster state in a quantum nanophotonic experiment, that allows for a realization of a quantum computer using a single atom coupled to light.
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• A. Glätzle, K. Ender, D. S. Wild, S. Choi, H. Pichler, M. Lukin, P. Zoller Quantum Spin Lenses in Atomic Arrays, Phys. Rev. X 7 31049 (2017-09-20), http://dx.doi.org/10.1103/PhysRevX.7.031049 doi:10.1103/PhysRevX.7.031049 (ID: 719790) Toggle Abstract
  We propose and discuss `quantum spin lenses', where quantum states of delocalized spin excitations in an atomic medium are `focused' in space in a coherent quantum process down to (essentially) single atoms. These can be employed to create controlled interactions in a quantum light-matter interface, where photonic qubits stored in an atomic ensemble are mapped to a quantum register represented by single atoms. We propose Hamiltonians for quantum spin lenses as inhomogeneous spin models on lattices, which can be realized with Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive spin-spin interactions lead to focusing dynamics conditional to the number of spin excitations. This allows the mapping of quantum superpositions of delocalized spin excitations to superpositions of spatial spin patterns, which can be addressed by light fields and manipulated. Finally, we propose multifocal quantum spin lenses as a way to generate and distribute entanglement between distant atoms in an atomic lattice array.
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• P. Guimond, M. Pletyukhov, H. Pichler, P. Zoller Delayed Coherent Quantum Feedback from a Scattering Theory and a Matrix Product State Perspective, Quantum Sci. Technol. 2 44012 (2017-09-08), http://dx.doi.org/10.1088/2058-9565/aa7f03 doi:10.1088/2058-9565/aa7f03 (ID: 719814) Toggle Abstract
  We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter's dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.
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• D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller, N. Goldman Probing topology by “heating”: Quantized circular dichroism in ultracold atoms, Sci. Adv. 3 e1701207 (2017-08-18), http://dx.doi.org/10.1126/sciadv.1701207 doi:10.1126/sciadv.1701207 (ID: 719782) Toggle Abstract
  We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic 2D Chern insulator subjected to a circular time-periodic perturbation: due to the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake. Most importantly, taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number of the populated band (ν ): this "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η 0 =ν/ℏ 2 . Contrary to the integer quantum Hall effect, this quantized response is found to be non-linear with respect to the strength of the driving field and it explicitly involves inter-band transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the non-linear photogalvanic effect predicted for Weyl semimetals. The quantized effect revealed in this work designates depletion-rate measurements as a universal probe for topological order in quantum matter.
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• J. Perczel, J. Borregaard, D. Chang, H. Pichler, S. F. Yelin, P. Zoller, M. Lukin Topological Quantum Optics in Two-Dimensional Atomic Arrays, Phys. Rev. Lett. 119 23603 (2017-07-14), http://dx.doi.org/10.1103/PhysRevLett.119.023603 doi:10.1103/PhysRevLett.119.023603 (ID: 719767) Toggle Abstract
  We demonstrate that two-dimensional atomic arrays with subwavelength spacing can be used to create topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with non-trivial Chern numbers. Such a system displays topologically protected bound states and unidirectional emission by individual atoms into long-lived edge states. Possible experimental realizations and applications are discussed.
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• A. Glätzle, R. van Bijnen, P. Zoller, W. Lechner A Coherent Quantum Annealer with Rydberg Atoms, Nat. Commun. 8 15813 (2017-06-22), http://dx.doi.org/10.1038/ncomms15813 doi:10.1038/ncomms15813 (ID: 719686) Toggle Abstract
  There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner-Hauke-Zoller~(LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a novel platform for quantum annealing. In LHZ a infinite-range spin-glass is mapped onto the low energy subspace of a spin-1/2 lattice gauge model with quasi-local 4-body parity constraints. This spin model can be emulated in a natural way with Rubidium and Cesium atoms in a bipartite optical lattice involving laser-dressed Rydberg-Rydberg interactions, which are several orders of magnitude larger than the relevant decoherence rates. This makes the exploration of coherent quantum enhanced optimization protocols accessible with state-of-the-art atomic physics experiments.
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• F. Iemini, L. Mazza, L. Fallani, P. Zoller, R. Fazio, M. Dalmonte Majorana Quasi-Particles Protected by Z 2 Angular Momentum Conservation, Phys. Rev. Lett. 118 200404 (2017-05-19), http://dx.doi.org/10.1103/PhysRevLett.118.200404 doi:10.1103/PhysRevLett.118.200404 (ID: 719762) Toggle Abstract
  We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated with density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years.
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• C. Laflamme, D. Yang, P. Zoller Continuous Measurement of an Atomic Current, Phys. Rev. A 95 43843 (2017-04-28), http://dx.doi.org/10.1103/PhysRevA.95.043843 doi:10.1103/PhysRevA.95.043843 (ID: 719758) Toggle Abstract
  We are interested in dynamics of quantum many-body systems under continuous observation, and its physical realizations involving cold atoms in lattices. In the present work we focus on continuous measurement of atomic currents in lattice models, including the Hubbard model. We describe a Cavity QED setup, where measurement of a homodyne current provides a faithful representation of the atomic current as a function of time. We employ the quantum optical description in terms of a diffusive stochastic Schr\"odinger equation to follow the time evolution of the atomic system conditional to observing a given homodyne current trajectory, thus accounting for the competition between the Hamiltonian evolution and measurement back-action. As an illustration, we discuss minimal models of atomic dynamics and continuous current measurement on rings with synthetic gauge fields, involving both real space and synthetic dimension lattices (represented by internal atomic states). Finally, by `not reading' the current measurements the time evolution of the atomic system is governed by a master equation, where - depending on the microscopic details of our CQED setups - we effectively engineer a current coupling of our system to a quantum reservoir. This provides novel scenarios of dissipative dynamics generating `dark' pure quantum many-body states.
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• J. Budich, A. Elben, M. Łącki, A. Sterdyniak, M. Baranov, P. Zoller Coupled Atomic Wires in a Synthetic Magnetic Field, Phys. Rev. A 95 43632 (2017-04-24), http://dx.doi.org/10.1103/PhysRevA.95.043632 doi:10.1103/PhysRevA.95.043632 (ID: 719753) Toggle Abstract
  We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e.~the Harper-Hofstadter model and the two leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semi-continuous Harper-Hofstadter model accessible with cold atom experiments. For the minimal setup of a double-wire, we explore how a sub-wavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in non-planar geometries such as cylinders, discs, and tori.
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• B. Vermersch, P. Guimond, H. Pichler, P. Zoller Quantum State Transfer via Noisy Photonic and Phononic Waveguides, Phys. Rev. Lett. 118 133601 (2017-03-27), http://dx.doi.org/10.1103/PhysRevLett.118.133601 doi:10.1103/PhysRevLett.118.133601 (ID: 719696) Toggle Abstract
  We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g. thermal noise) injected into the waveguide. We extend the model and protocol to a cavity QED setup, where atomic ensembles, or single atoms representing quantum memory, are coupled to a cavity mode. We present a detailed study of sensitivity to imperfections, and develop a quantum error correction protocol to account for random losses (or additions) of photons in the waveguide. Our numerical analysis is enabled by Matrix Product State techniques to simulate the complete quantum circuit, which we generalize to include thermal input fields. Our discussion applies both to photonic and phononic quantum networks.
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• J. Budich, Y. Hu, P. Zoller Helical Floquet Channels in 1D Lattices, Phys. Rev. Lett. 118 105302 (2017-03-07), http://dx.doi.org/10.1103/PhysRevLett.118.105302 doi:10.1103/PhysRevLett.118.105302 (ID: 719644) Toggle Abstract
  We show how dispersionless channels exhibiting perfect spin-momentum locking can arise in a 1D lattice model. While such spectra are forbidden by fermion doubling in static 1D systems, here we demonstrate their appearance in the stroboscopic dynamics of a periodically driven system. Remarkably, this phenomenon does not rely on any adiabatic assumptions, in contrast to the well known Thouless pump and related models of adiabatic spin pumps. The proposed setup is shown to be experimentally feasible with state of the art techniques used to control ultracold alkaline earth atoms in optical lattices.
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• P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, P. Zoller Chiral Quantum Optics, Nature 541 473 (2017-01-26), http://dx.doi.org/10.1038/nature21037 doi:10.1038/nature21037 (ID: 719634)
• C. Dlaska, B. Vermersch, P. Zoller Robust quantum state transfer via topologically protected edge channels in dipolar arrays, Quantum Sci. Technol. 2 15001 (2017-01-05), http://dx.doi.org/10.1088/2058-9565/2/1/015001 doi:10.1088/2058-9565/2/1/015001 (ID: 719597) Toggle Abstract
  We show how to realize quantum state transfer between distant qubits using the chiral edge states of a two-dimensional topological spin system. Our implementation based on Rydberg atoms allows to realize the quantum state transfer protocol in state of the art experimental setups. In particular, we show how to adapt the standard state transfer protocol to make it robust against dispersive and disorder effects.
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Book

• C. Gardiner, P. Zoller Quantum World Of Ultra-cold Atoms And Light, The - Book III: Ultra-cold Atoms , (2017-11-07), URL (ID: 719877)

2016

Articles

• M. Leib, P. Zoller, W. Lechner A Transmon Quantum Annealer: Decomposing Many-Body Ising Constraints Into Pair Interactions, Quantum Sci. Technol. 1 15008 (2016-12-16), http://dx.doi.org/10.1088/2058-9565/1/1/015008 doi:10.1088/2058-9565/1/1/015008 (ID: 719543) Toggle Abstract
  Adiabatic quantum computing is an analog quantum computing scheme with various applications in solving optimization problems. In the parity picture of quantum optimization, the problem is encoded in local fields that act on qubits which are connected via local 4-body terms. We present an implementation of a parity annealer with Transmon qubits with a specifically tailored Ising interaction from Josephson ring modulators.
• M. Łącki, M. Baranov, H. Pichler, P. Zoller Nano-Scale `Dark State' Optical Potentials for Cold Atoms, Phys. Rev. Lett. 117 233001 (2016-11-30), http://dx.doi.org/10.1103/PhysRevLett.117.233001 doi:10.1103/PhysRevLett.117.233001 (ID: 719619) Toggle Abstract
  We discuss generation of subwavelength optical barriers on the scale of tens of nanometers, as conservative optical potentials for cold atoms. These arise from non-adiabatic corrections to Born-Oppenheimer potentials from dressed `dark states' in atomic Λ -configurations. We illustrate the concepts with a double layer potential for atoms obtained from inserting an optical subwavelength barrier into a well generated by an off-resonant optical lattice, and discuss bound states of pairs of atoms interacting via magnetic dipolar interactions. The subwavelength optical barriers represent an optical `Kronig-Penney' potential. We present a detailed study of the bandstructure in optical `Kronig-Penney' potentials, including decoherence from spontaneous emission and atom loss to open `bright' channels.
• D. Yang, G. S. Giri, M. Johannig, C. Wunderlich, P. Zoller, P. Hauke Analog Quantum Simulation of (1+1)D Lattice QED with Trapped Ions, Phys. Rev. A 94 52321 (2016-11-16), http://dx.doi.org/10.1103/PhysRevA.94.052321 doi:10.1103/PhysRevA.94.052321 (ID: 719545) Toggle Abstract
  The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1+1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.
• Y. Hu, P. Zoller, J. Budich Dynamical Buildup of a Quantized Hall Response from Non-Topological States, Phys. Rev. Lett. 117 126803 (2016-09-16), http://dx.doi.org/10.1103/PhysRevLett.117.126803 doi:10.1103/PhysRevLett.117.126803 (ID: 719515) Toggle Abstract
  Motivated by the current interest in dynamically preparing topological states in ultracold atomic gases, we consider a two-dimensional system initialized in a topologically trivial state before its Hamiltonian is ramped into a Chern-insulator phase. Under coherent dynamics, the non-equilibrium Hall response is found to approach a topologically quantized time averaged value in the limit of slow parameter ramps, even though the Chern number of the state is constrained to remain trivial. Quite remarkably, the destruction of quantum coherence by dephasing stabilizes the Hall response towards its asymptotically quantized mean value by damping its oscillations. We demonstrate how this phenomenology generically arises from the interplay of Landau-Zener dynamics and dephasing. In the limit of a fast ramp (quench), we show how the presence of a cooling quantum bath enables a dynamical transition of the state's Chern number from trivial to non-trivial, accompanied by the onset of a quantized Hall response.
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• P. Guimond, H. Pichler, A. Rauschenbeutel, P. Zoller Chiral quantum optics with V-level atoms and coherent quantum feedback, Phys. Rev. A 94 33829 (2016-09-16), http://dx.doi.org/10.1103/PhysRevA.94.033829 doi:10.1103/PhysRevA.94.033829 (ID: 719590) Toggle Abstract
  We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time-delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure "dark" stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analogue of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady-state.
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• C. Laflamme, J. Budich, P. Zoller, M. Dalmonte Non-equilibrium 8π Josephson Effect in Atomic Kitaev Wires, Nat. Commun. 7 12280 (2016-08-02), http://dx.doi.org/10.1038/ncomms12280 doi:10.1038/ncomms12280 (ID: 719504) Toggle Abstract
  We theoretically study a Kitaev wire interrupted by an extra site which gives rise to super exchange coupling between two Majorana bound states. We show that this system hosts a tunable, non-equlibrium Josephson effect with a characteristic 8π periodicity of the Josephson current. We elucidate the physical mechanism deriving a minimal model for the junction and confirm its quantitative accuracy by comparison to the numerical solution of the full model. The visibility of the 8π periodicity of the Josephson current is then studied using time-dependent simulations including the effects of dephasing and particle losses. Our findings provide a novel signature of Majorana quasi-particles which is qualitatively different form the behavior of a conventional superconductor, and can be experimentally verified in cold atom systems using alkaline-earth-like atoms.
• E. A. Martínez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, R. Blatt Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature 534 519 (2016-06-22), http://dx.doi.org/10.1038/nature18318 doi:10.1038/nature18318 (ID: 719563) Toggle Abstract
  Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories.
• B. Vermersch, T. Ramos, P. Hauke, P. Zoller Implementation of Chiral Quantum Optics with Rydberg and Trapped-ion Setups, Phys. Rev. A 93 63830 (2016-06-17), http://dx.doi.org/10.1103/PhysRevA.93.063830 doi:10.1103/PhysRevA.93.063830 (ID: 719538) Toggle Abstract
  We propose two setups for realizing a chiral quantum network, where two-level systems representing the nodes interact via directional emission into discrete waveguides, as introduced in Ref.~[T.\ Ramos \emph{et al.}, arXiv:1602.00926]. The first implementation realizes a spin waveguide via Rydberg states in a chain of atoms, whereas the second one realizes a phonon waveguide via the localized vibrations of a string of trapped ions. For both architectures, we show that strong chirality can be obtained by a proper design of synthetic gauge fields in the couplings from the nodes to the waveguide. In the Rydberg case, this is achieved via intrinsic spin-orbit coupling in the dipole-dipole interactions, while for the trapped ions it is obtained by engineered sideband transitions. We take long-range couplings into account that appear naturally in these implementations, discuss useful experimental parameters, and analyze potential error sources. Finally, we describe effects that can be observed in these implementations within state-of-the-art technology, such as the driven-dissipative formation of entangled dimer states.
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• T. Ramos, B. Vermersch, P. Hauke, H. Pichler, P. Zoller Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons, Phys. Rev. A 93 62104 (2016-06-02), http://dx.doi.org/10.1103/PhysRevA.93.062104 doi:10.1103/PhysRevA.93.062104 (ID: 719497) Toggle Abstract
  We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to the familiar photonic networks consisting of driven two-level atoms exchanging photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D XX-spin chains representing a spin waveguide. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.
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• N. Goldman, J. Budich, P. Zoller Topological quantum matter with ultracold gases in optical lattices, Nature Phys. 12 645 (2016-05-25), http://dx.doi.org/10.1038/nphys3803 doi:10.1038/nphys3803 (ID: 719596) Toggle Abstract
  Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical lattices, give an overview of the theoretical and experimental advances and provide an outlook towards realizing strongly correlated topological phases.
• H. Pichler, G. Zhu, A. Seif, P. Zoller, M. Hafezi A Measurement Protocol for the Entanglement Spectrum of Cold Atoms, Phys. Rev. X 6 41033 (2016-05-17), http://dx.doi.org/10.1103/PhysRevX.6.041033 doi:10.1103/PhysRevX.6.041033 (ID: 719569) Toggle Abstract
  Entanglement plays a major role in characterizing many-body quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum many-body systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to this date, due to the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian, and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.
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• C. Laflamme, W. Evans, M. Dalmonte, U. Gerber, H. Mejia-Diaz, W. Bietenholz, U. Wiese, P. Zoller CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices, Ann. Phys. 370 127 (2016-04-23), http://dx.doi.org/10.1016/j.aop.2016.03.012 doi:10.1016/j.aop.2016.03.012 (ID: 719312) Toggle Abstract
  We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and θ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false θ-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
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• S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, F. Ferlaino Extended Bose-Hubbard Models with Ultracold Magnetic Atoms, Science 352 205 (2016-04-08), http://dx.doi.org/10.1126/science.aac9812 doi:10.1126/science.aac9812 (ID: 719290) Toggle Abstract
  The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics, and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interaction, which is a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of novel exotic many-body quantum phases.
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• P. Hauke, M. Heyl, L. Tagliacozzo, P. Zoller Measuring multipartite entanglement via dynamic susceptibilities, Nature Phys. 12 778 (2016-03-21), http://dx.doi.org/10.1038/nphys3700 doi:10.1038/nphys3700 (ID: 719333) Toggle Abstract
  Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signaturesin optical-lattice experiments.
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• T. Pichler, M. Dalmonte, E. Rico Ortega, P. Zoller, S. Montangero Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks, Phys. Rev. X 6 11023 (2016-03-03), http://dx.doi.org/10.1103/PhysRevX.6.011023 doi:10.1103/PhysRevX.6.011023 (ID: 719259) Toggle Abstract
  Tensor networks algorithms provide a suitable route to tackle real-time dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1) dimensions in the presence of dynamical matter for different mass and electric field couplings, a theory akin to quantum-electrodynamics in one-dimension, which displays string-breaking: the confining string between charges can spontaneously break during quench exper- iments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric field and particle fluctuations: We determine a dynamical state diagram for string breaking, and we quantitatively evaluate the time-scales for mass production. We show also that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, which demonstrates that the Schwinger mech- anism is tightly linked to entanglement spreading. To present the variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we access the quality of quantum simulations of these dynamics quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entan- glement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.
• H. Pichler, P. Zoller Photonic Quantum Circuits with Time Delays, Phys. Rev. Lett. 116 93601 (2016-03-03), http://dx.doi.org/10.1103/PhysRevLett.116.093601 doi:10.1103/PhysRevLett.116.093601 (ID: 719362) Toggle Abstract
  We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where the time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where a quantum signal is fed back on a system with a time delay. We develop a matrix product state approach to solve the quantum stochastic Schrödinger equation with time delays, which accounts in an efficient way for the entanglement of nodes with the stream of emitted photons in the waveguide, and thus the non-Markovian character of the dynamics. We illustrate this approach with two paradigmatic quantum optical examples: two coherently driven distant atoms coupled to a photonic waveguide with a time delay, and a driven atom coupled to its own output field with a time delay as an instance of a quantum feedback problem.
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• M. Łącki, H. Pichler, A. Sterdyniak, A. Lyras, V. Lembessis, O. Al-Dossary, J. Budich, P. Zoller Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices, Phys. Rev. A 93 13604 (2016-01-07), http://dx.doi.org/10.1103/PhysRevA.93.013604 doi:10.1103/PhysRevA.93.013604 (ID: 719282) Toggle Abstract
  We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by counter-propagating Laguerre-Gauss beams, i.e. light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.
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2015

Articles

• J. Budich, C. Laflamme, F. Tschirsich, S. Montangero, P. Zoller Synthetic Helical Liquids with Ultracold Atoms in Optical Lattices, Phys. Rev. B 92 245121 (2015-12-14), http://dx.doi.org/10.1103/PhysRevB.92.245121 doi:10.1103/PhysRevB.92.245121 (ID: 719243) Toggle Abstract
  We develop a new platform for the synthetic realization of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly correlated metallic state where spin polarization and propagation direction of the itinerant particles are locked to each other. We propose an unconventional one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the HTLL in the long wavelength limit, as we demonstrate with a combination of analytical (bosonization) and numerical (density matrix renormalization group) methods. An experimentally feasible scheme is provided for the realization of this model with ultracold fermionic atoms in optical lattices. Finally, we discuss how the robustness of the HTLL against backscattering and imperfections, well known from its realization at the edge of a two-dimensional topological insulators, is reflected in the present synthetic scenario.
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• W. Lechner, P. Hauke, P. Zoller A quantum annealing architecture with all-to-all connectivity from local interactions, Sci. Adv. 1 e1500838 (2015-10-23), http://dx.doi.org/10.1126/sciadv.1500838 doi:10.1126/sciadv.1500838 (ID: 719363) Toggle Abstract
  Quantum annealers are physical devices that aim at solving NP-complete optimization problems by exploiting quantum mechanics. The basic principle of quantum annealing is to encode the optimization problem in Ising interactions between quantum bits (qubits). A fundamental challenge in building a fully programmable quantum annealer is the competing requirements of full controllable all-to-all connectivity and the quasi-locality of the interactions between physical qubits. We present a scalable architecture with full connectivity, which can be implemented with local interactions only. The input of the optimization problem is encoded in local fields acting on an extended set of physical qubits. The output is—in the spirit of topological quantum memories—redundantly encoded in the physical qubits, resulting in an intrinsic fault tolerance. Our model can be understood as a lattice gauge theory, where long-range interactions are mediated by gauge constraints. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NV-centers, quantum dots, and atomic systems.
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• Y. Hu, Z. Cai, M. Baranov, P. Zoller Majoranas in Noisy Kitaev Wires, Phys. Rev. B 92 165118 (2015-10-16), http://dx.doi.org/10.1103/PhysRevB.92.165118 doi:10.1103/PhysRevB.92.165118 (ID: 719277) Toggle Abstract
  Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which is naturally immune against microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum system from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasi-static to the fast fluctuation regime. We present detailed results for the Majorana edge correlations, and fidelity of braiding operations for both global and local noise sources preserving parity symmetry, such as random chemical potentials and phase fluctuations. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations in presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and non-topological phases.
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• M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, L. Fallani Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science 349 1513 (2015-09-25), http://dx.doi.org/10.1126/science.aaa8736 doi:10.1126/science.aaa8736 (ID: 719172) Toggle Abstract
  Chiral edge states are a hallmark of quantum Hall physics. In electronic systems, they appear as a macroscopic consequence of the cyclotron orbits induced by a magnetic field, which are naturally truncated at the physical boundary of the sample. Here we report on the experimental realization of chiral edge states in a ribbon geometry with an ultracold gas of neutral fermions subjected to an artificial gauge field. By imaging individual sites along a synthetic dimension, we detect the existence of the edge states, investigate the onset of chirality as a function of the bulk-edge coupling, and observe the edge-cyclotron orbits induced during a quench dynamics. The realization of fermionic chiral edge states is a fundamental achievement, which opens the door towards experiments including edge state interferometry and the study of non-Abelian anyons in atomic systems.
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• W. Lechner, P. Zoller Spatial Patterns of Rydberg Excitations from Logarithmic Pair Interactions, Phys. Rev. Lett. 115 125301 (2015-09-18), http://dx.doi.org/10.1103/PhysRevLett.115.125301 doi:10.1103/PhysRevLett.115.125301 (ID: 719185) Toggle Abstract
  The collective excitations in ensembles of dissipative, laser driven ultracold atoms exhibit crystal-like patterns, a many-body effect of the Rydberg blockade mechanism. These crystalline structure are revealed in experiment from a post-selection of configurations with fixed numbers of excitations. Here, we show that these sub-ensemble can be well represented by ensembles of effective particles that interact via logarithmic pair potentials. This allows one to study the emergent patterns with a small number of effective particles to determine the phases of Rydberg crystals and to systematically study contributions from N -body terms.
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• R. Nath, M. Dalmonte, A. Glätzle, P. Zoller, F. Schmidt-Kaler, R. Gerritsma Hexagonal Plaquette Spin-spin Interactions and Quantum Magnetism in a Two-dimensional Ion Crystal, New J. Phys. 17 065018 (2015-06-25), http://dx.doi.org/10.1088/1367-2630/17/6/065018 doi:10.1088/1367-2630/17/6/065018 (ID: 719216) Toggle Abstract
  We propose a trapped ion scheme en route to realize spin Hamiltonians on a Kagome lattice which, at low energies, are described by emergent Z2 gauge fields, and support a topological quantum spin liquid ground state. The enabling element in our scheme is the hexagonal plaquette spin-spin interactions in a 2D ion crystal. For this, the phonon-mode spectrum of the crystal is engineered by standing-wave optical potentials or by using Rydberg excited ions, thus generating localized phonon-modes around a hexagon of ions selected out of the entire two-dimensional crystal. These tailored modes can mediate spin-spin interactions between ion-qubits on a hexagonal plaquette when subject to state-dependent optical dipole forces. We discuss how these interactions can be employed to emulate a generalized Balents-Fisher-Girvin model in minimal instances of one and two plaquettes. This model is an archetypical Hamiltonian in which gauge fields are the emergent degrees of freedom on top of the classical ground state manifold. Under realistic situations, we show the emergence of a discrete Gauss's law as well as the dynamics of a deconfined charge excitation on a gauge-invariant background using the two-plaquettes trapped ions spin-system. The proposed scheme in principle allows further scaling in a future trapped ion quantum simulator, and we conclude that our work will pave the way towards the simulation of emergent gauge theories and quantum spin liquids in trapped ion systems.
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• A. Glätzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, P. Zoller Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms, Phys. Rev. Lett. 114 173002 (2015-04-28), http://dx.doi.org/10.1103/PhysRevLett.114.173002 doi:10.1103/PhysRevLett.114.173002 (ID: 719027) Toggle Abstract
  We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop", and "flip-flip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time-scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-the-art experiments.
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• B. Vogell, T. Kampschulte, M. Rakher, A. Faber, P. Treutlein, K. Hammerer, P. Zoller Long Distance Coupling of a Quantum Mechanical Oscillator to the Internal States of an Atomic Ensemble, New J. Phys. 17 043044 (2015-04-22), http://dx.doi.org/10.1088/1367-2630/17/4/043044 doi:10.1088/1367-2630/17/4/043044 (ID: 719098) Toggle Abstract
  We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light eld which allows to couple the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benet from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the eective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.
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• J. Budich, P. Zoller, S. Diehl Dissipative preparation of Chern Insulators, Phys. Rev. A 91 042117 (2015-04-14), http://dx.doi.org/10.1103/PhysRevA.91.042117 doi:10.1103/PhysRevA.91.042117 (ID: 719006) Toggle Abstract
  Engineered dissipation can be employed to efficiently prepare interesting quantum many body states in a non-equilibrium fashion. Here, we study the open quantum system dynamics of fermions on a 2D lattice in the framework of a Lindblad master equation. In particular, we propose a novel mechanism to dissipatively prepare a topological state with non-zero Chern number as the unique steady state by means of short-range system bath interaction. This provides a genuine open quantum system approach to the preparation of topological states, which, quite remarkably, gives rise to a stable topological phase in a non-equilibrium phase diagram. We demonstrate how our theoretical construction can be implemented in a microscopic model that is experimentally feasible with cold atoms in optical lattices.
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• H. Pichler, T. Ramos, A. J. Daley, P. Zoller Quantum Optics of Chiral Spin Networks, Phys. Rev. A 91 042116 (2015-04-14), http://dx.doi.org/10.1103/PhysRevA.91.042116 doi:10.1103/PhysRevA.91.042116 (ID: 719040) Toggle Abstract
  We study the driven-dissipative dynamics of a network of spin-1/2 systems coupled to one or more chiral 1D bosonic waveguides within the framework of a Markovian master equation. We determine how the interplay between a coherent drive and collective decay processes can lead to the formation of pure multipartite entangled steady states. The key ingredient for the emergence of these many-body dark states is an asymmetric coupling of the spins to left and right propagating guided modes. Such systems are motived by experimental possibilities with internal states of atoms coupled to optical fibers, or motional states of trapped atoms coupled to a spin-orbit coupled Bose-Einstein condensate. We discuss the characterization of the emerging multipartite entanglement in this system in terms of the Fisher information.
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• Z. Xu, X. Li, P. Zoller, W. Liu Spontaneous quantum Hall effect in an atomic spinor Bose-Fermi mixture, Phys. Rev. Lett. 114 125303 (2015-03-27), http://dx.doi.org/10.1103/PhysRevLett.114.125303 doi:10.1103/PhysRevLett.114.125303 (ID: 718957) Toggle Abstract
  We study a mixture of spin-1 bosonic and spin-1/2 fermionic cold atoms, e.g., 87 Rb and 6 Li, confined in a triangular optical lattice. With fermions at 3/4 filling, Fermi surface nesting leads to spontaneous formation of various spin textures of bosons in the ground state, such as collinear, coplanar and even non-coplanar spin orders. The phase diagram is mapped out with varying boson tunneling and Bose-Fermi interactions. Most significantly, in one non-coplanar state the mixture is found to exhibit a spontaneous quantum Hall effect in fermions and crystalline superfluidity in bosons, both driven by interaction.
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• B. Vermersch, A. Glätzle, P. Zoller Magic distances in the blockade mechanism of Rydberg p and d states, Phys. Rev. A 91 023411 (2015-02-11), http://dx.doi.org/10.1103/PhysRevA.91.023411 doi:10.1103/PhysRevA.91.023411 (ID: 719085) Toggle Abstract
  We show that the Rydberg blockade mechanism, which is well known in the case of s states, can be significantly different for p and d states due to the van der Waals couplings between different Rydberg Zeeman sublevels and the presence of a magnetic-field. We show, in particular, the existence of magic distances corresponding to the laser-excitation of a superposition of doubly excited states.
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• M. Dalmonte, S. Mirzaei, P. R. Muppalla, D. Marcos, P. Zoller, G. Kirchmair Dipolar Spin Models with Arrays of Superconducting Qubits, Phys. Rev. B 92 174507 (2015-01-13), http://dx.doi.org/10.1103/PhysRevB.92.174507 doi:10.1103/PhysRevB.92.174507 (ID: 719116) Toggle Abstract
  We propose a novel platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D Transmon qubits where we use the naturally occurring dipolar interactions to realize interacting spin systems. This opens the way toward the realization of a broad class of tunable spin models in both two- and one-dimensional geometries. We illustrate the potential offered by these systems in the context of dimerized Majumdar-Ghosh-type phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder and decoherence, and could be observed within state-of-the-art experiments.
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• B. Vermersch, M. Punk, A. Glätzle, C. Gross, P. Zoller Dynamical preparation of laser-excited anisotropic Rydberg crystals in 2D optical lattices, New J. Phys. 17 013008 (2015-01-09), http://dx.doi.org/10.1088/1367-2630/17/1/013008 doi:10.1088/1367-2630/17/1/013008 (ID: 718969) Toggle Abstract
  We describe the dynamical preparation of anisotropic crystalline phases obtained by laser-exciting ultracold Alkali atoms to Rydberg p-states where they interact via anisotropic van derWaals interactions. We develop a timedependent variational mean field ansatz to model large, but finite two-dimensional systems in experimentally accessible parameter regimes, and we present numerical simulations to illustrate the dynamical formation of anisotropic Rydberg crystals.
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Book

• C. Gardiner, P. Zoller The Quantum World of Ultra-Cold Atoms and Light Book II: The Physics of Quantum-Optical Devices, The Quantum World of Ultra-Cold Atoms and Light Book II: The Physics of Quantum-Optical Devices 4 (2015-05-06), URL (ID: 719240)

Proceeding

• C. Laflamme, W. Evans, M. Dalmonte, U. Gerber, H. Mejia-Diaz, W. Bietenholz, U. Wiese, P. Zoller Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices, URL Proceedings of Science (2015-10-28), arXiv:1510.08492 arXiv:1510.08492 (ID: 719376) (local copy)

2014

Articles

• T. Ramos, H. Pichler, A. J. Daley, P. Zoller Quantum Spin-Dimers from Chiral Dissipation in Cold Atom Chains, Phys. Rev. Lett. 113 237203 (2014-12-03), http://dx.doi.org/10.1103/PhysRevLett.113.237203 doi:10.1103/PhysRevLett.113.237203 (ID: 718977) Toggle Abstract
  We consider the non-equilibrium dynamics of a driven dissipative spin chain with chiral coupling to a 1D bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasi-condensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left and right moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.
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• D. Marcos, P. Widmer, E. Rico Ortega, M. Hafezi, P. Rabl, U. Wiese, P. Zoller Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits, Ann. Phys. 351 654 (2014-09-10), http://dx.doi.org/10.1016/j.aop.2014.09.011 doi:10.1016/j.aop.2014.09.011 (ID: 718973) Toggle Abstract
  A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
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• J. Budich, J. Eisert, E. Bergholtz, S. Diehl, P. Zoller Search for localized Wannier functions of topological band structures via compressed sensing, Phys. Rev. B 90 115110 (2014-09-04), http://dx.doi.org/10.1103/PhysRevB.90.115110 doi:10.1103/PhysRevB.90.115110 (ID: 718935) Toggle Abstract
  We approach the problem of finding maximally localized Wannier functions from a viewpoint of compressed sensing. A practical toolbox is developed to search for maximally localized Wannier functions that exactly obey the underlying physical symmetries of a translationally invariant quantum lattice system under investigation. Each step of the iteration is an O(NlogN) algorithm in the number of lattice sites N . Most interestingly, we are able to generalize our construction to systematically identify the most localized representative of a topological equivalence class of band structures, i.e., the most localized set of Wannier functions that is adiabatically connected to a generic initial representative. We present benchmark results on one-dimensional topological superconductors demonstrating the power of these tools. Furthermore, we employ our method to address the open question whether compact Wannier functions can exist for symmetry protected topological states like topological insulators in two dimensions. The existence of such functions would imply exact flat band models with strictly finite range hopping. Here, we find strong numerical evidence for the absence of such functions. We briefly discuss applications in dissipative state preparation and in devising variational sets of states for tensor network methods.
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• X. Zhang, M. Bishof, S. L. Bromley, C. Kraus, M. Safronova, P. Zoller, A. M. Rey, J. Ye Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism, Science 1254978 (2014-08-21), http://dx.doi.org/10.1126/science.1254978 doi:10.1126/science.1254978 (ID: 718864) Toggle Abstract
  Symmetries play a fundamental role in the laws of nature. SU(N) symmetry can emerge in a quantum system with N single-particle spin states when the spin degree of freedom is decoupled from interactions. Such a system is anticipated to exhibit large degeneracy and exotic many-body behaviors. Owing to the strong decoupling between electronic-orbital and nuclear-spin degrees of freedom, alkaline-earth atoms (AEAs), prepared in the two lowest electronic states (clock states), are predicted to obey an accurate SU(N=2I+1) symmetry arising from the nuclear spin (I). So far, only indirect evidence for this symmetry exists, and the scattering parameters remain largely unknown. Here we report the first direct observation of SU(N=10) symmetry in 87Sr (I=9/2) using the state-of-the-art measurement precision offered by an ultra-stable laser. By encoding the electronic orbital degree of freedom in the two clock states, while keeping the system open to all 10 nuclear spin sublevels, we probe the non-equilibrium two-orbital SU(N) magnetism via Ramsey spectroscopy of atoms confined in an array of 2D optical traps. The motional degrees of freedom are frozen during the spin dynamics, which allows probing generic models of quantum magnetism at high temperatures. Compared with lattice models of spatially localized atoms coupled with short-range interactions, our system shows two key differences: the lattice is spanned by energy eigenvalues and the underlying interactions are long-range and nuclear spin independent. To elucidate the microscopic mechanism for SU(N) orbital physics, we model the spin-orbital dynamics and determine all relevant interaction parameters with an analytic relation between s- and p-wave scattering lengths. This work prepares for using AEAs as test-beds for iconic orbital models expected to describe transition metal oxides, heavy fermion materials, and spin liquid phases.
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• P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C. F. Roos Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature 511 202 (2014-07-10), http://dx.doi.org/10.1038/nature13461 doi:10.1038/nature13461 (ID: 718717) Toggle Abstract
  The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport, thermalisation, localisation and entanglement growth, and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.
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• W. Lechner, H. Büchler, P. Zoller Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules, Phys. Rev. Lett. 112 255301 (2014-06-25), http://dx.doi.org/10.1103/PhysRevLett.112.255301 doi:10.1103/PhysRevLett.112.255301 (ID: 718725) Toggle Abstract
  Two dimensional crystals melt via an intermediate \textit{hexatic} phase which is characterized by an anomalous scaling of spatial and orientational correlation functions and the absence of an attraction between dislocations. We propose a protocol to study the role of quantum fluctuations on the nature of this phase with a system of strongly correlated polar molecules in a parameter regime where thermal and quantum fluctuations are of the same order of magnitude. The dislocations can be located in experiment from local energy differences which induce internal stark shifts in dislocation molecules. We present a criterium to identify the hexatic phase from the statistics of the end points of topological defect strings and find a hexatic phase, which is dominated by quantum fluctuations, between crystal and superfluid phase.
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• A. Carmele, B. Vogell, K. Stannigel, P. Zoller Opto-Nanomechanics Strongly Coupled to a Rydberg Superatom: Coherent vs. Incoherent Dynamics, New J. Phys. 16 063042 (2014-06-19), http://dx.doi.org/10.1088/1367-2630/16/6/063042 doi:10.1088/1367-2630/16/6/063042 (ID: 718701) Toggle Abstract
  We propose a hybrid optomechanical quantum system consisting of a moving membrane strongly coupled to an ensemble of N atoms with a Rydberg state. Due to the strong van-der-Waals interaction between the atoms, the ensemble forms an effective two-level system, a Rydberg superatom, with a collectively enhanced atom-light coupling. Using this superatom imposed collective enhancement strong coupling between membrane and superatom is feasible for parameters within the range of current experiments. The quantum interface to couple the membrane and the superatom can be a pumped single mode cavity, or a laser field in free space, where the Rydberg superatom and the membrane are spatially separated. In addition to the coherent dynamics, we study in detail the impact of the typical dissipation processes, in particular the radiative decay as a source for incoherent superpositions of atomic excitations. We identify the conditions to suppress these incoherent dynamics and thereby a parameter regime for strong coupling. The Rydberg superatom in this hybrid system serves as a toolbox for the nanomechanical resonator allowing for a wide range of applications such as state transfer, sympathetic cooling and non-classical state preparation. As an illustration, we show that a thermally occupied membrane can be prepared in a non-classical state without the necessity of ground state cooling.
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• E. Rico Ortega, T. Pichler, M. Dalmonte, P. Zoller, S. Montangero Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation, Phys. Rev. Lett. 112 201601 (2014-05-23), http://dx.doi.org/10.1103/PhysRevLett.112.201601 doi:10.1103/PhysRevLett.112.201601 (ID: 718702) Toggle Abstract
  We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
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• A. Glätzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Mössner, P. Zoller Quantum Spin Ice and dimer models with Rydberg atoms, Phys. Rev. X 4 041037 (2014-04-21), http://dx.doi.org/10.1103/PhysRevX.4.041037 doi:10.1103/PhysRevX.4.041037 (ID: 718901) Toggle Abstract
  Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg p-states together with the possibility of designing step-like potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice.
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• K. Stannigel, P. Hauke, D. Marcos, M. Hafezi, S. Diehl, M. Dalmonte, P. Zoller Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms, Phys. Rev. Lett. 112 120406 (2014-03-26), http://dx.doi.org/10.1103/PhysRevLett.112.120406 doi:10.1103/PhysRevLett.112.120406 (ID: 718579) Toggle Abstract
  We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, non-local interaction patterns by global coupling to laser fields.
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• C. Laflamme, M. Baranov, P. Zoller, C. Kraus Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup, Phys. Rev. A 89 022319 (2014-02-14), http://dx.doi.org/10.1103/PhysRevA.89.022319 doi:10.1103/PhysRevA.89.022319 (ID: 718700) Toggle Abstract
  In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be implemented in this setup and introduce a proposal for the efficient, robust and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient non-destructive protocol to check for errors in the mapping.
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Book

• C. Gardiner, P. Zoller The Quantum World of Ultra-Cold Atoms and Light, Book I: Foundations of Quantum Optics, (2014-05-01), URL (ID: 718994)

2013

Articles

• P. Hauke, D. Marcos, M. Dalmonte, P. Zoller Quantum simulation of a lattice Schwinger model in a chain of trapped ions, Phys. Rev. X 3 041018 (2013-11-22), http://dx.doi.org/10.1103/PhysRevX.3.041018 doi:10.1103/PhysRevX.3.041018 (ID: 718532) Toggle Abstract
  We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich quantum-simulation toolbox available in state-of-the-art trapped-ion experiments, we show how one can engineer an effectively gauge-invariant dynamics by imposing energetic constraints, provided by strong Ising-like interactions. Applying exact diagonalization to ground-state and time-dependent properties, we study the underlying microscopic model, and discuss undesired interaction terms and other imperfections. As our analysis shows, the proposed scheme allows for the observation in realistic setups of spontaneous parity- and charge-symmetry breaking, as well as false-vacuum decay. Besides an implementation aimed at larger ion chains, we also discuss a minimal setting, consisting of only four ions in a simpler experimental setup, which enables to probe basic physical phenomena related to the full many-body problem. The proposal opens a new route for analog quantum simulation of high-energy and condensed-matter models where gauge symmetries play a prominent role.
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• C. Kraus, P. Zoller, M. Baranov Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm, Phys. Rev. Lett. 111 203001 (2013-11-11), http://dx.doi.org/10.1103/PhysRevLett.111.203001 doi:10.1103/PhysRevLett.111.203001 (ID: 718425) Toggle Abstract
  We propose an efficient protocol for braiding atomic Majorana fermions in wire networks with AMO techniques and demonstrate its robustness against experimentally relevant errors. Based on this protocol we provide a topologically protected implementation of the Deutsch-Josza algorithm.
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• W. Lechner, P. Zoller From Classical to Quantum Glasses with Ultracold Polar Molecules, Phys. Rev. Lett. 111 185306 (2013-10-30), http://dx.doi.org/10.1103/PhysRevLett.111.185306 doi:10.1103/PhysRevLett.111.185306 (ID: 718563) Toggle Abstract
  Using experiments with single particle resolution and computer simulations we study the collective behaviour of multiple vacancies injected into two-dimensional crystals. We find that the defects assemble into linear strings that propagate through the crystal in a succession of rapid one-dimensional gliding phases and rare rotations, during which the direction of motion changes. At both ends, strings are terminated by dislocations with anti-parallel Burgers vectors. By monitoring the separation of the dislocations, we measure their effective interactions with high precision, for the first time beyond spontaneous formation and annihilation, and explain the double-well form of the dislocation interaction in terms of continuum elasticity theory. Our results give a detailed picture of the motion and interaction of dislocations in two dimensions and enhance our understanding of topological defects in two-dimensional nano-materials.
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• C. Kraus, M. Dalmonte, M. Baranov, A. Läuchli, P. Zoller Majorana edge states in two atomic wires coupled by pair-hopping, Phys. Rev. Lett. 111 173004 (2013-10-23), http://dx.doi.org/10.1103/PhysRevLett.111.173004 doi:10.1103/PhysRevLett.111.173004 (ID: 718420) Toggle Abstract
  We present evidence for the existence of Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by a pair hopping. Our analysis is based on the combination of a qualitative low energy approach and numerical techniques using the Density Matrix Renormalization Group. We also discuss an experimental realization of pair-hopping interactions in cold atom gases confined in optical lattices, and its possible alternative applications to quantum simulation.
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• O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, J. I. Cirac Superconducting Vortex Lattices for Ultracold Atoms, Phys. Rev. Lett. 111 145304 (2013-10-04), http://dx.doi.org/10.1103/PhysRevLett.111.145304 doi:10.1103/PhysRevLett.111.145304 (ID: 718430) Toggle Abstract
  The ability to trap and manipulate ultracold atoms in lattice structures has lead to a remarkable experimental progress to build quantum simulators for Hubbard models. A prominent example is atoms in optical lattices where lasers are used to create lattices with spacing set by the laser wavelength as well as to control and measure the many-body states. In contrast, here we propose and analyze a nanoengineered vortex array in a thin-film type-II superconductor as a magnetic lattice for ultracold atoms. This proposal addresses several of the key questions in the development of atomic quantum simulators. By trapping atoms close to the surface, tools of nanofabrication and structuring of lattices on the scale of few tens of nanometers become available with a corresponding benefit in energy scales and temperature requirements. This can be combined with the possibility of magnetic single site addressing and manipulation together with a favorable scaling of superconducting surface induced decoherence.
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• D. Marcos, P. Rabl, E. Rico Ortega, P. Zoller Superconducting circuits for quantum simulation of dynamical gauge fields, Phys. Rev. Lett. 111 110504 (2013-09-13), http://dx.doi.org/10.1103/PhysRevLett.111.110504 doi:10.1103/PhysRevLett.111.110504 (ID: 718537) Toggle Abstract
  We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.
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• C. Bardyn, M. Baranov, C. Kraus, E. Rico Ortega, A. Imamoglu, P. Zoller, S. Diehl Topology by dissipation, New J. Phys. 15 085001 (2013-08-01), http://dx.doi.org/10.1088/1367-2630/15/8/085001 doi:10.1088/1367-2630/15/8/085001 (ID: 718440) Toggle Abstract
  Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.
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• H. Pichler, L. Bonnes, A. J. Daley, A. Läuchli, P. Zoller Thermal versus entanglement entropy: a measurement protocol for fermionic atoms with a quantum gas microscope, New J. Phys. 15 063003 (2013-06-06), http://dx.doi.org/10.1088/1367-2630/15/6/063003 doi:10.1088/1367-2630/15/6/063003 (ID: 718531) Toggle Abstract
  We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi–Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.
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• P. Schindler, M. Müller, D. Nigg, J. T. Barreiro, E. A. Martínez, M. Hennrich, T. Monz, S. Diehl, P. Zoller, R. Blatt Quantum simulation of open-system dynamical maps with trapped ions, Nature Phys. 9 367 (2013-05-19), http://dx.doi.org/10.1038/nphys2630 doi:10.1038/nphys2630 (ID: 718325) Toggle Abstract
  Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single particle level. Here we extend the concept of dynamical maps to an open-system, many-particle context: We experimentally explore the stroboscopic dynamics of a complex many-body spin model by means of a universal quantum simulator using up to five ions. In particular, we generate long-range phase coherence of spin by an iteration of purely dissipative quantum maps. We also demonstrate the characteristics of competition between combined coherent and dissipative non-equilibrium evolution. This opens the door for studying many-particle non-equilibrium physics and associated dynamical phase transitions with no immediate counterpart in equilibrium condensed matter systems. An error detection and reduction toolbox that facilitates the faithful quantum simulation of larger systems is developed as a first step in this direction.
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• S. Habraken, W. Lechner, P. Zoller Resonances in dissipative optomechanics with nanoparticles: Sorting, speed rectification and transverse cooling, Phys. Rev. A 87 053808 (2013-05-06), http://dx.doi.org/10.1103/PhysRevA.87.053808 doi:10.1103/PhysRevA.87.053808 (ID: 718463) Toggle Abstract
  The interaction between dielectric particles and a laser-driven optical cavity gives rise to both conservative and dissipative dynamics, which can be used to levitate, trap and cool nanoparticles. We analytically and numerically study a two-mode setup in which the optical potentials along the cavity axis cancel, so that the resulting dynamics is almost purely dissipative. For appropriate detunings of the laser-drives, this dissipative optomechanical dynamics can be used to sort particles according to their size, to rectify their velocities and to enhance transverse cooling.
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• S. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, M. Lukin Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing, Phys. Rev. Lett. 110 156402 (2013-04-09), http://dx.doi.org/10.1103/PhysRevLett.110.156402 doi:10.1103/PhysRevLett.110.156402 (ID: 718345) Toggle Abstract
  We propose and analyze a novel mechanism for long-range spin-spin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogen-vacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phonon-mediated effective spin-spin interactions that can be used to generate squeezed states of a spin ensemble. We show that spin dephasing and relaxation can be largely suppressed, allowing for substantial spin squeezing under realistic experimental conditions. Our approach has implications for spin-ensemble magnetometry, as well as phonon-mediated quantum information processing with spin qubits.
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• N. Goldman, J. Dalibard, A. Dauphin, F. Gerbier, M. Lewenstein, P. Zoller, I. Spielman Direct imaging of topological edges states with cold atoms, Proc. Natl. Acad. U.S.A. 6 (2013-04-08), http://dx.doi.org/10.1073/pnas.1300170110 doi:10.1073/pnas.1300170110 (ID: 718336) Toggle Abstract
  Detecting topological order in cold-atom experiments is an outstanding challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes - guaranteed by the existence of non-trivial topological invariants - have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas, and imaging its time-evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides the first method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
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• W. Lechner, S. Habraken, N. Kiesel, M. Aspelmeyer, P. Zoller Cavity Optomechanics of Levitated Nano-Dumbbells: Non-Equilibrium Phases and Self-Assembly, Phys. Rev. Lett. 110 143604 (2013-04-05), http://dx.doi.org/10.1103/PhysRevLett.110.143604 doi:10.1103/PhysRevLett.110.143604 (ID: 718335) Toggle Abstract
  Levitated nanospheres in optical cavities open a novel route to study many-body systems out of solution and highly isolated from the environment. We show that properly tuned optical parameters allow for the study of the non-equilibrium dynamics of composite nano-particles with non-isotropic optical friction. We find friction induced ordering and nematic transitions with non-equilibrium analogs to liquid crystal phases for ensembles of dimers.
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• D. Banerjee, M. Bögli, M. Dalmonte, E. Rico Ortega, P. Stebler, U. Wiese, P. Zoller Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories, Phys. Rev. Lett. 110 125303 (2013-03-21), http://dx.doi.org/10.1103/PhysRevLett.110.125303 doi:10.1103/PhysRevLett.110.125303 (ID: 718423) Toggle Abstract
  Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.
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• N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, I. J. Cirac, P. Zoller, M. Lukin Topologically Protected Quantum State Transfer in a Chiral Spin Liquid, Nat. Commun. 4 1585 (2013-03-12), http://dx.doi.org/10.1038/ncomms2531 doi:10.1038/ncomms2531 (ID: 717921) Toggle Abstract
  Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed.
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• H. Pichler, J. Schachenmayer, A. J. Daley, P. Zoller Heating dynamics of bosonic atoms in a noisy optical lattice, Phys. Rev. A 87 033606 (2013-03-05), http://dx.doi.org/10.1103/PhysRevA.87.033606 doi:10.1103/PhysRevA.87.033606 (ID: 718344) Toggle Abstract
  We analyze the heating of interacting bosonic atoms in an optical lattice due to intensity fluctuations of the lasers forming the lattice. We focus in particular on fluctuations at low frequencies below the band gap frequency, such that the dynamics is restricted to the lowest band. We derive stochastic equations of motion, and analyze the effects on different many-body states, characterizing heating processes in both strongly and weakly interacting regimes. In the limit where the noise spectrum is flat at low frequencies, we can derive an effective Master equation describing the dynamics. We compute heating rates and changes to characteristic correlation functions both in the perturbation theory limit, and using a full time-dependent calculation of the stochastic many-body dynamics in 1D based on time-dependent density-matrix-renormalization-group methods.
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• B. Vogell, K. Stannigel, P. Zoller, K. Hammerer, M. T. Rakher, M. Korppi, A. Jöckel, P. Treutlein Cavity-Enhanced Long-Distance Coupling of an Atomic Ensemble to a Micromechanical Membrane, Phys. Rev. A 87 023816 (2013-02-14), http://dx.doi.org/10.1103/PhysRevA.87.023816 doi:10.1103/PhysRevA.87.023816 (ID: 718342) Toggle Abstract
  We discuss a hybrid quantum system where a dielectric membrane situated inside an optical cavity is coupled to a distant atomic ensemble trapped in an optical lattice. The coupling is mediated by the exchange of sideband photons of the lattice laser, and is enhanced by the cavity finesse as well as the square root of the number of atoms. In addition to observing coherent dynamics between the two systems, one can also switch on a tailored dissipation by laser cooling the atoms, thereby allowing for sympathetic cooling of the membrane. The resulting cooling scheme does not require resolved sideband conditions for the cavity, which relaxes a constraint present in standard optomechanical cavity cooling. We present a quantum mechanical treatment of this modular open system which takes into account the dominant imperfections, and identify optimal operation points for both coherent dynamics and sympathetic cooling. In particular, we find that ground state cooling of a cryogenically pre-cooled membrane is possible for realistic parameters.
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• T. Ramos, V. Sudhir, K. Stannigel, P. Zoller, T. J. Kippenberg Nonlinear Quantum Optomechanics via Individual Intrinsic Two-Level Defects, Phys. Rev. Lett. 110 193602 (2013-02-07), http://dx.doi.org/10.1103/PhysRevLett.110.193602 doi:10.1103/PhysRevLett.110.193602 (ID: 718426) Toggle Abstract
  We propose to use the intrinsic two-level system (TLS) defect states found naturally in integrated optomechanical devices for exploring cavity QED-like phenomena with localized phonons. The Jaynes-Cummings-type interaction between TLS and mechanics can reach the strong coupling regime for existing nano-optomechanical systems, observable via clear signatures in the optomechanical output spectrum. These signatures persist even at finite temperature, and we derive an explicit expression for the temperature at which they vanish. Further, the ability to drive the defect with a microwave field allows for realization of phonon blockade, and the available controls are sufficient to deterministically prepare non-classical states of the mechanical resonator.
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• P. Komar, S. D. Bennett, K. Stannigel, S. Habraken, P. Rabl, P. Zoller, M. Lukin Single-photon nonlinearities in two-mode optomechanics, Phys. Rev. A 87 013839 (2013-01-28), http://dx.doi.org/10.1103/PhysRevA.87.013839 doi:10.1103/PhysRevA.87.013839 (ID: 718245) Toggle Abstract
  We present a detailed theoretical analysis of a weakly driven multimode optomechanical system, in which two optical modes are strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculate one- and two-time intensity correlations of the two optical fields and compare them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arise when the optomechanical coupling $g$ exceeds the cavity decay rate $\kappa$, and we discuss signatures of one- and two-photon resonances as well as quantum interference. We also find a long-lived correlation that decays slowly with the mechanical decay rate $\gamma$, reflecting the heralded preparation of a single phonon state after detection of a photon. Our results provide insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.
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Issue

• R. Blatt, I. Bloch, I. J. Cirac, P. Zoller Quantum simulation - an exciting adventure, Ann. Phys. 525 (2013-11-04), http://dx.doi.org/10.1002/andp.201370100 doi:10.1002/andp.201370100 (ID: 718616)

2012

Articles

• N. Y. Yao, C. R. Laumann, A. V. Gorshkov, S. D. Bennett, E. Demler, P. Zoller, M. Lukin Topological Flat Bands from Dipolar Spin Systems, Phys. Rev. Lett. 109 266804 (2012-12-26), http://dx.doi.org/10.1103/PhysRevLett.109.266804 doi:10.1103/PhysRevLett.109.266804 (ID: 718171) Toggle Abstract
  We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered.
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• M. Gullans, T. Tiecke, S. Chang, J. Feist, J. D. Thompson, I. J. Cirac, P. Zoller, M. Lukin Nanoplasmonic Lattices for Ultracold Atoms, Phys. Rev. Lett. 109 235309 (2012-12-07), http://dx.doi.org/10.1103/PhysRevLett.109.235309 doi:10.1103/PhysRevLett.109.235309 (ID: 718190) Toggle Abstract
  We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed.
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• C. Kraus, S. Diehl, P. Zoller, M. Baranov Preparing and probing atomic Majorana fermions and topological order in optical lattices, New J. Phys. 14 113036 (2012-11-27), http://dx.doi.org/10.1088/1367-2630/14/11/113036 doi:10.1088/1367-2630/14/11/113036 (ID: 717882) Toggle Abstract
  We introduce a one-dimensional system of fermionic atoms in an optical lattice whose phase diagram includes topological states of different symmetry classes. These states can be identified by their zero-energy edge modes which are Majorana fermions. We propose several universal methods of detecting the Majorana edge states, based on their genuine features: zero-energy, localized character of the wave functions, and induced non-local fermionic correlations.
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• H. Pichler, J. Schachenmayer, J. Simon, P. Zoller, A. J. Daley Noise- and disorder-resilient optical lattices, Phys. Rev. A 86 051605 (2012-11-16), http://dx.doi.org/10.1103/PhysRevA.86.051605 doi:10.1103/PhysRevA.86.051605 (ID: 718093) Toggle Abstract
  We show how a dressed lattice scheme can provide control over certain types of noise for atomic quantum gases in the lowest band of an optical lattice, removing the effects of global lattice amplitude noise to first order for particular choices of the dressing field parameters. We investigate the nonequilibrium many-body dynamics of bosons and fermions induced by noise away from this parameter regime, and show how the same technique can reduce spatial disorder in projected lattice potentials.
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• S. Habraken, K. Stannigel, M. Lukin, P. Zoller, P. Rabl Continuous mode cooling and phonon routers for phononic quantum networks, New J. Phys. 24 115004 (2012-11-05), http://dx.doi.org/10.1088/1367-2630/14/11/115004 doi:10.1088/1367-2630/14/11/115004 (ID: 718101) Toggle Abstract
  We study the implementation of quantum state transfer protocols in phonon networks, where in analogy to optical networks, quantum information is transmitted through propagating phonons in extended mechanical resonator arrays or phonon waveguides. We describe how the problem of a non-vanishing thermal occupation of the phononic quantum channel can be overcome by implementing optomechanical multi- and continuous mode cooling schemes to create a 'cold' frequency window for transmitting quantum states. In addition, we discuss the implementation of phonon circulators and switchable phonon routers, which rely on strong coherent optomechanical interactions only, and do not require strong magnetic fields or specific materials. Both techniques can be applied and adapted to various physical implementations, where phonons coupled to spin or charge based qubits are used for on-chip networking applications.
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• D. Banerjee, M. Dalmonte, M. Müller, E. Rico Ortega, P. Stebler, U. Wiese, P. Zoller Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench, Phys. Rev. Lett. 109 175302 (2012-10-23), http://dx.doi.org/10.1103/PhysRevLett.109.175302 doi:10.1103/PhysRevLett.109.175302 (ID: 718094) Toggle Abstract
  Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
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• A. Glätzle, R. Nath, B. Zhao, G. Pupillo, P. Zoller Driven-dissipative dynamics of a strongly interacting Rydberg gas, Phys. Rev. A 86 043403 (2012-10-02), http://dx.doi.org/10.1103/PhysRevA.86.043403 doi:10.1103/PhysRevA.86.043403 (ID: 718134) Toggle Abstract
  We study the non-equilibrium many-body dynamics of a cold gas of ground state alkali atoms weakly admixed by Rydberg states with laser light. On a timescale shorter than the lifetime of the dressed states, effective dipole-dipole or van der Waals interactions between atoms can lead to the formation of strongly correlated phases, such as atomic crystals. Using a semiclassical approach, we study the long-time dynamics where decoherence and dissipative processes due to spontaneous emission and blackbody radiation dominate, leading to heating and melting of atomic crystals as well as particle losses. These effects can be substantially mitigated by performing active laser cooling in the presence of atomic dressing.
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• C. Bardyn, M. Baranov, E. Rico Ortega, A. Imamoglu, P. Zoller, S. Diehl Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number, Phys. Rev. Lett. 109 130402 (2012-09-25), http://dx.doi.org/10.1103/PhysRevLett.109.130402 doi:10.1103/PhysRevLett.109.130402 (ID: 717881) Toggle Abstract
  We investigate dissipation-induced p-wave paired states of fermions in two dimensions and show that dissipation can break the bulk-edge correspondence present in Hamiltonian systems in a way that leads to the appearance of spatially separated Majorana zero modes in a phase with vanishing Chern number. We construct an explicit model of a dissipative vortex that traps a single of these modes and establish its topological origin by mapping it to a one-dimensional wire where we observe a non-equilibrium topological phase transition characterized by an abrupt change of a topological invariant (winding number). Engineered dissipation opens up possibilities for experimentally realizing such states with no Hamiltonian counterpart.
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• A. Tomadin, S. Diehl, M. Lukin, P. Rabl, P. Zoller Reservoir engineering and dynamical phase transitions in optomechanical arrays, Phys. Rev. A 86 033821 (2012-09-14), http://dx.doi.org/10.1103/PhysRevA.86.033821 doi:10.1103/PhysRevA.86.033821 (ID: 718117) Toggle Abstract
  We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number conserving non-unitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studied in detail, and it is shown to be a realistic setup where the key processes of the driven-dissipative dynamics can be seen.
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• M. Baranov, M. Dalmonte, G. Pupillo, P. Zoller Condensed Matter Theory of Dipolar Quantum Gases, Chem. Rev. (2012-08-09), http://dx.doi.org/10.1021/cr2003568 doi:10.1021/cr2003568 (ID: 718140) Toggle Abstract
  Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.
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• A. J. Daley, H. Pichler, J. Schachenmayer, P. Zoller Measuring entanglement growth in quench dynamics of bosons in an optical lattice, Phys. Rev. Lett. 109 020505 (2012-07-12), http://dx.doi.org/10.1103/PhysRevLett.109.020505 doi:10.1103/PhysRevLett.109.020505 (ID: 718070) Toggle Abstract
  We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Renyi entropies can be extracted using tunnel-coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a Superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfections in the measurements.
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• K. Stannigel, P. Komar, S. Habraken, S. D. Bennett, M. Lukin, P. Zoller, P. Rabl Optomechanical quantum information processing with photons and phonons, Phys. Rev. Lett. 109 013603 (2012-07-06), http://dx.doi.org/10.1103/PhysRevLett.109.013603 doi:10.1103/PhysRevLett.109.013603 (ID: 717990) Toggle Abstract
  We describe how strong resonant interactions in multimode optomechanical systems can be used to induce controlled nonlinear couplings between single photons and phonons. Combined with linear mapping schemes between photons and phonons, these techniques provide a universal building block for various classical and quantum information processing applications. Our approach is especially suited for nano-optomechanical devices, where strong optomechanical coupling on a single photon level is within experimental reach.
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• K. Stannigel, P. Rabl, P. Zoller Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New J. Phys. 14 063014 (2012-06-14), http://dx.doi.org/10.1088/1367-2630/14/6/063014 doi:10.1088/1367-2630/14/6/063014 (ID: 717830) Toggle Abstract
  We study the dissipative dynamics and the formation of entangled states in driven cascaded quantum networks, where multiple systems are coupled to a common unidirectional bath. Specifically, we identify the conditions under which emission and coherent reabsorption of radiation drives the whole network into a pure stationary state with non-trivial quantum correlations between the individual nodes. For the case of cascaded two-level systems, we present an explicit preparation scheme that allows for tuning the network into different classes of multi-partite entangled states. We discuss potential realizations of such cascaded networks with optical and microwave photons, where these effects could be used, for example, for new long-distance entanglement distribution protocols.
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• B. Zhao, A. Glätzle, G. Pupillo, P. Zoller Atomic Rydberg Reservoirs for Polar Molecules, Phys. Rev. Lett. 108 193007 (2012-05-11), http://dx.doi.org/10.1103/PhysRevLett.108.193007 doi:10.1103/PhysRevLett.108.193007 (ID: 717841) Toggle Abstract
  We discuss laser dressed dipolar and Van der Waals interactions between atoms and polar molecules, so that a cold atomic gas with laser admixed Rydberg levels acts as a designed reservoir for both elastic and inelastic collisional processes. The elastic scattering channel is characterized by large elastic scattering cross sections and repulsive shields to protect from close encounter collisions. In addition, we discuss a dissipative (inelastic) collision where a spontaneously emitted photon carries away (kinetic) energy of the collision partners, thus providing a significant energy loss in a single collision. This leads to the scenario of rapid thermalization and cooling of a molecule in the mK down to the uK regime by cold atoms.
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• W. Yi, S. Diehl, A. J. Daley, P. Zoller Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice, New J. Phys. 14 055002 (2012-05-01), http://dx.doi.org/10.1088/1367-2630/14/5/055002 doi:10.1088/1367-2630/14/5/055002 (ID: 717858) Toggle Abstract
  We discuss the preparation of many-body states of cold fermionic atoms in an optical lattice via controlled dissipative processes induced by coupling the system to a reservoir. Based on a mechanism combining Pauli blocking and phase locking between adjacent sites, we construct complete sets of jump operators describing coupling to a reservoir that leads to dissipative preparation of pairing states for fermions with various symmetries in the absence of direct inter-particle interactions. We discuss the uniqueness of these states, and demonstrate it with small-scale numerical simulations. In the late time dissipative dynamics, we identify a "dissipative gap" that persists in the thermodynamic limit. This gap implies exponential convergence of all many-body observables to their steady state values. We then investigate how these pairing states can be used as a starting point for the preparation of the ground state of Fermi-Hubbard Hamiltonian via an adiabatic state preparation process also involving the parent Hamiltonian of the pairing state. We also provide a proof-of-principle example for implementing these dissipative processes and the parent Hamiltonians of the pairing states, based on Yb171 atoms in optical lattice potentials.
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• I. Cirac, P. Zoller Goals and opportunities in quantum simulation, Nature Phys. 8 266 (2012-04-02), http://dx.doi.org/10.1038/nphys2275 doi:10.1038/nphys2275 (ID: 718063) Toggle Abstract
  Richard Feynman's presentation 'There's plenty of room at the bottom'1 at the American Physical Society meeting in 1959 is widely acknowledged as one of the main inspirations for the development of nanotechnologies. In the same talk, Feynman also anticipated the possibilities that quantum mechanics can offer us in the microscopic world: “When we get to the very, very small world we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics. So, as we go down and fiddle around with the atoms down there, we are working with different laws, and we can expect to do different things.” The field of quantum information explores such 'different things' and tries to exploit the laws of quantum mechanics that involve the superposition principle to carry out computational tasks in a more efficient way than is possible with devices governed by classical physics. Experimental progress during the past decades has been extraordinary, and has enabled us to isolate single microscopic particles, to manipulate and control their internal quantum states, and to detect them with almost perfect fidelity. Those advances notwithstanding, a quantum computer is still a long-term goal, requiring the full control of a many-body system and, eventually, the implementation of sophisticated error-correction protocols to achieve fault tolerance. So, as we still have to wait for a fully fledged universal quantum-information processor, is it possible to build on the experimental advances made so far, and construct a device not quite at the level of complexity of a quantum computer, but one that still could perform some tasks that classical devices cannot?
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Book

• M. Müller, S. Diehl, G. Pupillo, P. Zoller Engineered Open Systems and Quantum Simulations with Atoms and Ions, Advances In Atomic, Molecular, and Optical Physics Volume 61 Adv. Atom. Molec. and Opt. Physics 61 (2012-03-29), arXiv:1203.6595v1 arXiv:1203.6595v1 (ID: 718032) Toggle Abstract
  The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even many-body ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the well-established concept of engineering of many-body Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in many-body quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions. This comprises digital quantum simulations in a general open system setting, as well as engineering and understanding new classes of systems far away from thermodynamic equilibrium.
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Proceeding

• M. Müller, P. Zoller Digital and Open System Quantum simulation, Digital and Open System Quantum simulation Erwin-Schrödinger-Symposium (Vienna, Austria, 2011-01-13) (2012-02-29), (ID: 717985)

2011

Articles

• K. Stannigel, P. Rabl, A. Sorensen, M. Lukin, P. Zoller Optomechanical transducers for quantum information processing, Phys. Rev. A 84 042341 (2011-10-31), http://dx.doi.org/10.1103/PhysRevA.84.042341 doi:10.1103/PhysRevA.84.042341 (ID: 717703) Toggle Abstract
  We discuss the implementation of optical quantum networks where the interface between stationary and photonic qubits is realized by optomechanical transducers [K. Stannigel et al., PRL 105, 220501 (2010)]. This approach does not rely on the optical properties of the qubit and thereby enables optical quantum communication applications for a wide range of solid-state spin- and charge-based systems. We present an effective description of such networks for many qubits and give a derivation of a state transfer protocol for long-distance quantum communication. We also describe how to mediate local on-chip interactions by means of the optomechanical transducers that can be used for entangling gates. We finally discuss experimental systems for the realization of our proposal.
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• R. Sandner, M. Müller, A. J. Daley, P. Zoller Spatial Pauli blocking of spontaneous emission in optical lattices, Phys. Rev. A 84 043825 (2011-10-14), http://dx.doi.org/10.1103/PhysRevA.84.043825 doi:10.1103/PhysRevA.84.043825 (ID: 717732) Toggle Abstract
  Spontaneous emission by an excited fermionic atom can be suppressed due to the Pauli exclusion principle if the relevant final states after the decay are already occupied by identical atoms in the ground state. Here we discuss a setup where a single atom is prepared in the first excited state on a single site of an optical lattice under conditions of very tight trapping. We investigate these phenomena in the context of two experimental realizations: (1) with alkali atoms, where the decay rate of the excited state is large and (2) with alkaline earth-like atoms, where the decay rate from metastable states can be tuned in experiments. This phenomenon has potential applications towards reservoir engineering and dissipative many-body state preparation in an optical lattice.
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• M. Ortner, Y. Zhou, P. Rabl, P. Zoller Quantum information processing in self-assembled crystals of cold polar molecules, Quant. Inf. Proc. 10 819 (2011-10-13), http://dx.doi.org/10.1007/s11128-011-0301-7 doi:10.1007/s11128-011-0301-7 (ID: 717726) Toggle Abstract
  We discuss the implementation of quantum gate operations in a self-assembled dipolar crystal of polar molecules. Here qubits are encoded in long-lived spin states of the molecular ground state and stabilized against collisions by repulsive dipole-dipole interactions. To overcome the single site addressability problem in this high density crystalline phase, we describe a new approach for implementing controlled single and two-qubit operations based on resonantly enhanced spin-spin interactions mediated by a localized phonon mode. This local mode is created at a specified lattice position with the help of an additional marker molecule such that individual qubits can be manipulated by using otherwise global static and microwave fields only. We present a general strategy for generating state and time dependent dipole moments to implement a universal set of gate operations for molecular qubits and we analyze the resulting gate fidelities under realistic conditions. Our analysis demonstrates the experimental feasibility of this approach for scalable quantum computing or digital quantum simulation schemes with polar molecules.
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• M. Dalmonte, P. Zoller, G. Pupillo Trimer liquids and crystals of polar molecules in coupled wires, Phys. Rev. Lett. 107 163202 (2011-10-11), http://dx.doi.org/10.1103/PhysRevLett.107.163202 doi:10.1103/PhysRevLett.107.163202 (ID: 717651) Toggle Abstract
  We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons or fermions. We show that these exotic quantum phases should be realizable under current experimental conditions in finite-size confining potentials.
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• S. Diehl, E. Rico Ortega, M. Baranov, P. Zoller Topology by Dissipation in Atomic Quantum Wires, Nature Phys. 7 971 (2011-10-02), http://dx.doi.org/10.1038/nphys2106 doi:10.1038/nphys2106 (ID: 717686) Toggle Abstract
  Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been exclusively discussed in a Hamiltonian context, we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems with engineered dissipation. The specific system studied here is a quantum wire of spinless atomic fermions in an optical lattice coupled to a bath. The key feature of the dissipative dynamics described by a Lindblad master equation is the existence of Majorana edge modes, representing a non-local decoherence free subspace. The isolation of the edge states is enforced by a dissipative gap in the p-wave paired bulk of the wire. We describe dissipative non-Abelian braiding operations within the Majorana subspace, and we illustrate the insensitivity to imperfections. Topological protection is granted by a nontrivial winding number of the system density matrix.
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• B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, C. F. Roos Universal Digital Quantum Simulation with Trapped Ions, Science 334 57 (2011-09-01), http://dx.doi.org/10.1126/science.1208001 doi:10.1126/science.1208001 (ID: 717768) Toggle Abstract
  A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the full-time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.
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• M. Müller, K. Hammerer, Y. Zhou, C. F. Roos, P. Zoller Simulating open quantum systems: from many-body interactions to stabilizer pumping, New J. Phys. 13 085007 (2011-08-10), http://dx.doi.org/10.1088/1367-2630/13/8/085007 doi:10.1088/1367-2630/13/8/085007 (ID: 717750) Toggle Abstract
  In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions. Using up to five ions, dynamics were realized by sequences that combined single- and multi-qubit entangling gate operations with optical pumping. This enabled the implementation of both coherent many-body dynamics and dissipative processes by controlling the coupling of the system to an artificial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In this paper, we present the theoretical framework of this gate-based ('digital') simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach, minimal instances of spin models of interest in the context of topological quantum computing and condensed matter physics can be realized in state-of-the-art linear ion-trap quantum computing architectures. We outline concrete simulation schemes for Kitaev's toric code Hamiltonian and a recently suggested color code model. The presented simulation protocols can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.
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• A. J. Daley, J. Ye, P. Zoller State-dependent lattices for quantum computing with alkaline-earth-metal atoms, Eur. Phys. J. D 65 217 (2011-07-29), http://dx.doi.org/10.1140/epjd/e2011-20095-2 doi:10.1140/epjd/e2011-20095-2 (ID: 717608) Toggle Abstract
  Recent experimental progress with Alkaline-Earth atoms has opened the door to quantum computing schemes in which qubits are encoded in long-lived nuclear spin states, and the metastable electronic states of these species are used for manipulation and readout of the qubits. Here we discuss a variant of these schemes, in which gate operations are performed in nuclear-spin-dependent optical lattices, formed by near-resonant coupling to the metastable excited state. This provides an alternative to a previous scheme [A. J. Daley, M. M. Boyd, J. Ye, and P. Zoller, Phys. Rev. Lett 101, 170504 (2008)], which involved independent lattices for different electronic states. As in the previous case, we show how existing ideas for quantum computing with Alkali atoms such as entanglement via controlled collisions can be freed from important technical restrictions. We also provide additional details on the use of collisional losses from metastable states to perform gate operations via a lossy blockade mechanism.
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• L. Jiang, T. Kitagawa, J. Alicea, A. Akhmerov, D. Pekker, G. Refael, I. J. Cirac, E. Demler, M. Lukin, P. Zoller Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires, Phys. Rev. Lett. 106 220402 (2011-06-02), http://dx.doi.org/10.1103/PhysRevLett.106.220402 doi:10.1103/PhysRevLett.106.220402 (ID: 717687) Toggle Abstract
  We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition—simultaneously inducing an effective spin-orbit interaction and magnetic field—while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as “Floquet Majorana fermions” when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.
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• J. Schachenmayer, A. J. Daley, P. Zoller Atomic matter-wave revivals with definite atom number in an optical lattice, Phys. Rev. A 83 043614 (2011-04-18), http://dx.doi.org/10.1103/PhysRevA.83.043614 doi:10.1103/PhysRevA.83.043614 (ID: 717393) Toggle Abstract
  We study the collapse and revival of interference patterns in the momentum distribution of atoms in optical lattices, using a projection technique to properly account for the fixed total number of atoms in the system. We consider the common experimental situation in which weakly interacting bosons are loaded into a shallow lattice, which is suddenly made deep. The collapse and revival of peaks in the momentum distribution is then driven by interactions in a lattice with essentially no tunnelling. The projection technique allows to us to treat inhomogeneous (trapped) systems exactly in the case that non-interacting bosons are loaded into the system initially, and we use time-dependent density matrix renormalization group techniques to study the system in the case of finite tunnelling in the lattice and finite initial interactions. For systems of more than a few sites and particles, we find good agreement with results calculated via a naive approach, in which the state at each lattice site is described by a coherent state in the particle occupation number. However, for systems on the order of 10 lattice sites, we find experimentally measurable discrepancies to the results predicted by this standard approach.
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• F. Schmidt-Kaler, T. Feldker, D. Kolbe, J. Walz, M. Müller, P. Zoller, W. Li, I. Lesanovsky Rydberg excitation of trapped cold ions: A detailed case study, New J. Phys. 13 075014 (2011-04-15), http://dx.doi.org/10.1088/1367-2630/13/7/075014 doi:10.1088/1367-2630/13/7/075014 (ID: 717667) Toggle Abstract
  We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss anticipated theoretical and experimental challenges on the way towards its realization.
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• J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, R. Blatt An open-system quantum simulator with trapped ions, Nature 470 491 (2011-02-24), http://dx.doi.org/10.1038/nature09801 doi:10.1038/nature09801 (ID: 717617) Toggle Abstract
  The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating quantum systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate our ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.
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• A. Tomadin, S. Diehl, P. Zoller Nonequilibrium phase diagram of a driven and dissipative many-body system, Phys. Rev. A 83 013611 (2011-01-18), http://dx.doi.org/10.1103/PhysRevA.83.013611 doi:10.1103/PhysRevA.83.013611 (ID: 717765) Toggle Abstract
  We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long-range order. We investigate how the coherent interaction affects the properties of the steady state of the system qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long-range order. The phase diagram also exhibits an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of low particle density, we provide a precise analytical description of the time evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.
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2010

Articles

• H. Pichler, A. J. Daley, P. Zoller Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission, Phys. Rev. A 82 063605 (2010-12-06), http://dx.doi.org/10.1103/PhysRevA.82.063605 doi:10.1103/PhysRevA.82.063605 (ID: 717301) Toggle Abstract
  We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the time scale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based on both perturbation-theory calculations and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for one-dimensional systems by combining time-dependent density-matrix-renormalization-group methods with quantum trajectory techniques.
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• K. Stannigel, P. Rabl, A. Sorensen, P. Zoller, M. Lukin Optomechanical Transducers for Long-Distance Quantum Communication, Phys. Rev. Lett. 105 220501 (2010-11-23), http://dx.doi.org/10.1103/PhysRevLett.105.220501 doi:10.1103/PhysRevLett.105.220501 (ID: 717347) Toggle Abstract
  We describe a new scheme to interconvert stationary and photonic qubits which is based on indirect qubit-light interactions mediated by a mechanical resonator. This approach does not rely on the specific optical response of the qubit and thereby enables optical quantum interfaces for a wide range of solid state spin and charge based systems. We discuss the implementation of state transfer protocols between distant nodes of a quantum network and show that high transfer fidelities can be achieved under realistic experimental conditions.
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• S. Diehl, W. Yi, A. J. Daley, P. Zoller Dissipation-Induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice, Phys. Rev. Lett. 105 227001 (2010-11-22), http://dx.doi.org/10.1103/PhysRevLett.105.227001 doi:10.1103/PhysRevLett.105.227001 (ID: 717276) Toggle Abstract
  We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a \\\\\\\"parent\\\\\\\" Liouvillian operator so that a BCS-type state of a given symmetry, e.g. a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number conserving and quasi-local processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.
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• M. Dalmonte, G. Pupillo, P. Zoller One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase, Phys. Rev. Lett. 105 140401 (2010-09-28), http://dx.doi.org/10.1103/PhysRevLett.105.140401 doi:10.1103/PhysRevLett.105.140401 (ID: 717312) Toggle Abstract
  We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|β, with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a “Luttinger staircase.” Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.
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• F. Cinti, P. Jain, M. Boninsegni, A. Micheli, P. Zoller, G. Pupillo Supersolid Droplet Crystal in a Dipole-Blockaded Gas, Phys. Rev. Lett. 105 135301 (2010-09-21), http://dx.doi.org/10.1103/PhysRevLett.105.135301 doi:10.1103/PhysRevLett.105.135301 (ID: 717214) Toggle Abstract
  A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential \"softened\" at short distances. Using exact numerical techniques, we study the low temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighbouring droplets.
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• K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch Optical Lattices with Micromechanical Mirrors, Phys. Rev. A 82 021803(R) (2010-08-25), http://dx.doi.org/10.1103/PhysRevA.82.021803 doi:10.1103/PhysRevA.82.021803 (ID: 717187) Toggle Abstract
  We investigate a setup where a cloud of atoms is trapped in an optical lattice potential of a standing-wave laser field which is created by retroreflection on a micromembrane. The membrane vibrations itself realize a quantum mechanical degree of freedom. We show that the center-of-mass mode of atoms can be coupled to the vibrational mode of the membrane in free space. Via laser cooling of atoms a significant sympathetic cooling effect on the membrane vibrations can be achieved. Switching off laser cooling brings the system close to a regime of strong coherent coupling. This setup provides a controllable segregation between the cooling and coherent dynamics regimes, and allows one to keep the membrane in a cryogenic environment and atoms at a distance in a vacuum chamber.
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• S. Diehl, M. Baranov, A. J. Daley, P. Zoller Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments, Phys. Rev. B 82 064509 (2010-08-13), http://dx.doi.org/10.1103/PhysRevB.82.064509 doi:10.1103/PhysRevB.82.064509 (ID: 716839) Toggle Abstract
  We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a ``constraint principle'' operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low lying excitations are holes and di-holes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work [13].
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• S. Diehl, M. Baranov, A. J. Daley, P. Zoller Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part II: Application to the Many-Body Problem, Phys. Rev. B 82 064510 (2010-08-13), http://dx.doi.org/10.1103/PhysRevB.82.064510 doi:10.1103/PhysRevB.82.064510 (ID: 716840) Toggle Abstract
  We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [11]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean field plus spin wave approach. First, we determine shifts in the mean field phase border, which are most pronounced in the low density regime. Second, the investigation of the strong coupling limit reveals the existence of a new collective mode, which emerges as a consequence of enhanced symmetries in this regime. Third, we show that the Ising type phase transition, driven first order via the competition of long wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
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• A. Micheli, Z. Idziaszek, G. Pupillo, M. Baranov, P. Zoller, P. S. Julienne Universal rates for reactive ultracold polar molecules in reduced dimensions, Phys. Rev. Lett. 105 073202 (2010-08-13), http://dx.doi.org/10.1103/PhysRevLett.105.073202 doi:10.1103/PhysRevLett.105.073202 (ID: 717207) Toggle Abstract
  Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.
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• Z. Idziaszek, T. Calarco, P. Zoller Ion-assisted ground-state cooling of a trapped polar molecule, Phys. Rev. A 83 053413 (2010-08-11), http://dx.doi.org/10.1103/PhysRevA.83.053413 doi:10.1103/PhysRevA.83.053413 (ID: 717300) Toggle Abstract
  We propose and analyze a scheme for sympathetic cooling of the translational motion of polar molecules in an optical lattice, interacting one by one with laser-cooled ions in a radio-frequency trap. The energy gap between the excitation spectra of the particles in their respective trapping potentials is bridged by means of a parametric resonance, provided by the additional modulation of the RF field. We analyze two scenarios: simultaneous laser cooling and energy exchange between the ion and the molecule, and a scheme when these two processes take place separately. We calculate the lowest final energy of the molecule and the cooling rate depending on the amplitude of the parametric modulation. For small parametric modulation, the dynamics can be solved analytically within the rotating wave approximation.
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• S. Diehl, A. Tomadin, A. Micheli, R. Fazio, P. Zoller Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems, Phys. Rev. Lett. 105 015702 (2010-07-01), http://dx.doi.org/10.1103/PhysRevLett.105.015702 doi:10.1103/PhysRevLett.105.015702 (ID: 717159) Toggle Abstract
  We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. Within a generalized Gutzwiller approach which includes the description of mixed state density matrices, we characterize the complete phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.
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• G. Pupillo, A. Micheli, M. Boninsegni, I. Lesanovsky, P. Zoller Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics, Phys. Rev. Lett. 104 223002 (2010-06-01), http://dx.doi.org/10.1103/PhysRevLett.104.223002 doi:10.1103/PhysRevLett.104.223002 (ID: 716985) Toggle Abstract
  We discuss techniques to generate long-range interactions in a gas of ground state alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover.
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• P. Rabl, S. J. Kolkowitz, F. H. Koppens, J. Harris, P. Zoller, M. Lukin A quantum spin transducer based on nanoelectromechanical resonator arrays, Nature Phys. 608 (2010-05-30), http://dx.doi.org/10.1038/nphys1679 doi:10.1038/nphys1679 (ID: 702633) Toggle Abstract
  Isolated electronic and nuclear spins in solids are at present being actively explored for potential quantum-computing applications. Spin degrees of freedom provide an excellent quantum memory, owing to their weak magnetic interactions with the environment. For the same reason, however, it is difficult to achieve controlled interactions of spins over distances larger than tens of nanometres. Here we propose a new realization of a quantum data bus for spin qubits where spins are coupled to the motion of magnetized mechanical resonators through magnetic-field gradients. Provided that the mechanical system is charged, the magnetic moments associated with spin qubits can be effectively amplified to enable a coherent spin–spin coupling over long distances through Coulomb forces. Our approach is applicable to a wide class of electronic spin qubits, which can be localized near magnetized tips and can be used for the implementation of hybrid quantum-computing architectures.
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• B. Zhao, K. Hammerer, M. Müller, P. Zoller Efficient quantum repeater based on deterministic Rydberg gates, Phys. Rev. A 81 052329 (2010-05-21), http://dx.doi.org/10.1103/PhysRevA.81.052329 doi:10.1103/PhysRevA.81.052329 (ID: 717186) Toggle Abstract
  We propose an efficient quantum repeater architecture with mesoscopic atomic ensembles, where the Rydberg blockade is employed for deterministic local entanglement generation, entanglement swapping, and entanglement purification. Compared to a conventional atomic-ensemble-based quantum repeater, the entanglement distribution rate is improved by up to two orders of magnitude with the help of the deterministic Rydberg gate. This quantum repeater scheme is robust and fast, and thus opens up a way for practical long-distance quantum communication.
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• A. Kantian, A. J. Daley, P. Zoller An eta-condensate of fermionic atom pairs via adiabatic state preparation, Phys. Rev. Lett. 104 (2010-05-19), http://dx.doi.org/10.1103/PhysRevLett.104.240406 doi:10.1103/PhysRevLett.104.240406 (ID: 716970) Toggle Abstract
  We discuss how an $\\eta$-condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalisation group methods, we analyse a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
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• S. Diehl, M. Baranov, A. J. Daley, P. Zoller Observability of Quantum Criticality and a Continuous Supersolid in Atomic Gases, Phys. Rev. Lett. 104 165301 (2010-04-20), http://dx.doi.org/10.1103/PhysRevLett.104.165301 doi:10.1103/PhysRevLett.104.165301 (ID: 716766) Toggle Abstract
  We analyze the Bose-Hubbard model with three-body onsite hardcore constraint, which stabilizes the system for an attractive interparticle interaction and allows, in particular, the formation of a superfluid phase of bosonic dimers. Our approach is based on an exact mapping of the constrained Hamiltonian to a theory of two coupled bosonic degrees of freedom. We demonstrate that the phase transition between atomic and dimer superfluidity is generically of the first order as a result of the Coleman-Weinberg phenomenon, while at unit filling we identify an Ising quantum critical point. At this filling, furthermore, a symmetry enhancement in the strong coupling limit leads to a continuous supersolid phase for deeply bound dimers, observable in experiments.
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• A. Glätzle, K. Hammerer, A. J. Daley, R. Blatt, P. Zoller A single trapped atom in front of an oscillating mirror, Opt. Com. 283 765 (2010-03-15), http://dx.doi.org/10.1016/j.optcom.2009.10.063 doi:10.1016/j.optcom.2009.10.063 (ID: 717009) Toggle Abstract
  We investigate the Wigner–Weisskopf decay of a two-level atom in front of an oscillating mirror. This work builds on and extends previous theoretical and experimental studies of the effects of a static mirror on spontaneous decay and resonance fluorescence. The spontaneously emitted field is inherently non-stationary due to the time-dependent boundary conditions and in order to study its spectral distribution we employ the operational definition of the spectrum of non-stationary light due to the seminal work by Eberly and Wódkiewicz. We find a rich dependence of this spectrum as well as of the effective decay rates and level shifts on the mirror–atom distance and on the amplitude and frequency of the mirror’s oscillations. The results presented here provide the basis for future studies of more complex setups, where the motion of the atom and/or the mirror are included as quantum degrees of freedom.
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• H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, H. Büchler A Rydberg Quantum Simulator, Nature Phys. 6 388 (2010-03-14), http://dx.doi.org/10.1038/nphys1614 doi:10.1038/nphys1614 (ID: 695077) Toggle Abstract
  Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (QS) is a controlled quantum device which reproduces the dynamics of any other many particle quantum system with short range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. We investigate how laser excited Rydberg atoms in large spacing optical or magnetic lattices can provide an efficient implementation of a universal QS for spin models involving (high order) n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such as the Kitaev toric code, color code, and lattice gauge theories with spin liquid phases. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates.
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• A. V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P. S. Julienne, J. Ye, P. Zoller, E. Demler, M. Lukin, A. M. Rey Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms, Nature Phys. 6 295 (2010-02-28), http://dx.doi.org/10.1038/nphys1535 doi:10.1038/nphys1535 (ID: 681277) Toggle Abstract
  Fermionic alkaline-earth atoms have unique properties that make them attractive candidates for the realization of atomic clocks and degenerate quantum gases. At the same time, they are attracting considerable theoretical attention in the context of quantum information processing. Here we demonstrate that when such atoms are loaded in optical lattices, they can be used as quantum simulators of unique many-body phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement many-body systems with an unprecedented degree of symmetry, characterized by the SU(N) group with N as large as 10. Moreover, the interplay of the nuclear spin with the electronic degree of freedom provided by a stable optically excited state should enable the study of physics governed by the spin–orbital interaction. Such systems may provide valuable insights into the physics of strongly correlated transition-metal oxides, heavy-fermion materials and spin-liquid phases.
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• M. Baranov, A. Micheli, S. Ronen, P. Zoller Bilayer superfluidity of fermionic polar molecules: many body effects, Phys. Rev. A 83 043602 (2010-02-24), http://dx.doi.org/10.1103/PhysRevA.83.043602 doi:10.1103/PhysRevA.83.043602 (ID: 717481) Toggle Abstract
  We study the BCS superfluid transition in a single-component fermionic gas of dipolar particles loaded in a tight bilayer trap, with the electric dipole moments polarized perpendicular to the layers. Based on the detailed analysis of the interlayer scattering, we calculate the critical temperature of the interlayer superfluid pairing transition when the layer separation is both smaller (dilute regime) and of the order or larger (dense regime) than the mean interparticle separation in each layer. Our calculations go beyond the standard BCS approach and include the many-body contributions resulting in the mass renormalization, as well as additional contributions to the pairing interaction. We find that the many-body effects have a pronounced effect on the critical temperature, and can either decrease (in the very dilute limit) or increase (in the dense and moderately dilute limits) the transition temperature as compared to the BCS approach.
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• B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo Quantum Phases of Cold Polar Molecules in 2D Optical Lattices, Phys. Rev. Lett. 104 125301 (2010-02-23), http://dx.doi.org/10.1103/PhysRevLett.104.125301 doi:10.1103/PhysRevLett.104.125301 (ID: 686428) Toggle Abstract
  We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil’s staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.
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• M. Wallquist, K. Hammerer, P. Zoller, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, H. Kimble Single-atom cavity QED and optomicromechanics, Phys. Rev. A 81 023816 (2010-02-18), http://dx.doi.org/10.1103/PhysRevA.81.023816 doi:10.1103/PhysRevA.81.023816 (ID: 716968) Toggle Abstract
  In a recent publication [K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, Phys. Rev. Lett. 103, 063005 (2009)] we have shown the possibility to achieve strong coupling of the quantized motion of a micron-sized mechanical system to the motion of a single trapped atom. In the proposed setup the coherent coupling between a SiN membrane and a single atom is mediated by the field of a high finesse cavity and can be much larger than the relevant decoherence rates. This makes the well-developed tools of cavity quantum electrodynamics with single atoms available in the realm of cavity optomechanics. In this article we elaborate on this scheme and provide detailed derivations and technical comments. Moreover, we give numerical as well as analytical results for a number of possible applications for transfer of squeezed or Fock states from atom to membrane as well as entanglement generation, taking full account of dissipation. In the limit of strong-coupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.
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2009

Articles

• P. Zoller, M. Wallquist, K. Hammerer, P. Rabl, M. Lukin Hybrid quantum devices and quantum engineering, Physica Scripta 014001 (2009-12-14), http://dx.doi.org/10.1088/0031-8949/2009/T137/014001 doi:10.1088/0031-8949/2009/T137/014001 (ID: 716806) Toggle Abstract
  We discuss prospects of building hybrid quantum devices involving elements of atomic and molecular physics, quantum optics and solid-state elements with the attempt to combine advantages of the respective systems in compatible experimental setups. In particular, we summarize our recent work on quantum hybrid devices and briefly discuss recent ideas for quantum networks. These include interfacing of molecular quantum memory with circuit QED, and using nanomechanical elements strongly coupled to qubits represented by electronic spins, as well as single atoms or atomic ensembles.
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• A. Kantian, M. Dalmonte, S. Diehl, W. Hofstetter, P. Zoller, A. J. Daley Atomic Color Superfluid via Three-Body Loss, Phys. Rev. Lett. 103 240401 (2009-12-09), http://dx.doi.org/10.1103/PhysRevLett.103.240401 doi:10.1103/PhysRevLett.103.240401 (ID: 707092) Toggle Abstract
  Large three-body loss rates in a three-component Fermi gas confined in an optical lattice can dynamically prevent atoms from tunneling so as to occupy a lattice site with three atoms. This effective constraint not only suppresses the occurrence of actual loss events, but stabilizes BCS-pairing phases by suppressing the formation of trions. We study the effect of the constraint on the many-body physics using bosonization and density matrix renormalization group techniques, and also investigate the full dissipative dynamics including loss for the example of 6Li.
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• D. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. Kimble, P. Zoller Cavity opto-mechanics using an optically levitated nanosphere, Proc. Natl. Acad. U.S.A. 107 1010 (2009-11-10), http://dx.doi.org/10.1073/pnas.0912969107 doi:10.1073/pnas.0912969107 (ID: 719878)
• D. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, P. Zoller Cavity optomechanics using an optically levitated nanosphere, Proc. Natl. Acad. U.S.A. 107 1010 (2009-10-17), URL (ID: 708587) Toggle Abstract
  Recently, remarkable advances have been made in coupling a number of high-Q modes of nano-mechanical systems to high-finesse optical cavities, with the goal of reaching regimes in which quantum behavior can be observed and leveraged toward new applications. To reach this regime, the coupling between these systems and their thermal environments must be minimized. Here we propose a novel approach to this problem, in which optically levitating a nano-mechanical system can greatly reduce its thermal contact, while simultaneously eliminating dissipation arising from clamping. Through the long coherence times allowed, this approach potentially opens the door to ground-state cooling and coherent manipulation of a single mesoscopic mechanical system or entanglement generation between spatially separate systems, even in room-temperature environments. As an example, we show that these goals should be achievable when the mechanical mode consists of the center-of-mass motion of a levitated nanosphere.
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• D. Chang, J. D. Thompson, H. Park, V. Vuletic, P. Zoller, A. Zibrov, M. Lukin Trapping and manipulation of isolated atoms using nanoscale plasmonic structures, Phys. Rev. Lett. 103 123004 (2009-09-18), http://dx.doi.org/10.1103/PhysRevLett.103.123004 doi:10.1103/PhysRevLett.103.123004 (ID: 686216) Toggle Abstract
  We propose and analyze a scheme to interface individual neutral atoms with nanoscale solid-state systems. The interface is enabled by optically trapping the atom via the strong near-field generated by a sharp metallic nanotip. We show that under realistic conditions, a neutral atom can be trapped with position uncertainties of just a few nanometers, and within tens of nanometers of other surfaces. Simultaneously, the guided surface plasmon modes of the nanotip allow the atom to be optically manipulated, or for fluorescence photons to be collected, with very high efficiency. Finally, we analyze the surface forces, heating and decoherence rates acting on the trapped atom.
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• Y. Han, Y. Chan, W. Yi, A. J. Daley, S. Diehl, P. Zoller, L. Duan Stabilization of the p-wave superfluid state in an optical lattice, Phys. Rev. Lett. 103 070404 (2009-08-14), http://dx.doi.org/10.1103/PhysRevLett.103.070404 doi:10.1103/PhysRevLett.103.070404 (ID: 707070) Toggle Abstract
  It is hard to stabilize the p-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the p-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable p-wave superfluid state where the multiatom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the p-wave superfluid state and different types of insulator states induced either by interaction or by dissipation.
• K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, H. J. Kimble Strong coupling of a mechanical oscillator and a single atom, Phys. Rev. Lett. 103 063005 (2009-08-06), http://dx.doi.org/10.1103/PhysRevLett.103.063005 doi:10.1103/PhysRevLett.103.063005 (ID: 680115) Toggle Abstract
  We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven high-finesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox for coherent manipulation, preparation and measurement of micro- and nanomechanical oscillators via the tools of atomic physics.
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• K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. Polzik, P. Zoller Cavity-assisted squeezing of a mechanical oscillator, Phys. Rev. A 79 063819 (2009-06-11), http://dx.doi.org/10.1103/PhysRevA.79.063819 doi:10.1103/PhysRevA.79.063819 (ID: 679748) Toggle Abstract
  We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane/mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions of ground state cooling, we predict mechanical squashing to be observable in current systems.
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• M. Ortner, A. Micheli, G. Pupillo, P. Zoller Quantum Simulations of Extended Hubbard Models with Dipolar Crystals, New J. Phys. 11 055045 (2009-05-14), http://dx.doi.org/10.1088/1367-2630/11/5/055045 doi:10.1088/1367-2630/11/5/055045 (ID: 665436) Toggle Abstract
  In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.
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• M. Müller, I. Lesanovsky, H. Weimer, H. Büchler, P. Zoller Mesoscopic Rydberg Gate based on Electromagnetically Induced Transparency, Phys. Rev. Lett. 102 170502 (2009-04-28), http://dx.doi.org/10.1103/PhysRevLett.102.170502 doi:10.1103/PhysRevLett.102.170502 (ID: 628410) Toggle Abstract
  We demonstrate theoretically a parallelized C-NOT gate which allows to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond timescale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering Electromagnetically Induced Transparency (EIT). By this we can robustly implement a conditional transfer of all ensemble atoms among two logical states, depending on the state of the control atom. We outline a many body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.
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• C. Schwenke, T. Calarco, P. Zoller, C. Koch Collective Rydberg excitations of an atomic gas confined in a ring lattice, Phys. Rev. A 79 043419 (2009-04-24), http://dx.doi.org/10.1103/PhysRevA.79.043419 doi:10.1103/PhysRevA.79.043419 (ID: 650348) Toggle Abstract
  We study the excitation dynamics of Rydberg atoms in a one-dimensional lattice with periodic boundary conditions where the atomic Rydberg states are resonantly excited from the electronic ground state. Our description of the corresponding dynamics is numerically exact within the perfect blockade regime, i.e. no two atoms in a given range can be excited. The time-evolution of the mean Rydberg density, density-density correlations as well as entanglement properties are analyzed in detail. We demonstrate that the short time dynamics is universal and dominated by quantum phenomena, while for larger time the characteristics of the lattice become important and the classical features determine the dynamics. The results of the perfect blockade approach are compared to the predictions of an effective Hamiltonian which includes the interaction of two neighboring Rydberg atoms up to second order perturbation theory.
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• A. V. Gorshkov, A. M. Rey, A. J. Daley, M. M. Boyd, J. Ye, P. Zoller, M. Lukin Alkaline-Earth Atoms as Few-Qubit Quantum Registers, Phys. Rev. Lett. 102 110503 (2009-03-18), http://dx.doi.org/10.1103/PhysRevLett.102.110503 doi:10.1103/PhysRevLett.102.110503 (ID: 644448) Toggle Abstract
  We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth-metal atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with subwavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed.
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• S. Montangero, R. Fazio, P. Zoller, G. Pupillo Dipole oscillations of confined lattice bosons in one dimension, Phys. Rev. A 79 041602(R) (2009-03-10), http://dx.doi.org/10.1103/PhysRevA.79.041602 doi:10.1103/PhysRevA.79.041602 (ID: 620456) Toggle Abstract
  We study the dynamics of a non-integrable system comprising interacting cold bosons trapped in an optical lattice in one-dimension by means of exact time-dependent numerical DMRG techniques. Particles are confined by a parabolic potential, and dipole oscillations are induced by displacing the trap center of a few lattice sites. Depending on the system parameters this motion can vary from undamped to overdamped. We study the dipole oscillations as a function of the lattice displacement, the particle density and the strength of interparticle interactions. These results explain the recent experiment C.D. Fertig et al., Phys. Rev. Lett. 94, 120403 (2005).
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• A. J. Daley, J. Taylor, S. Diehl, M. Baranov, P. Zoller Atomic three-body loss as a dynamical three-body interaction, Phys. Rev. Lett. 102 040402 (2009-01-30), http://dx.doi.org/10.1103/PhysRevLett.102.040402 doi:10.1103/PhysRevLett.102.040402 (ID: 627388) Toggle Abstract
  We discuss how large three-body loss of atoms in an optical lattice can give rise to effective hard-core three-body interactions. For bosons, in addition to the usual atomic superfluid, a dimer superfluid can then be observed for attractive two-body interactions. The non-equilibrium dynamics of preparation and stability of these phases are studied in 1D by combining time-dependent Density Matrix Renormalisation Group techniques with a quantum trajectories method.
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• I. Lesanovsky, M. Müller, P. Zoller Trap assisted creation of giant molecules and Rydberg-mediated coherent charge transfer in a Penning trap, Phys. Rev. A 79 010701(R) (2009-01-14), http://dx.doi.org/10.1103/PhysRevA.79.010701 doi:10.1103/PhysRevA.79.010701 (ID: 620459) Toggle Abstract
  We study two ions confined in a Penning trap. We show that electronically highly excited states exist in which an electron is delocalized among the two ions forming a giant molecule of several micrometer size. At energies close to the top of the Coulomb barrier these molecular states can be regarded as superpositions of Rydberg states of individual ions. We illuminate the possibility to observe coherent charge transfer between the ions. Beyond a critical principal quantum number the electron can coherently tunnel through the Coulomb barrier to an adjacent doubly charged ion. The tunneling occurs on timescales on which the dynamics of the nuclei can be considered frozen and radiative decay can be neglected.
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• K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller Establishing Einstein-Poldosky-Rosen Channels between Nanomechanics and Atomic Ensembles, Phys. Rev. Lett. 102 020501 (2009-01-12), http://dx.doi.org/10.1103/PhysRevLett.102.020501 doi:10.1103/PhysRevLett.102.020501 (ID: 637866) Toggle Abstract
  We suggest interfacing nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation, and measurement are available. This allows, in particular, for a quantum nondemolition Bell measurement, projecting the coupled system, atomic-ensemble–nanomechanical resonator, into an entangled EPR state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.
• B. Capogrosso-Sansone, S. Wessel, H. Büchler, P. Zoller, G. Pupillo Phase diagram of one-dimensional hard-core bosons with three-body interactions, Phys. Rev. B 79 020503 (R) (2009-01-09), http://dx.doi.org/10.1103/PhysRevB.79.020503 doi:10.1103/PhysRevB.79.020503 (ID: 603828) Toggle Abstract
  We determine the phase diagram of a one-dimensional system of hard-core lattice bosons interacting via repulsive three-body interactions by analytic methods and extensive quantum Monte Carlo simulations. Such three-body interactions can be derived from a microscopic theory for polar molecules trapped in an optical lattice. Depending on the strength of the interactions and the particle density, we find superfluid and solid phases, the latter appearing at an unconventional filling of the lattice and displaying a coexistence of charge-density wave and bond orders
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2008

Articles

• A. J. Daley, M. M. Boyd, J. Ye, P. Zoller Quantum Computing with Alkaline-Earth-Metal Atoms, Phys. Rev. Lett. 101 170504 (2008-10-23), http://dx.doi.org/10.1103/PhysRevLett.101.170504 doi:10.1103/PhysRevLett.101.170504 (ID: 606889) Toggle Abstract
  We present a complete scheme for quantum information processing using the unique features of alkaline earth atoms. We show how two completely independent lattices can be formed for the $^1$S$_0$ and $^3$P$_0$ states, with one used as a storage lattice for qubits encoded on the nuclear spin, and the other as a transport lattice to move qubits and perform gate operations. We discuss how the $^3$P$_2$ level can be used for addressing of individual qubits, and how collisional losses from metastable states can be used to perform gates via a lossy blockade mechanism.
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• M. Müller, L. Liang, I. Lesanovsky, P. Zoller Trapped Rydberg Ions: From Spin Chains to Fast Quantum Gates, New J. Phys. 10 093009 (2008-09-10), http://dx.doi.org/10.1088/1367-2630/10/9/093009 doi:10.1088/1367-2630/10/9/093009 (ID: 520204) Toggle Abstract
  We study the quantum dynamics of trapped ions in Rydberg states, which have large electric dipole moments induced by the trapping fields. In the limit where the localization of the ion core is much smaller than the Rydberg orbit the dynamics of the system is determined by the interplay between large dipole-dipole energy shifts and strong tunable internal-state-dependent forces due to dipole-charge interactions. This provides a new tool for manipulating and entangling ions by strong interactions and on fast time scales.
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• S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. Büchler, P. Zoller Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms, Nature Phys. 4 883 (2008-09-07), http://dx.doi.org/10.1038/nphys1073 doi:10.1038/nphys1073 (ID: 576233) Toggle Abstract
  An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a \emph{driven dissipative Bose Einstein Condensate} of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing \emph{local dissipation}. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a Kosterlitz-Thouless critical phase at finite temperature, with the role of the ``finite temperature'' played by the interactions.
• A. V. Gorshkov, P. Rabl, G. Pupillo, A. Micheli, P. Zoller, M. Lukin, H. Büchler Suppression of Inelastic Collisions Between Polar Molecules With a Repulsive Shield, Phys. Rev. Lett. 101 073201 (2008-08-14), http://dx.doi.org/10.1103/PhysRevLett.101.073201 doi:10.1103/PhysRevLett.101.073201 (ID: 582039) Toggle Abstract
  We propose and analyze a technique that allows to suppress inelastic collisions and simultaneously enhance elastic interactions between cold polar molecules. The main idea is to cancel the leading dipole-dipole interaction with a suitable combination of static electric and microwave fields in such a way that the remaining van-der-Waals-type potential forms a three-dimensional repulsive shield. We analyze the elastic and inelastic scattering cross sections relevant for evaporative cooling of polar molecules and discuss the prospect for the creation of crystalline structures
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• S. Morrison, A. Kantian, A. J. Daley, H. Katzgraber, M. Lewenstein, H. Büchler, P. Zoller Physical replicas and the Bose-glass in cold atomic gases, New J. Phys. 10 073032 (2008-07-16), http://dx.doi.org/10.1088/1367-2630/10/7/073032 doi:10.1088/1367-2630/10/7/073032 (ID: 582497) Toggle Abstract
  We study cold atomic gases in a disorder potential and analyse the correlations between different systems subjected to the same disorder landscape. Such independent copies with the same disorder landscape are known as replicas. While, in general, these are not accessible experimentally in condensed matter systems, they can be realized using standard tools for controlling cold atomic gases in an optical lattice. Of special interest is the overlap function which represents a natural order parameter for disordered systems and is a correlation function between the atoms of two independent replicas with the same disorder. We demonstrate an efficient measurement scheme for the determination of this disorder-induced correlation function. As an application, we focus on the disordered Bose–Hubbard model and determine the overlap function within the perturbation theory and a numerical analysis. We find that the measurement of the overlap function allows for the identification of the Bose-glass phase in certain parameter regimes.
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• W. Yi, A. J. Daley, G. Pupillo, P. Zoller State-dependent, addressable subwavelength lattices with cold atoms, New J. Phys. 10 073015 (2008-07-08), http://dx.doi.org/10.1088/1367-2630/10/7/073015 doi:10.1088/1367-2630/10/7/073015 (ID: 582500) Toggle Abstract
  We discuss how adiabatic potentials can be used to create addressable lattices on a subwavelength scale, which can be used as a tool for local operations and readout within a lattice substructure, while taking advantage of the faster timescales and higher energy and temperature scales determined by the shorter lattice spacing. For alkaline-earth-like atoms with non-zero nuclear spin, these potentials can be made state dependent, for which we give specific examples with $^{171}$Yb atoms. We discuss in detail the limitations in generating the lattice potentials, in particular non-adiabatic losses, and show that the loss rates can always be made exponentially small by increasing the laser power.
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• M. Wallquist, P. Rabl, M. Lukin, P. Zoller Theory of cavity-assisted microwave cooling of polar molecules, New J. Phys. 10 063005 (2008-06-04), http://dx.doi.org/10.1088/1367-2630/10/6/063005 doi:10.1088/1367-2630/10/6/063005 (ID: 567588) Toggle Abstract
  We analyze cavity-assisted cooling schemes for polar molecules in the microwave domain, where molecules are excited on a rotational transition and energy is dissipated via strong interactions with a lossy stripline cavity, as recently proposed by André et al 2006 Nat. Phys. 2 636. We identify the dominant cooling and heating mechanisms in this setup and study cooling rates and final temperatures in various parameter regimes. In particular, we analyze the effects of a finite environment temperature on the cooling efficiency, and find minimal temperature and optimized cooling rate in the strong drive regime. Further, we discuss the trade-off between efficiency of cavity cooling and robustness with respect to ubiquitous imperfections in a realistic experimental setup, such as anharmonicity of the trapping potential.
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• B. Kraus, H. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller Preparation of Entangled States by Quantum Markov Processes, Phys. Rev. A 78 042307 (2008-05-02), http://dx.doi.org/10.1103/PhysRevA.78.042307 doi:10.1103/PhysRevA.78.042307 (ID: 576234) Toggle Abstract
  We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is the unique stationary state and solve the corresponding master equation analytically. For certain states, such as the cluster states, we use this process to show that the jump operators can be chosen quasilocally, i.e. they act nontrivially only on a few, neighboring qubits. Furthermore, the relaxation time of this dissipative process is independent of the number of subsystems. We demonstrate the general formalism by considering arbitrary matrix-product states or projected entangled pair states. In particular, we show that the ground state of the Affleck-Kennedy-Lieb-Tasaki model can be prepared employing a quasi-local dissipative process.
• L. Jiang, G. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. Lukin, P. Zoller Anyonic interferometry and protected memories in atomic spin lattices, Nature Phys. 4 482 (2008-04-20), http://dx.doi.org/10.1038/nphys943 doi:10.1038/nphys943 (ID: 538104) Toggle Abstract
  Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.
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• A. J. Daley, P. Zoller, B. Trauzettel Andreev-like reflections with cold atoms, Phys. Rev. Lett. 100 110404 (2008-03-20), http://dx.doi.org/10.1103/PhysRevLett.100.110404 doi:10.1103/PhysRevLett.100.110404 (ID: 530306) Toggle Abstract
  We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time-dependently using cold atoms in a 1D optical lattice. Using time-dependent Density Matrix Renormalisation Group methods we analyse the wavepacket dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.
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• A. V. Gorshkov, L. Jiang, M. Greiner, P. Zoller, M. Lukin Coherent Quantum Optical Control with Subwavelength Resolution, Phys. Rev. Lett. 100 093005 (2008-03-07), http://dx.doi.org/10.1103/PhysRevLett.100.093005 doi:10.1103/PhysRevLett.100.093005 (ID: 519563) Toggle Abstract
  We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed.
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• G. Pupillo, A. Griessner, A. Micheli, M. Ortner, Wang, Daw-Wei, P. Zoller Cold Atoms and Molecules in Self-Assembled Dipolar Lattices, Phys. Rev. Lett. 100 050402 (2008-02-05), http://dx.doi.org/10.1103/PhysRevLett.100.050402 doi:10.1103/PhysRevLett.100.050402 (ID: 519056) Toggle Abstract
  We study the realization of lattice models, where cold atoms and molecules move as extra particles in a dipolar crystal of trapped polar molecules. The crystal is a self-assembled floating mesoscopic lattice structure with quantum dynamics given by phonons. We show that within an experimentally accessible parameter regime extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of dressed particles.
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• T. Calarco, P. Grangier, A. Wallraff, P. Zoller Quantum leaps in small steps, Nature Phys. 4 3 (2008-01-01), http://dx.doi.org/10.1038/nphys818 doi:10.1038/nphys818 (ID: 602500) (local copy)

Proceeding

• R. Blatt, J. F. Poyatos, J. I. Cirac, P. Zoller "Quantum motion of a trapped ion: Schrödinger cats, ion interferometry and quantum tomography" in Proceedings of the 5th Symposium on Frequency Standards and Metrology, 20 (2008-10-11), (ID: 628467)

2007

Articles

• A. Kantian, A. J. Daley, P. Törmä, P. Zoller Atomic lattice excitons: from condensates to crystals, New J. Phys. 9 407 (2007-11-13), http://dx.doi.org/10.1088/1367-2630/9/11/407 doi:10.1088/1367-2630/9/11/407 (ID: 514263) Toggle Abstract
  We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean setup to study fundamental properties of excitons, ranging from condensation to exciton crystals (which appear for a large effective mass ratio between particles and holes). Using both mean-field treatments and 1D numerical computation, we discuss the properities of ALEs under varying conditions, and discuss in particular their preparation and measurement.
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• P. Rabl, P. Zoller Molecular Dipolar Crystals as High Fidelity Quantum Memory for Hybrid Quantum Computing, Phys. Rev. A 76 042308 (2007-10-04), http://dx.doi.org/10.1103/PhysRevA.76.042308 doi:10.1103/PhysRevA.76.042308 (ID: 494007) Toggle Abstract
  We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high fidelity quantum memory. While dipolar crystals are formed in the high density limit of cold clouds of polar molecules under 1D and 2D trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the life time of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a 1D dipolar chain.
• A. Micheli, G. Pupillo, H. Büchler, P. Zoller Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases, Phys. Rev. A 76 043604 (2007-10-03), http://dx.doi.org/10.1103/PhysRevA.76.043604 doi:10.1103/PhysRevA.76.043604 (ID: 460560) Toggle Abstract
  We discuss techniques to engineer effective long-range interactions between polar molecules using external static electric and microwave fields. We consider a setup where molecules are trapped in a two-dimensional pancake geometry by a far-off-resonance optical trap, which ensures the stability of the dipolar collisions. We detail how to modify the shape and the strength of the long-range part of interaction potentials, which can be utilized to realize interesting quantum phases in the context of cold molecular gases.
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• Z. Idziaszek, T. Calarco, P. Zoller Controlled collisions of a single atom and ion guided by movable trapping potentials, Phys. Rev. A 76 033409 (2007-09-19), http://dx.doi.org/10.1103/PhysRevA.76.033409 doi:10.1103/PhysRevA.76.033409 (ID: 470101) Toggle Abstract
  We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an r^{-4} dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the s-wave scattering length. When the separation between traps is changed we observe trap-induced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasi-one-dimensional geometries, when the scattering exhibit confinement-induced resonances, similar to the ones studied before for short-range interactions. For quasi-one-dimensional systems we investigate the effects of coupling between the center of mass and relative motion, which occurs for different trapping frequencies of atom and ion traps. Finally, we show how the two types of resonances can be employed for quantum state control and spectroscopy of atom-ion molecules.
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• H. Büchler, A. Micheli, P. Zoller Three-body interactions with cold polar molecules, Nature Phys. 3 731 (2007-07-22), http://dx.doi.org/10.1038/nphys678 doi:10.1038/nphys678 (ID: 462909) Toggle Abstract
  We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.
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• G. Brennen, A. Micheli, P. Zoller Designing spin-1 lattice models using polar molecules, New J. Phys. 9 138 (2007-05-18), http://dx.doi.org/10.1088/1367-2630/9/5/138 doi:10.1088/1367-2630/9/5/138 (ID: 430363) Toggle Abstract
  We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipole-dipole coupled excited states. Using multiple fields anistropic models in one, two, or three dimensions, can be built with tunable spatial range. An illustrative example in one dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases.
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• H. Büchler, E. Demler, M. Lukin, A. Micheli, N. Prokofev, G. Pupillo, P. Zoller Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential, Phys. Rev. Lett. 98 060404 (2007-02-08), http://dx.doi.org/10.1103/PhysRevLett.98.060404 doi:10.1103/PhysRevLett.98.060404 (ID: 376275) Toggle Abstract
  We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of bosonic polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low-dimensional trapping geometries. As an illustration, we discuss the 2D superfluid-crystal quantum phase transition for polar molecules interacting via an electric-field-induced dipole-dipole potential.
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• S. Tewari, S. D. Sarma, C. Nayak, C. Zhang, P. Zoller Quantum Computation using Vortices and Majorana Zero Modes of a px+ipy Superfluid of Fermionic Cold Atoms, Phys. Rev. Lett. 98 010506 (2007-01-05), http://dx.doi.org/10.1103/PhysRevLett.98.010506 doi:10.1103/PhysRevLett.98.010506 (ID: 436036) Toggle Abstract
  We propose to use the recently predicted two-dimensional “weak-pairing” px+ipy superfluid state of fermionic cold atoms as a platform for topological quantum computation. In the core of a vortex, this state supports a zero-energy Majorana mode, which moves to finite energy in the corresponding topologically trivial “strong-pairing” state. By braiding vortices in the “weak-pairing” state, unitary quantum gates can be applied to the Hilbert space of Majorana zero modes. For readout of the topological qubits, we propose realistic schemes suitable for atomic superfluids.
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• A. Griessner, A. J. Daley, S. Clark, D. Jaksch, P. Zoller Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: Dark state cooling of atoms within a Bloch band of an optical lattice, New J. Phys. 9 44 (2007), http://dx.doi.org/10.1088/1367-2630/9/2/044 doi:10.1088/1367-2630/9/2/044 (ID: 428626) Toggle Abstract
  We analyse a laser assisted sympathetic cooling scheme for atoms within the lowest Bloch band of an optical lattice. This scheme borrows ideas from sub-recoil laser cooling, implementing them in a new context in which the atoms in the lattice are coupled to a Bose–Einstein condensate (BEC) reservoir. In this scheme, excitation of atoms between Bloch bands replaces the internal structure of atoms in normal laser cooling, and spontaneous emission of photons is replaced by creation of excitations in the BEC reservoir. We analyse the cooling process for many bosons and fermions, and obtain possible temperatures corresponding to a small fraction of the Bloch band width within our model. This system can be seen as a novel realisation of a many-body open quantum system.
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2006

Articles

• A. Griessner, A. J. Daley, S. Clark, D. Jaksch, P. Zoller Dark state cooling of atoms by superfluid immersion, Phys. Rev. Lett. 97 220403 (2006-12-04), http://dx.doi.org/10.1103/PhysRevLett.97.220403 doi:10.1103/PhysRevLett.97.220403 (ID: 375452) Toggle Abstract
  We propose and analyze a scheme to cool atoms in an optical lattice to ultralow temperatures within a Bloch band and away from commensurate filling. The protocol is inspired by ideas from dark-state laser cooling but replaces electronic states with motional levels and spontaneous emission of photons by emission of phonons into a Bose-Einstein condensate, in which the lattice is immersed. In our model, achievable temperatures correspond to a small fraction of the Bloch bandwidth and are much lower than the reservoir temperature. This is also a novel realization of an open quantum optical system, where known tools are combined with new ideas involving cooling via a reservoir.
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• André, A, D. DeMille, J. Doyle, M. Lukin, S. E. Maxwell, P. Rabl, R. J. Schoelkopf, P. Zoller A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators, Nature Phys. 2 636 (2006-08-27), http://dx.doi.org/10.1038/nphys386 doi:10.1038/nphys386 (ID: 363758) Toggle Abstract
  Building a scalable quantum processor requires coherent control and preservation of quantum coherence in a large-scale quantum system. Mesoscopic solid-state systems such as Josephson junctions and quantum dots feature robust control techniques using local electrical signals and self-evident scaling; however, in general the quantum states decohere rapidly. In contrast, quantum optical systems based on trapped ions and neutral atoms exhibit much better coherence properties, but their miniaturization and integration with electrical circuits remains a challenge. Here we describe methods for the integration of a single-particle system—an isolated polar molecule—with mesoscopic solid-state devices in a way that produces robust, coherent, quantum-level control. Our setup provides a scalable cavity-QED-type quantum computer architecture, where entanglement of distant qubits stored in long-lived rotational molecular states is achieved via exchange of microwave photons.
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• M. Cozzini, T. Calarco, A. Recati, P. Zoller Fast Rydberg gates without dipole blockade via quantum control, Opt. Com. 264 375 (2006-08-15), arXiv:quant-ph/0511118 arXiv:quant-ph/0511118 (ID: 313117) Toggle Abstract
  We propose a scheme for controlling interactions between Rydberg-excited neutral atoms in order to perform a fast high-fidelity quantum gate. Unlike dipole-blockade mechanisms already found in the literature, we drive resonantly the atoms with a state-dependent excitation to Rydberg levels, and we exploit the resulting dipole–dipole interaction to induce a controlled atomic motion in the trap, in a similar way as discussed in recent ion-trap quantum computing proposals. This leads atoms to gain the required gate phase, which turns out to be a combination of a dynamic and a geometrical contribution. The fidelity of this scheme is studied including small anharmonicity and temperature effects, with promising results for reasonably achievable experimental parameters.
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• P. Rabl, D. DeMille, J. Doyle, M. Lukin, R. J. Schoelkopf, P. Zoller Hybrid Quantum Processors: molecular ensembles as quantum memory for solid state circuits, Phys. Rev. Lett. 97 033003 (2006-07-21), http://dx.doi.org/10.1103/PhysRevLett.97.033003 doi:10.1103/PhysRevLett.97.033003 (ID: 353814) Toggle Abstract
  We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few µm, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.
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• S. Trebst, U. Schollwöck, M. Troyer, P. Zoller d-Wave Resonating Valence Bond States of Fermionic Atoms in Optical Lattices, Phys. Rev. Lett. 96 250402 (2006-06-30), http://dx.doi.org/10.1103/PhysRevLett.96.250402 doi:10.1103/PhysRevLett.96.250402 (ID: 372594) Toggle Abstract
  We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.
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• K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. J. Daley, A. Kantian, H. Büchler, P. Zoller Repulsively bound atom pairs in an optical lattice, Nature 441 853 (2006-06-15), http://dx.doi.org/10.1038/nature04918 doi:10.1038/nature04918 (ID: 371157) Toggle Abstract
  Throughout physics, stable composite objects are usually formed by way of attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report the observation of such an exotic bound state, which comprises a pair of ultracold rubidium atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under conditions when they collide with one another. Signatures of the pairs are also recognized in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, owing to the presence of strong decay channels. Our results exemplify the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose–Hubbard model—a link that is vital for future applications of these systems to the study of strongly correlated condensed matter and to quantum information.
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• A. Micheli, G. Brennen, P. Zoller A toolbox for lattice spin models with polar molecules, Nature Phys. 2 341 (2006-05-00), http://dx.doi.org/10.1038/nphys287 doi:10.1038/nphys287 (ID: 313100) Toggle Abstract
  There is growing interest in states of matter with topological order. These are characterized by highly stable ground states robust to perturbations that preserve the topology, and which support excitations with so-called anyonic statistics. Topologically ordered states can arise in two-dimensional lattice-spin models, which were proposed as the basis for a new class of quantum computation. Here, we show that the relevant hamiltonians for such spin lattice models can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single-valence electron of a heteronuclear molecule. The combination of microwave excitation with dipole–dipole interactions and spin–rotation couplings enables building a complete toolbox for effective two-spin interactions with designable range, spatial anisotropy and coupling strengths significantly larger than relevant decoherence rates. Finally, we illustrate two models: one with an energy gap providing for error-resilient qubit encoding, and another leading to topologically protected quantum memory.
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• P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, P. Zoller Feedback cooling of a single trapped ion, Phys. Rev. Lett. 96 043003 (2006-02-03), http://dx.doi.org/10.1103/PhysRevLett.96.043003 doi:10.1103/PhysRevLett.96.043003 (ID: 332288) Toggle Abstract
  Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electromechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical master equation.

Proceedings

• A. J. Daley, A. Kantian, H. Büchler, P. Zoller, K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag Repulsively bound atom pairs: Overview, Simulations and Links, Proceedings of ICAP-2006 (2006-08-31), arXiv:cond-mat/0608721 arXiv:cond-mat/0608721 (ID: 387364) Toggle Abstract
  We review the basic physics of repulsively bound atom pairs in an optical lattice, which were recently observed in the laboratory, including the theory and the experimental implementation. We also briefly discuss related many-body numerical simulations, in which time-dependent Density Matrix Renormalisation Group (DMRG) methods are used to model the many-body physics of a collection of interacting pairs, and give a comparison of the single-particle quasimomentum distribution measured in the experiment and results from these simulations. We then give a short discussion of how these repulsively bound pairs relate to bound states in some other physical systems.
• H. Büchler, G. Pupillo, A. Micheli, E. Demler, M. Lukin, N. Prokofev, P. Zoller Designing interactions in polar molecules: towards novel quantum phase, Proceedings of ICAP-2006 ICAP 2006 (Innsbruck, Austria, 2006-07-16) (2006), (ID: 395229)
• André, A, D. DeMille, J. Doyle, M. Lukin, S. E. Maxwell, P. Rabl, R. J. Schoelkopf, P. Zoller Hybrid Quantum Information Processing with Polar Molecules, The 20th International Conference on Atomic Physics (ICAP 2006) (Innsbruck, Austria, 2006-07-00) 283 (2006), (ID: 432482)

2005

Articles

• P. Zoller, T. Beth, D. Binosi, R. Blatt, H. J. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Louwenhofen, S. Kröll, G. Leuchs, M. Quantum information processing and communication, Eur. Phys. J. D 36/2 203 - 228 (2005-11-01), http://dx.doi.org/10.1140/epjd/e2005-00251-1 doi:10.1140/epjd/e2005-00251-1 (ID: 375863) Toggle Abstract
  We present an excerpt of the document “Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe”, which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipc-sr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here. Dedicated to the memory of Prof. Th. Beth, one of the pioneers of QIPC, whose contributions have had a significant scientific impact on the development as well as on the visibility of a field that he enthusiastically helped to shape since its early days.
• A. J. Daley, S. Clark, D. Jaksch, P. Zoller Numerical analysis of coherent many-body currents in a single atom transistor, Phys. Rev. A 72 043618 (2005-10-28), http://dx.doi.org/10.1103/PhysRevA.72.043618 doi:10.1103/PhysRevA.72.043618 (ID: 308211) Toggle Abstract
  We study the dynamics of many atoms in the recently proposed single-atom-transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev. Lett. 93, 140408 (2004)] using recently developed numerical methods. In this setup, a localized spin-1/2 impurity is used to switch the transport of atoms in a one-dimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single-atom mirror. We calculate time-dependent currents for bosons passing the impurity atom, and find interesting many-body effects. These include substantially different transport properties for bosons in the strongly interacting (Tonks) regime when compared with fermions, and an unexpected decrease in the current when weakly interacting probe atoms are initially accelerated to a nonzero mean momentum. We also provide more insight into the application of our numerical methods to this system, and discuss open questions about the currents approached by the system on long time scales.
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• P. Rabl, V. Steixner, P. Zoller Quantum-limited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency, Phys. Rev. A 72 043823 (2005-10-27), http://dx.doi.org/10.1103/PhysRevA.72.043823 doi:10.1103/PhysRevA.72.043823 (ID: 308209) Toggle Abstract
  We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven Lambda-system based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantum-limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.
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• J. I. Cirac, P. Zoller Qubits, Gatter und Register, Physik Journal 11 31 (2005-10-00), URL (ID: 332271)
• A. Griessner, A. J. Daley, D. Jaksch, P. Zoller Fault-tolerant dissipative preparation of atomic quantum registers with fermions, Phys. Rev. A 72 032332 (2005-09-28), http://dx.doi.org/10.1103/PhysRevA.72.032332 doi:10.1103/PhysRevA.72.032332 (ID: 308207) Toggle Abstract
  We propose a fault-tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum-information processing and the modeling of strongly correlated systems. A cold reservoir of fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site and then decay to the motional ground state, creating particle-hole pairs in the reservoir. Atoms transferred into the ground motional level are no longer coupled back to the reservoir, and doubly occupied sites in the motional ground state are prevented by Pauli blocking. This scheme has strong conceptual connections with optical pumping and can be extended to load high-fidelity patterns of atoms.
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• U. Dorner, T. Calarco, P. Zoller, A. Browaeys, P. Grangiere Quantum logic via optimal control in holographic dipole traps, J. Opt. B: Quantum Semiclass. Opt. 7 341-346 (2005-09-21), http://dx.doi.org/10.1088/1464-4266/7/10/020 doi:10.1088/1464-4266/7/10/020 (ID: 308221) Toggle Abstract
  We propose a scheme for quantum logic with neutral atoms stored in an array of holographic dipole traps where the positions of the atoms can be rearranged by using holographic optical tweezers. In particular, this allows for the transport of two atoms to the same well where an external control field is used to perform gate operations via the molecular interaction between the atoms. We show that optimal control techniques allow for the fast implementation of the gates with high fidelity.
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• W. H. Zurek, U. Dorner, P. Zoller Dynamics of a Quantum Phase Transition, Phys. Rev. Lett. 95 105701 (2005-09-01), http://dx.doi.org/10.1103/PhysRevLett.95.105701 doi:10.1103/PhysRevLett.95.105701 (ID: 325892) Toggle Abstract
  We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.
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• V. Steixner, P. Rabl, P. Zoller Quantum feedback cooling of a single trapped ion in front of a mirror, Phys. Rev. A 72 043826 (2005-08-31), http://dx.doi.org/10.1103/PhysRevA.72.043826 doi:10.1103/PhysRevA.72.043826 (ID: 308208) Toggle Abstract
  We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.
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• K. Osterloh, M. Baig, L. Santos, P. Zoller, M. Lewenstein Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory, Phys. Rev. Lett. 95 010403 (2005-06-28), http://dx.doi.org/10.1103/PhysRevLett.95.010403 doi:10.1103/PhysRevLett.95.010403 (ID: 308223) Toggle Abstract
  We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k×k matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
• J. Taylor, W. Dür, P. Zoller, A. Yacoby, C. M. Marcus, M. Lukin Solid-State Circuit for Spin Entanglement Generation and Purification, Phys. Rev. Lett. 94 236803 (2005-06-15), http://dx.doi.org/10.1103/PhysRevLett.94.236803 doi:10.1103/PhysRevLett.94.236803 (ID: 308222) Toggle Abstract
  We show how realistic charge manipulation and measurement techniques, combined with the exchange interaction, allow for the robust generation and purification of four-particle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherence-free subspace; all additional errors are corrected by a purification protocol. This approach may find application in quantum computation, communication, and metrology.
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• J. J. García-Ripoll, P. Zoller, J. I. Cirac Coherent control of trapped ions using off-resonant lasers, Phys. Rev. A 71 062309 (2005-06-09), http://dx.doi.org/10.1103/PhysRevA.71.062309 doi:10.1103/PhysRevA.71.062309 (ID: 308224) Toggle Abstract
  In this paper we develop a unified framework to study the coherent control of trapped ions subject to state-dependent forces. Taking different limits in our theory, we can reproduce previous designs of quantum gates and propose a different design of fast gates based on continuous laser beams. We demonstrate how to simulate Ising Hamiltonians in a many ions setup, and how to create highly entangled states and induce squeezing. Finally, in a detailed analysis we identify the physical limits of this technique and study the dependence of errors on the temperature.
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• J. J. García-Ripoll, P. Zoller, J. I. Cirac Quantum information processing with cold atoms and trapped ions, J. Phys. B: At. Mol. Opt. Phys. 38 567-578 (2005-04-25), http://dx.doi.org/10.1088/0953-4075/38/9/008 doi:10.1088/0953-4075/38/9/008 (ID: 308228) Toggle Abstract
  This paper summarizes some important achievements of quantum information processing with trapped ions or neutral atoms. In particular, we describe the storage of information and realization of two-qubit gates with ions, as well as the creation of entanglement and quantum simulation with cold atoms in optical lattices.
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• A. Micheli, P. Zoller A Single Atom Mirror for 1D Atomic Lattice Gases, Phys. Rev. A 73 043613 (2005-04-20), http://dx.doi.org/10.1103/PhysRevA.73.043613 doi:10.1103/PhysRevA.73.043613 (ID: 313116) Toggle Abstract
  We propose a scheme utilizing quantum interference to control the transport of atoms in a 1D optical lattice by a single impurity atom. The two internal state of the impurity represent a spin-1/2 (qubit), which in one spin state is perfectly transparent to the lattice gas, and in the other spin state acts as a single atom mirror, confining the lattice gas. This allows to ``amplify'' the state of the qubit, and provides a single-shot quantum non-demolition measurement of the state of the qubit. We derive exact analytical expression for the scattering of a single atom by the impurity, and give approximate expressions for the dynamics a gas of many interacting bosonic of fermionic atoms.
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• A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, P. Zoller Atomic Quantum Dots Coupled to a Reservoir of a Superfluid Bose-Einstein Condensate, Phys. Rev. Lett. 94 040404 (2005-02-02), http://dx.doi.org/10.1103/PhysRevLett.94.040404 doi:10.1103/PhysRevLett.94.040404 (ID: 308229) Toggle Abstract
  We study the dynamics of an atomic quantum dot, i.e., a single atom in a tight optical trap which is coupled to a superfluid reservoir via laser transitions. Quantum interference between the collisional interactions and the laser induced coupling results in a tunable dot-bath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spin-boson model with Ohmic coupling, which exhibits a dissipative phase transition and allows us to directly measure atomic Luttinger parameters.
• J. Taylor, H. Engel, W. Dür, A. Yacoby, C. M. Marcus, P. Zoller, M. Lukin Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins, Nature Phys. 1 177-183 (2005-01-01), http://dx.doi.org/10.1038/nphys174 doi:10.1038/nphys174 (ID: 308201) Toggle Abstract
  Information processing using quantum systems provides new paradigms for computation and communication and may yield insights into our understanding of the limits of quantum mechanics. However, realistic systems are never perfectly isolated from their environment, hence all quantum operations are subject to errors. Realization of a physical system for processing of quantum information that is tolerant of errors is a fundamental problem in quantum science and engineering. Here, we develop an architecture for quantum computation using electrically controlled semiconductor spins by extending the Loss–DiVincenzo scheme and by combining actively protected quantum memory and long-distance coupling mechanisms. Our approach is based on a demonstrated encoding of qubits in long-lived two-electron states, which immunizes qubits against the dominant error from hyperfine interactions. We develop a universal set of quantum gates compatible with active error suppression for these encoded qubits and an effective long-range interaction between the qubits by controlled electron transport. This approach yields a scalable architecture with favourable error thresholds for fault-tolerant operation, consistent with present experimental parameters.
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• H. Büchler, M. Hermele, S. D. Huber, M. P. Fisher, P. Zoller Atomic quantum simulator for lattice gauge theories and ring exchange models, Phys. Rev. Lett. 95 040402 (2005), arXiv:cond-mat/0503254 arXiv:cond-mat/0503254 (ID: 302730) Toggle Abstract
  We present the design of a ring exchange interaction in cold atomic gases subjected to an optical lattice using well understood tools for manipulating and controlling such gases. The strength of this interaction can be tuned independently and describes the correlated hopping of two bosons. We discuss a setup where this coupling term may allows for the realization and observation of exotic quantum phases, including a deconfined insulator described by the Coulomb phase of a three-dimensional U(1) lattice gauge theory.
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• D. Jaksch, P. Zoller The cold atom Hubbard toolbox, Ann. Phys. 315 52-79 (2005), http://dx.doi.org/10.1016/j.aop.2004.09.010 doi:10.1016/j.aop.2004.09.010 (ID: 308231) Toggle Abstract
  We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then, we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally, we explain how defects and atomic quantum dots can be introduced in a controlled way in optical lattice systems.
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• L. Tian, R. Blatt, P. Zoller Scalable ion trap quantum computing without moving ions, Eur. Phys. J. D 32 201-208 (2005), http://dx.doi.org/10.1140/epjd/e2004-00172-5 doi:10.1140/epjd/e2004-00172-5 (ID: 308239) Toggle Abstract
  A hybrid quantum computing scheme is studied where the hybrid qubit is made of an ion trap qubit serving as the information storage and a solid-state charge qubit serving as the quantum processor, connected by a superconducting cavity. In this paper, we extend our previous work [1] and study the decoherence, coupling and scalability of the hybrid system. We present our calculations of the decoherence of the coupled ion-charge system due to the charge fluctuations in the solid-state system and the dissipation of the superconducting cavity under laser radiation. A gate scheme that exploits rapid state flips of the charge qubit to reduce decoherence by the charge noise is designed. We also study a superconducting switch that is inserted between the cavity and the charge qubit and provides tunable coupling between the qubits. The scalability of the hybrid scheme is discussed together with several potential experimental obstacles in realizing this scheme.

Document

• P. Zoller, J. I. Cirac Quantum information processing with atoms and ions, (2005), URL (ID: 313123)

Proceedings

• P. Zoller, J. I. Cirac Quantum information processing with atoms and ions, Quantum Information Processing & Communications in Europe 155 (2005-11-00), URL (ID: 379325)
• T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. J. Arlt, A. Kantian, L. Sanchez-Palencia, L. Santos, A. Sanpera, K. Sacha, P. Zoller, M. Lewenstein, J. Zakrzewski Cold Atomic Gases in Optical Lattices with Disorder, The 2nd Workshop on Quantum Chaos and Localisation Phenomena (Warsaw, Poland, 2005-05-19) A. Phys. Pol. A 109 89 (2005-05-19), URL (ID: 444464) Toggle Abstract
  Cold atomic gases placed in optical lattices enable studies of simple condensed matter theory models with parameters that may be tuned relatively easily. When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.

2004

Articles

• J. I. Cirac, P. Zoller New Frontiers in Quantum Information With Atoms and Ions,, Physics Today 38-44 (2004-03-00), URL (ID: 324583) Toggle Abstract
  Both the precision control of trapped-ion systems and very large samples of cold neutral atoms are opening important new possibilities for quantum computation and simulation
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• P. O. Fedichev, M. J. Bijlsma, P. Zoller Extended Molecules and Geometric Scattering Resonances in Optical Lattices, Phys. Rev. Lett. 92 080401 (2004-02-00), http://dx.doi.org/10.1103/PhysRevLett.92.080401 doi:10.1103/PhysRevLett.92.080401 (ID: 324597) Toggle Abstract
  We develop a theory describing neutral atom scattering at low energies in an optical lattice. We show that, for a repulsive interaction, as the microscopic scattering length increases the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.
• A. J. Daley, P. O. Fedichev, P. Zoller Single-atom cooling by superfluid immersion: A nondestructive method for qubits, Phys. Rev. A 69 022306 (2004-02-00), http://dx.doi.org/10.1103/PhysRevA.69.022306 doi:10.1103/PhysRevA.69.022306 (ID: 324602) Toggle Abstract
  We present a scheme to cool the motional state of neutral atoms confined in sites of an optical lattice by immersing the system in a superfluid. The motion of the atoms is damped by the generation of excitations in the superfluid, and under appropriate conditions the internal state of the atom remains unchanged. This scheme can thus be used to cool atoms used to encode a series of entangled qubits nondestructively. Within realizable parameter ranges, the rate of cooling to the ground state is found to be sufficiently large to be useful in experiments.
• B. Paredes, P. Zoller, J. I. Cirac, J. J. García-Ripoll Strong correlation effects and quantum information theory of low dimensional atomic gases, J. Phys. IV 116 135-168 (2004), http://dx.doi.org/10.1051/jp4:2004116005 doi:10.1051/jp4:2004116005 (ID: 314540) Toggle Abstract
  These lecture notes present an introduction to the strongly correlated regime of low dimensional atomic gases. The discussion is concentrated on situations in which the strongly correlated limit is achieved by creating degeneracies in the one-particle motional states. Three different schemes of experimental relevance are analyzed: bosonic atoms in a two dimensional rapidly rotating trap, bosonic atoms in a one dimensional optical lattice, and bosonic atoms with frozen motional degrees of freedom and two internal states. The corresponding entangled multiparticle states (Laughlin liquids, Mott phases, squeezed states), and the different strongly correlated phenomena that appear (fermionization, fractional statistics) are studied. Emphasis is given to the possibility of observing novel strongly correlated phenomena as well as to the possible implementations for quantum computation and quantum information.
• P. Zoller, L. Tian Coupled Ion-Nanomechanical Systems, Phys. Rev. Lett. 93 266403 (2004), http://dx.doi.org/10.1103/PhysRevLett.93.266403 doi:10.1103/PhysRevLett.93.266403 (ID: 314555) Toggle Abstract
  We study ions in a nanotrap, where the electrodes are nanomechanical resonators. The ions play the role of a quantum optical system that acts as a probe and control, and allows entanglement with or between nanomechanical resonators.
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• A. Micheli, A. J. Daley, D. Jaksch, P. Zoller Single Atom Transistor in a 1D Optical Lattice, Phys. Rev. Lett. 93 140408 (2004), http://dx.doi.org/10.1103/PhysRevLett.93.140408 doi:10.1103/PhysRevLett.93.140408 (ID: 314620) Toggle Abstract
  We propose a scheme utilizing a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum nondemolition measurement of the qubit spin.
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• W. V. Liu, F. Wilczek, P. Zoller Spin-dependent Hubbard model and a quantum phase transition in cold atoms, Phys. Rev. A 70 033603 (2004), http://dx.doi.org/10.1103/PhysRevA.70.033603 doi:10.1103/PhysRevA.70.033603 (ID: 314622) Toggle Abstract
  We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength can be controlled with an external magnetic field. We suggest that exotic superfluidities will arise in this framework. An especially interesting possibility is a class of states that support coexisting superfluid and normal components, even at zero temperature. The quantity of normal component varies with external parameters. We discuss some aspects of the quantum phase transition that arises at the point where it vanishes.
• H. Büchler, P. Zoller, W. Zwerger Spectroscopy of Superfluid Pairing in Atomic Fermi Gases, Phys. Rev. Lett. 93 080401 (2004), http://dx.doi.org/10.1103/PhysRevLett.93.080401 doi:10.1103/PhysRevLett.93.080401 (ID: 314630) Toggle Abstract
  We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.
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• T. Calarco, U. Dorner, P. S. Julienne, C. Williams, P. Zoller Quantum computations with atoms in optical lattices: Marker qubits and molecular interactions, Phys. Rev. A 70 012306 (2004), http://dx.doi.org/10.1103/PhysRevA.70.012306 doi:10.1103/PhysRevA.70.012306 (ID: 314632) Toggle Abstract
  We develop a scheme for quantum computation with neutral atoms, based on the concept of "marker" atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic external traps to operate quantum gates between physically distant qubits. This allows for relaxing a number of experimental constraints for quantum computation with neutral atoms in microscopic potential, including single-atom laser addressability. We discuss the advantages of this approach in a concrete physical scenario involving molecular interactions.
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• L. Tian, P. Rabl, R. Blatt, P. Zoller Interfacing Quantum-Optical and Solid-State Qubits, Phys. Rev. Lett. 92 247902 (2004), http://dx.doi.org/10.1103/PhysRevLett.92.247902 doi:10.1103/PhysRevLett.92.247902 (ID: 314633) Toggle Abstract
  We present a generic model of coupling quantum-optical and solid-state qubits, and the corresponding transfer protocols. The example discussed is a trapped ion coupled to a charge qubit (e.g., Cooper pair box). To enhance the coupling and to achieve compatibility between the different experimental setups we introduce a superconducting cavity as the connecting element.
• J. J. García-Ripoll, J. I. Cirac, P. Zoller, C. Kollath, U. Schollwöck, J. von Delft Variational ansatz for the superfluid Mott-insulator transition in optical lattices, Opt. Express 12 42-54 (2004), arXiv:cond-mat/0306162 arXiv:cond-mat/0306162 (ID: 314640) Toggle Abstract
  We develop a variational wave function for the ground state of a one-dimensional bosonic lattice gas. The variational theory is initially developed for the quantum rotor model and later on extended to the Bose- Hubbard model. This theory is compared with quasi-exact numerical results obtained by Density Matrix Renormalization Group (DMRG) studies and with results from other analytical approximations. Our approach accurately gives local properties for strong and weak interactions, and it also describes the crossover from the superfluid phase to the Mott-insulator phase.
• I. Martin, A. Shnirman, L. Tian, P. Zoller Ground-state cooling of mechanical resonators, Phys. Rev. B 69 125339 (2004), http://dx.doi.org/10.1103/PhysRevB.69.125339 doi:10.1103/PhysRevB.69.125339 (ID: 314642) Toggle Abstract
  We propose an application of a single Cooper pair box (Josephson qubit) for active cooling of nanomechanical resonators. Latest experiments with Josephson qubits demonstrated that long coherence time of the order of microsecond can be achieved in special symmetry points. Here we show that this level of coherence is sufficient to perform an analog of the well known in quantum optics "laser" cooling of a nanomechanical resonator capacitively coupled to the qubit. By applying an ac driving to the qubit or the resonator, resonators with frequency of order 100 MHz and quality factors higher than 103 can be efficiently cooled down to their ground state, while lower-frequency resonators can be cooled down to micro-Kelvin temperatures. We also consider an alternative setup where dc-voltage-induced Josephson oscillations play the role of the ac driving and show that cooling is possible in this case as well.
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• E. Pazy, T. Calarco, P. Zoller Spin state readout by quantum jump technique: for the purpose of quantum computing, IEEE Transactions on Nanotechnology 3 10 - 16 (2004), http://dx.doi.org/10.1109/TNANO.2003.820516 doi:10.1109/TNANO.2003.820516 (ID: 314773) Toggle Abstract
  Utilizing the Pauli-blocking mechanism we show that shining circular polarized light on a singly-charged quantum dot induces spin dependent fluorescence. Employing the quantum-jump technique we demonstrate that this resonance luminescence, due to a spin dependent optical excitation, serves as an excellent readout mechanism for measuring the spin state of a single electron confined to a quantum dot.
• P. Rabl, A. Shnirman, P. Zoller Generation of Squeezed States of Nanomechanical Resonators by Reservoir Engineering, Phys. Rev. B 70 205304 (2004), http://dx.doi.org/10.1103/PhysRevB.70.205304 doi:10.1103/PhysRevB.70.205304 (ID: 335015) Toggle Abstract
  An experimental demonstration of a nonclassical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary resonator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5–0.2. These values are obtained for a 100 MHz resonator with a Q-value of 104 to 105 and for support temperatures of T[approximate]25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed state via measurements of the excited state population. Furthermore, by extending this measurement procedure a complete quantum state tomography of the resonator state can be performed. This provides a universal tool to detect a large variety of different states and to prove the quantum nature of nanomechanical systems.
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• A. Griessner, D. Jaksch, P. Zoller Cavity-assisted nondestructive laser cooling of atomic qubits, J. Phys. B: At. Mol. Opt. Phys. 37 1432 (2004), http://dx.doi.org/10.1088/0953-4075/37/7/004 doi:10.1088/0953-4075/37/7/004 (ID: 335134) Toggle Abstract
  We analyse two configurations for laser cooling of neutral atoms whose internal states store qubits. The atoms are trapped in an optical lattice which is placed inside a cavity. We show that the coupling of the atoms to the damped cavity mode can provide a mechanism which leads to cooling of the motion without destroying the quantum information.
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• I. Wilson-Rae, P. Zoller, A. Imamoglu Laser Cooling of a Nanomechanical Resonator Mode to its Quantum Ground State, Phys. Rev. Lett. 92 075507 (2004), http://dx.doi.org/10.1103/PhysRevLett.92.075507 doi:10.1103/PhysRevLett.92.075507 (ID: 336649) Toggle Abstract
  We show that it is possible to cool a nanomechanical resonator mode to its ground state. The proposed technique is based on resonant laser excitation of a phonon sideband of an embedded quantum dot. The strength of the sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot optical transition. Possible applications of this scheme include generation of nonclassical states of mechanical motion.

Book

• C. Gardiner, P. Zoller Quantum Noise, (2004-08-27), URL (ID: 566863) Toggle Abstract
  This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quantum amplifier theory, non-Markovian quantum stochastic processes, quantum input--output theory, and positive P-representations. It is the first book in which quantum noise is described by a mathematically complete theory in a form that is also suited to practical applications. Special attention is paid to non-classical effects, such as squeezing and antibunching. Chapters added to the previous edition, on the stochastic Schrödinger equation, and on cascaded quantum systems, and now supplemented, in the third edition by a chapter on recent developments in various pertinent fields such as laser cooling, Bose-Einstein condensation, quantum feedback and quantum information.

Proceeding

• A. J. Daley, P. O. Fedichev, P. Rabl, P. Zoller, A. Recati, J. I. Cirac, J. von Delft, W. Zwerger Spectroscopy of Strongly Correlated Cold Atoms, Proceedings of the XVI International Conference on Laser Spectroscopy 145-152 (2004), (ID: 325299)

2003

Articles

• L. Jacak, P. Machnikowski, J. Krasnyj, P. Zoller Coherent and incoherent phonon processes in artificial atoms Optical Physics, The European Physical Journal D 22 / 3 319 - 331 (2003-05-00), http://dx.doi.org/10.1140/epjd/e2003-00020-2 doi:10.1140/epjd/e2003-00020-2 (ID: 375605) Toggle Abstract
  Carrier-phonon interaction in semiconductor quantum dots leads to three classes of phenomena: coherent effects (spectrum reconstruction) due to the nearly-dispersionless LO phonons, incoherent effects (transitions) induced by acoustical phonons and dressing phenomena, related to non-adiabatic, sub-picosecond excitation. Polaron spectra, relaxation times and dressing-related decoherence rates are calculated, in accordance with experiment.
• E. Pazy, T. Calarco, I. D'Amico, P. Zanardi, F. Rossi, P. Zoller All Optical Spin-Based Quantum Information Processing, J Supercond Nov Magn 16/2 383 - 385 (2003-04-01), http://dx.doi.org/10.1023/A:1023646326888 doi:10.1023/A:1023646326888 (ID: 375698) Toggle Abstract
  We propose a spin-based ultra-fast laser driven implementation of quantum information processing based on the Pauli blocking effect in semiconductors, which acts as a spin dependent switching mechanism for auxiliary exciton states. spintronics - quantum information - quantum dot - Pauli blocking effect
• P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, P. Zoller Defect-Suppressed Atomic Crystals in an Optical Lattice, Phys. Rev. Lett. 91 110403 (2003), http://dx.doi.org/10.1103/PhysRevLett.91.110403 doi:10.1103/PhysRevLett.91.110403 (ID: 335014) Toggle Abstract
  We present a coherent filtering scheme which dramatically reduces the site occupation number defects for atoms in an optical lattice by transferring a chosen number of atoms to a different internal state via adiabatic passage. With the addition of superlattices it is possible to engineer states with a specific number of atoms per site (atomic crystals), which are required for quantum computation and the realization of models from condensed matter physics, including doping and spatial patterns. The same techniques can be used to measure two-body spatial correlation functions.
• J. I. Cirac, L. Duan, D. Jaksch, P. Zoller Quantum information processing with quantum optics, Ann. Henri Poincare 4 661 (2003), (ID: 336650) Toggle Abstract
  We review theoretical proposals for implementation of quantum computing and quantum communication with quantum optical methods.
• A. Recati, P. O. Fedichev, W. Zwerger, P. Zoller Fermi 1D quantum gas: Luttinger liquid approach and spin-charge separation, J. Opt. B: Quantum Semiclass. Opt. 5 55 (2003), http://dx.doi.org/10.1088/1464-4266/5/2/359 doi:10.1088/1464-4266/5/2/359 (ID: 336651) Toggle Abstract
  We discuss the properties of quasi-1D quantum gases of fermionic atoms using the Luttinger liquid theory, including the presence of an optical lattice and of a longitudinal trapping potential. We analyze in particular the nature and manifestations of spin-charge separation, where in the case of atoms ``spin'' and ``charge'' refers to two internal atomic states and the atomic mass density, respectively.
• L. Tian, P. Zoller Quantum computing with atomic Josephson junction arrays, Phys. Rev. A 68 042321 (2003), http://dx.doi.org/10.1103/PhysRevA.68.042321 doi:10.1103/PhysRevA.68.042321 (ID: 336652) Toggle Abstract
  We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off-resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single-qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.
• J. J. García-Ripoll, P. Zoller, J. I. Cirac Speed Optimized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Computing, Phys. Rev. Lett. 91 157901 (2003), http://dx.doi.org/10.1103/PhysRevLett.91.157901 doi:10.1103/PhysRevLett.91.157901 (ID: 336653) Toggle Abstract
  We propose a new concept for a two-qubit gate operating on a pair of trapped ions based on laser coherent control techniques. The gate is insensitive to the temperature of the ions, works also outside the Lamb-Dicke regime, requires no individual addressing by lasers, and can be orders of magnitude faster than the trap period, which is presently the speed limit of all two-qubit proposals.
• T. Calarco, A. Datta, P. O. Fedichev, E. Pazy, P. Zoller Spin-based all-optical quantum computation with quantum dots: Understanding and suppressing decoherence, Phys. Rev. A 68 012310 (2003), http://dx.doi.org/10.1103/PhysRevA.68.012310 doi:10.1103/PhysRevA.68.012310 (ID: 336655) Toggle Abstract
  We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing, and phonon decoherence. We introduce an adiabatic gate procedure that allows one to circumvent these effects and evaluate quantitatively its fidelity.
• A. Imamoglu, E. Knill, L. Tian, P. Zoller Optical Pumping of Quantum-Dot Nuclear Spins, Phys. Rev. Lett. 91 017402 (2003), http://dx.doi.org/10.1103/PhysRevLett.90.017402 doi:10.1103/PhysRevLett.90.017402 (ID: 336656) Toggle Abstract
  Hyperfine interactions with randomly oriented nuclear spins present a fundamental decoherence mechanism for electron spin in a quantum dot, that can be suppressed by polarizing the nuclear spins. Here, we analyze an all-optical scheme that uses hyperfine interactions to implement laser cooling of quantum-dot nuclear spins. The limitation imposed on spin cooling by the dark states for collective spin relaxation can be overcome by modulating the electron wave function.
• U. Dorner, P. O. Fedichev, D. Jaksch, M. Lewenstein, P. Zoller Entangling Strings of Neutral Atoms in 1D Atomic Pipeline Structures, Phys. Rev. Lett. 91 073601 (2003), http://dx.doi.org/10.1103/PhysRevLett.91.073601 doi:10.1103/PhysRevLett.91.073601 (ID: 336657) Toggle Abstract
  We study a string of neutral atoms with nearest neighbor interaction in a 1D beam splitter configuration, where the longitudinal motion is controlled by a moving optical lattice potential. The dynamics of the atoms crossing the beam splitter maps to a 1D spin model with controllable time dependent parameters, which allows the creation of maximally entangled states of atoms by crossing a quantum phase transition. Furthermore, we show that this system realizes protected quantum memory, and we discuss the implementation of one- and two-qubit gates in this setup.
• B. Damski, J. Zakrzewski, L. Santos, P. Zoller, M. Lewenstein Atomic Bose and Anderson Glasses in Optical Lattices, Phys. Rev. Lett. 91 080403 (2003), http://dx.doi.org/10.1103/PhysRevLett.91.080403 doi:10.1103/PhysRevLett.91.080403 (ID: 336658) Toggle Abstract
  An ultracold atomic Bose gas in an optical lattice is shown to provide an ideal system for the controlled analysis of disordered Bose lattice gases. This goal may be easily achieved under the current experimental conditions by introducing a pseudorandom potential created by a second additional lattice or, alternatively, by placing a speckle pattern on the main lattice. We show that, for a noncommensurable filling factor, in the strong-interaction limit, a controlled growing of the disorder drives a dynamical transition from superfluid to Bose-glass phase. Similarly, in the weak interaction limit, a dynamical transition from superfluid to Anderson-glass phase may be observed. In both regimes, we show that even very low-intensity disorder-inducing lasers cause large modifications of the superfluid fraction of the system.
• E. Pazy, T. Calarco, I. D'Amico, P. Zanardi, F. Rossi, P. Zoller Implementation of an all-optical spin-based quantum computer, Physica Status Solidi B 238 418 (2003), http://dx.doi.org/10.1002/pssb.200303154 doi:10.1002/pssb.200303154 (ID: 336659) Toggle Abstract
  An all-optical implementation scheme of a spin-based quantum computer is presented. Our quantum memory consists of the spin of electrons confined to quantum dots. Utilizing the Pauli blocking effect we are able to have ultra-fast control and read out of the electronic spin degrees of freedom by conditionally coupling them with charged excitations of the quantum dot. Imperfections effecting gate operations are discussed and we show that final readout can still be performed by a quantum-jump technique even in the presence of hole mixing, when the Pauli-blocking selection rule is violated.
• J. I. Cirac, P. Zoller How to Manipulate Cold Atoms, Science 301 176 (2003), http://dx.doi.org/10.1126/science.1085130 doi:10.1126/science.1085130 (ID: 336660) Toggle Abstract
  Since Bose-Einstein condensates were first realized in 1995, experimentalists have focused on characterizing and manipulating these weakly interacting systems. In their Perspective, Cirac and Zoller look ahead toward the next challenge for atomic physics: strongly interacting atomic systems that may be of use in quantum computing and may clarify fundamental properties of quantum mechanics. They explain how optical lattices can be used to tune the interactions between cold atoms and how a quantum simulator may be constructed. The latter may enable the first quantum computers that can outperform ordinary computers for nontrivial problems.
• D. Jaksch, P. Zoller Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms, New J. Phys. 5 56 (2003), http://dx.doi.org/10.1088/1367-2630/5/1/356 doi:10.1088/1367-2630/5/1/356 (ID: 336661) Toggle Abstract
  We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non-vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This set-up is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields—which is not experimentally accessible for electrons in metals—where a fractal band structure, the Hofstadter butterfly, characterizes the system.
• E. Jané, G. Vidal, W. Dür, P. Zoller, J. I. Cirac Simulation of quantum dynamics with quantum optical systems, Quantum Information and Computation (online) 3 37 (2003), URL (ID: 336662) Toggle Abstract
  We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral atoms stored in optical lattices, while the second scheme consists of ions stored in an array of micro--traps. Each atom (ion) supports a two--level system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring two--level systems is achieved by conditionally displacing the corresponding atoms (ions) Then, average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians.
• E. Pazy, E. Biolatti, T. Calarco, I. D'Amico, P. Zanardi, F. Rossi, P. Zoller Spin-based optical quantum computation via Pauli blocking in semiconductor quantum dots, 62 181 (2003), http://dx.doi.org/10.1209/epl/i2003-00343-4 doi:10.1209/epl/i2003-00343-4 (ID: 336663) Toggle Abstract
  We present a solid-state implementation of an all-optical spin-based quantum computer. Our proposal for a quantum-computing device is based on the spin degrees of freedom of electrons confined in semiconductor quantum dots, thus benefitting from relatively long coherence times. Combining Pauli blocking effects with properly tailored ultrafast laser pulses, we obtain sub-picosecond spin-dependent switching of the Coulomb interaction, which is the essence of our gating operations. This allows us to realize fast quantum gates which do not translate into fast decoherence times and pave the way for an all-optical spin-based quantum computer.
• B. Damski, L. Santos, E. Tiemann, M. Lewenstein, S. Kotochigova, P. S. Julienne, P. Zoller Creation of a Dipolar Superfluid in Optical Lattices, Phys. Rev. Lett. 90 110401 (2003), http://dx.doi.org/10.1103/PhysRevLett.90.110401 doi:10.1103/PhysRevLett.90.110401 (ID: 336664) Toggle Abstract
  We show that, by loading a Bose-Einstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mott-insulator phase with exactly one atom of each species per lattice site. A subsequent photoassociation leads to the formation of one heteronuclear molecule with a large electric dipole moment, at each lattice site. The melting of such a dipolar Mott insulator creates a dipolar superfluid, and eventually a dipolar molecular condensate.
• A. Recati, P. O. Fedichev, W. Zwerger, P. Zoller Spin-Charge Separation in Ultracold Quantum Gases, Phys. Rev. Lett. 90 020401 (2003), http://dx.doi.org/10.1103/PhysRevLett.90.020401 doi:10.1103/PhysRevLett.90.020401 (ID: 336665) Toggle Abstract
  We investigate the physical properties of quasi-1D quantum gases of fermionic atoms confined in harmonic traps. Using the fact that for a homogeneous gas the low-energy properties are exactly described by a Luttinger model, we analyze the nature and manifestations of spin-charge separation, where in the case of atoms "spin" and "charge" refer to two internal atomic states and the atomic mass density, respectively. We discuss the necessary physical conditions and experimental limitations confronting possible experimental implementations.
• A. Micheli, D. Jaksch, J. I. Cirac, P. Zoller Many-particle entanglement in two-component Bose-Einstein condensates, Phys. Rev. A 67 013607 (2003), http://dx.doi.org/10.1103/PhysRevA.67.013607 doi:10.1103/PhysRevA.67.013607 (ID: 336666) Toggle Abstract
  We investigate schemes to dynamically create many-particle entangled states of a two-component Bose-Einstein condensate in a very short time proportional to 1/N, where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for N>=50. We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections.

Proceedings

• P. Zoller, J. I. Cirac, L. Duan, J. J. García-Ripoll Quantum entanglement and information processing, Quantum communication and quantum computing with cold atoms and photons (France) URL (2003-07-30), URL (ID: 383442)
• A. J. Daley, P. O. Fedichev, P. Rabl, A. Recati, J. I. Cirac, J. von Delft, P. Zoller, W. Zwerger Spectroscopy of strongly correlated cold atoms, Laser Spectroscopy, proceedings of the XVI International Conference (Queensland, Australia, 2003-07-13) 145 - 152 (2003), (ID: 381813)
• L. Duan, W. Dür, J. I. Cirac, D. Jaksch, G. Vidal, P. Zoller Quantum computing and quantum communication with atoms, Proceedings of the XVIII International Conference on Atomic Physics 273-282 (2003), URL (ID: 381815) Toggle Abstract
  We review recent theoretical proposals for implementation of quantum computing and quantum communication with atoms. The first example deals with the realization of a universal quantum simulator with atoms and ions. The second example outlines the implementation of a quantum repeater with atomic ensembles.

2002

Articles

• W. Hofstetter, J. I. Cirac, P. Zoller, E. Demler, M. Lukin High-Temperature Superfluidity of Fermionic Atoms in Optical Lattices, Phys. Rev. Lett. 89 220407 (2002-11-12), http://dx.doi.org/10.1103/PhysRevLett.89.220407 doi:10.1103/PhysRevLett.89.220407 (ID: 337567) Toggle Abstract
  Fermionic atoms confined in a potential created by standing wave light can undergo a phase transition to a superfluid state at a dramatically increased transition temperature. Depending upon carefully controlled parameters, a transition to a superfluid state of Cooper pairs, antiferromagnetic states or d-wave pairing states can be induced and probed under realistic experimental conditions. We describe an atomic physics experiment that can provide critical insight into the origin of high-temperature superconductivity in cuprates.
• B. Paredes, P. Zoller, J. I. Cirac Fermionizing a small gas of ultracold bosons, Phys. Rev. A 66 033609 (2002-09-20), http://dx.doi.org/10.1103/PhysRevA.66.033609 doi:10.1103/PhysRevA.66.033609 (ID: 337568) Toggle Abstract
  We study the physics of a rapidly rotating gas of ultracold atomic bosons, with an internal degree of freedom. We show that in the limit of rapid rotation of the trap the problem exactly maps onto that of noninteracting fermions with spin in the lowest Landau level. The spectrum of the real bosonic system is identical to the one of the effective fermions, with the same eigenvalues and the same density of states. When the ratio of the number of atoms to the spin degeneracy is an integer number, the ground state for the effective fermions is an integer quantum Hall state. The corresponding bosonic state is a fractional quantum Hall liquid whose filling factor ranges in the sequence $\nu$= 1/2,2/3,3/4,..., as the spin degeneracy increases. Anyons with 1/2,1/3,1/4,... statistics can be created by inserting lasers with the appropriate polarizations. A special situation appears when the spin degeneracy equals the number of atoms in the gas. The ground state is then the product of a completely antisymmetric spin state and a nu= 1 Laughlin state. In this case the system exhibits fermionic excitations with fermionic statistics although the real components are bosonic atoms.
• A. Recati, T. Calarco, P. Zanardi, J. I. Cirac, P. Zoller Holonomic quantum computation with neutral atoms, Phys. Rev. A 66 032309 (2002-09-17), http://dx.doi.org/10.1103/PhysRevA.66.032309 doi:10.1103/PhysRevA.66.032309 (ID: 337570) Toggle Abstract
  We propose an all-geometric implementation of quantum computation using neutral atoms in cavity QED. We show how to perform generic single- and two-qubit gates, the latter by encoding a two-atom state onto a single, many-level atom. We compare different strategies to overcome limitations due to cavity imperfections.
• L. Duan, J. I. Cirac, P. Zoller Three-dimensional theory for interaction between atomic ensembles and free-space light, Phys. Rev. A 66 023818 (2002-08-27), http://dx.doi.org/10.1103/PhysRevA.66.023818 doi:10.1103/PhysRevA.66.023818 (ID: 337569) Toggle Abstract
  Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles. For description of these interactions, one assumed either a cavity-QED model or a one-dimensional light propagation model, which is still inadequate for a full prediction and understanding of most of the current experimental efforts that are actually taken in the three-dimensional free space. Here, we propose a perturbative theory to describe the three-dimensional effects in interaction between atomic ensembles and free-space light with a level configuration important for several applications. The calculations reveal some significant effects that were not known before from the other approaches, such as the inherent mode-mismatching noise and the optimal mode-matching conditions. The three-dimensional theory confirms the collective enhancement of the signal-to-noise ratio which is believed to be one of the main advantages of the ensemble-based quantum information processing schemes, however, it also shows that this enhancement needs to be understood in a more subtle way with an appropriate mode-matching method.
• U. Dorner, P. Zoller Laser-driven atoms in half-cavities, Phys. Rev. A 66 023816 (2002-08-26), http://dx.doi.org/10.1103/PhysRevA.66.023816 doi:10.1103/PhysRevA.66.023816 (ID: 337571) Toggle Abstract
  The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.
• T. Calarco, D. Jaksch, J. I. Cirac, P. Zoller Controlling dynamical phases in quantum optics,, J. Opt. B: Quantum Semiclass. Opt. 4 S430 (2002-07-29), http://dx.doi.org/10.1088/1464-4266/4/4/334 doi:10.1088/1464-4266/4/4/334 (ID: 337572) Toggle Abstract
  We review and compare several schemes for inducing precisely controlled quantum phases in quantum optical systems. We focus in particular onto conditional dynamical phases, i.e., phases obtained via state- and time-dependent interactions between trapped two-level atoms and ions. We describe different possibilities for the kind of interaction to be exploited, including cold controlled collisions, electrostatic forces, and dipole-dipole interactions.
• D. Jaksch, V. Venturi, J. I. Cirac, C. Williams, P. Zoller Creation of a Molecular Condensate by Dynamically Melting a Mott Insulator, Phys. Rev. Lett. 89 040402 (2002-07-02), http://dx.doi.org/10.1103/PhysRevLett.89.040402 doi:10.1103/PhysRevLett.89.040402 (ID: 337573) Toggle Abstract
  We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.
• P. Zoller Making it with molecules, Nature 417 493 (2002-05-30), http://dx.doi.org/10.1038/417493a doi:10.1038/417493a (ID: 337575) Toggle Abstract
  Following the creation of atomic Bose–Einstein condensates in the mid-1990s, a major goal has been to produce a condensate of molecules.Technical challenges remain, but that achievement is now tantalizingly close.
• D. Jaksch, J. I. Cirac, P. Zoller Dynamically turning off interactions in a two-component condensate, Phys. Rev. A 65 033625 (2002-03-01), http://dx.doi.org/10.1103/PhysRevA.65.033625 doi:10.1103/PhysRevA.65.033625 (ID: 337576) Toggle Abstract
  We propose a mechanism to change the interaction strengths of a two-component condensate. It is shown that the application of pi/2 pulses allows us to alter the effective interspecies-interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable ones and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many-body entangled states.
• L. Duan, J. I. Cirac, P. Zoller Quantum entanglement in spinor Bose-Einstein condensates, Phys. Rev. A 65 033619 (2002-02-27), http://dx.doi.org/10.1103/PhysRevA.65.033619 doi:10.1103/PhysRevA.65.033619 (ID: 337577) Toggle Abstract
  We propose a scheme to generate and detect various kinds of quantum entanglement in a spin-1 Bose-Einstein condensate. It is shown that substantial many-particle entanglement can be generated directly in the spin-1 condensate by free dynamical evolution with a properly prepared initial state. The scheme also provides a simple method to generate three-mode entanglement in the second-quantization picture and to detect the continuous variable type of entanglement between two effective modes in the spin-1 condensate.

Proceeding

• E. Pazy, E. Biolatti, T. Calarco, I. D'Amico, P. Zanardi, F. Rossi, P. Zoller Paving the road for an all-optical spin-based quantum computer, Poster contribution to QCMC02 (Sixth International Conference on Quantum Communication, Measurement and Computing) MIT-Boston (2002-07-22), URL (ID: 383445)

2001

Articles

• L. Duan, M. Lukin, J. I. Cirac, P. Zoller Long-distance quantum communication with atomic ensembles and linear optics, Nature 414 413 (2001-11-22), http://dx.doi.org/10.1038/35106500 doi:10.1038/35106500 (ID: 337580) Toggle Abstract
  Quantum communication holds promise for absolutely secure transmission of secret messages and the faithful transfer of unknown quantum states. Photonic channels appear to be very attractive for the physical implementation of quantum communication. However, owing to losses and decoherence in the channel, the communication fidelity decreases exponentially with the channel length. Here we describe a scheme that allows the implementation of robust quantum communication over long lossy channels. The scheme involves laser manipulation of atomic ensembles, beam splitters, and single-photon detectors with moderate efficiencies, and is therefore compatible with current experimental technology. We show that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances.
• G. Giedke, B. Kraus, L. Duan, P. Zoller, M. Lewenstein, J. I. Cirac Separability and Distillability of bipartite Gaussian States - the Complete Story, Fortschr. Phys. 49 980 (2001-10-25), http://dx.doi.org/10.1002/1521-3978(200110)49:10/11 doi:10.1002/1521-3978(200110)49:10/11 (ID: 337579) Toggle Abstract
  We present necessary and sufficient conditions for both the separability and the distillability of bipartite Gaussian states of an arbitrary number of modes. The conditions can be easily checked by direct calculations, thus providing operational criteria for both properties. This solves the separability and distillability problems for Gaussian states.
• G. Giedke, L. Duan, J. I. Cirac, P. Zoller Distillability Criterion for all bipartite Gaussian States, Quantum Information and Computation (online) 1 79 (2001-10-00), URL (ID: 337581) Toggle Abstract
  We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if and only if its partial transpose is not positive.
• G. M. Bruun, P. Törmä, M. Rodriguez, P. Zoller Laser probing of Cooper-paired trapped atoms, Phys. Rev. A 64 033609 (2001-08-16), http://dx.doi.org/10.1103/PhysRevA.64.033609 doi:10.1103/PhysRevA.64.033609 (ID: 337586) Toggle Abstract
  We consider a gas of trapped Cooper-paired fermionic atoms that are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length (superfluid) to one with weaker interactions (normal gas). We show that the process can be used to detect the presence of the superconducting order parameter. Also, we propose a direct way of measuring the size of the gap in the trap. The efficiency and feasibility of this probing method is investigated in detail in different physical situations.
• B. Paredes, P. O. Fedichev, J. I. Cirac, P. Zoller (1/2)-Anyons in Small Atomic Bose-Einstein Condensates, Phys. Rev. Lett. 87 010402 (2001-07-02), http://dx.doi.org/10.1103/PhysRevLett.87.010402 doi:10.1103/PhysRevLett.87.010402 (ID: 337583) Toggle Abstract
  We discuss a way of creating, manipulating, and detecting anyons in rotating Bose-Einstein condensates consisting of a small number of atoms. By achieving a quasidegeneracy in the atomic motional states we drive the system into a (1/2)-Laughlin state for fractional quantum Hall bosons. Localized (1/2)-quasiholes can be created by focusing lasers at the desired positions. We show how to manipulate these quasiholes in order to probe directly their (1/2)-statistics.
• M. Lukin, M. Fleischhauer, R. Cote, L. Duan, D. Jaksch, J. I. Cirac, P. Zoller Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles, Phys. Rev. Lett. 87 037901 (2001-06-26), http://dx.doi.org/10.1103/PhysRevLett.87.037901 doi:10.1103/PhysRevLett.87.037901 (ID: 337584) Toggle Abstract
  We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.
• L. Duan, J. I. Cirac, P. Zoller Geometric Manipulation of Trapped Ions for Quantum Computation, Science 292 1695 (2001-06-01), http://dx.doi.org/10.1126/science.1058835 doi:10.1126/science.1058835 (ID: 337578) Toggle Abstract
  We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.
• D. Jaksch, S. Gardiner, K. Schulze, J. I. Cirac, P. Zoller Uniting Bose-Einstein Condensates in Optical Resonators, Phys. Rev. Lett. 86 004733 (2001-05-21), http://dx.doi.org/10.1103/PhysRevLett.86.4733 doi:10.1103/PhysRevLett.86.4733 (ID: 337582) Toggle Abstract
  The relative phase of two initially independent Bose-Einstein condensates can be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we show that this phase cooling process already appears within a semiclassical model. We calculate the stationary states, find regions of bistable behavior, and suggest a Ramsey-type experiment to measure the buildup of phase coherence between the condensates. We also study quantum effects and imperfections of the system.
• T. Calarco, J. I. Cirac, P. Zoller Entangling ions in arrays of microscopic traps, Phys. Rev. A 63 062304 (2001-05-14), http://dx.doi.org/10.1103/PhysRevA.63.062304 doi:10.1103/PhysRevA.63.062304 (ID: 337587) Toggle Abstract
  We consider a system of particles in an array of microscopic traps, coupled to each other via electrostatic interaction, and pushed by an external state-dependent force. We show how to implement a two-qubit quantum gate between two such particles with a high fidelity.
• S. Gardiner, K. M. Gheri, P. Zoller Cavity-assisted quasiparticle damping in a Bose-Einstein condensate, Phys. Rev. A 63 051603(R) (2001-04-19), http://dx.doi.org/10.1103/PhysRevA.63.051603 doi:10.1103/PhysRevA.63.051603 (ID: 337585) Toggle Abstract
  We consider an atomic Bose-Einstein condensate held within an optical cavity and interacting with laser fields. We show how the interaction of the cavity mode with the condensate can cause energy due to excitations to be coupled to a lossy cavity mode, which then decays, thus damping the condensate. We show how to choose parameters for damping specific excitations, and how to target a range of different excitations to potentially produce extremely cold condensates.
• L. J. Garay, J. R. Anglin, J. I. Cirac, P. Zoller Sonic black holes in dilute Bose-Einstein condensates, Phys. Rev. A 63 023611 (2001-01-17), http://dx.doi.org/10.1103/PhysRevA.63.023611 doi:10.1103/PhysRevA.63.023611 (ID: 337591) Toggle Abstract
  The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein condensates is investigated. It is shown that there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit behaviors completely analogous to that of gravitational black holes. The dynamical instabilities involve the creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an "atom sink," and a tight ring-shaped condensate. We also simulate the creation of a stable sonic black hole by solving the Gross-Pitaevskii equation numerically for a condensate subject to a trapping potential which is adiabatically deformed. A sonic black hole could, in this way, be created experimentally with state-of-the-art or planned technology.
• A. Sorensen, L. Duan, J. I. Cirac, P. Zoller Many-particle entanglement with Bose−Einstein condensates, Nature 409 63 (2001-01-04), http://dx.doi.org/10.1038/35051038 doi:10.1038/35051038 (ID: 337588) Toggle Abstract
  The possibility of creating and manipulating entangled states of systems of many particles is of significant interest for quantum information processing; such a capability could lead to new applications that rely on the basic principles of quantum mechanics1. So far, up to four atoms have been entangled in a controlled way. A crucial requirement for the production of entangled states is that they can be considered pure at the single-particle level. Bose−Einstein condensates fulfil this requirement; hence it is natural to investigate whether they can also be used in some applications of quantum information. Here we propose a method to achieve substantial entanglement of a large number of atoms in a Bose−Einstein condensate. A single resonant laser pulse is applied to all the atoms in the condensate, which is then allowed to evolve freely; in this latter stage, collisional interactions produce entanglement between the atoms. The technique should be realizable with present technology.
• C. Menotti, J. R. Anglin, J. I. Cirac, P. Zoller Dynamic splitting of a Bose-Einstein condensate, Phys. Rev. A 63 023601 (2001-01-04), http://dx.doi.org/10.1103/PhysRevA.63.023601 doi:10.1103/PhysRevA.63.023601 (ID: 337590) Toggle Abstract
  We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows us to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover, we can get some insight into the collective modes that are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.

Proceeding

• J. I. Cirac, L. Duan, P. Zoller Quantum optical implementation of quantum information processing, Proceedings of International School of Physics (2001), URL (ID: 383447) Toggle Abstract
  By popular request we post these old (from 2001) lecture notes of the Varenna Summer School Proceedings. The original was published as J. I. Cirac, L. M. Duan, and P. Zoller, in "Experimental Quantum Computation and Information" Proceedings of the International School of Physics "Enrico Fermi", Course CXLVIII, p. 263, edited by F. Di Martini and C. Monroe.

2000

Articles

• L. Duan, J. I. Cirac, P. Zoller, E. Polzik Quantum Communication between Atomic Ensembles Using Coherent Light, Phys. Rev. Lett. 85 005643 (2000-12-25), http://scitation.aip.org/jhtml/doi.jsp http://scitation.aip.org/jhtml/doi.jsp (ID: 337594) Toggle Abstract
  Protocols for quantum communication between massive particles, such as atoms, are usually based on making use of nonclassical light, and/or superhigh finesse optical cavities are normally needed to enhance interaction between atoms and photons. We demonstrate a remarkable result: by using only coherent light, entanglement can be generated between distant free space atomic ensembles, and an unknown quantum state can thus be teleported from one to another. Neither nonclassical light nor cavities are needed in the scheme, which greatly simplifies its experimental implementation.
• L. J. Garay, J. R. Anglin, J. I. Cirac, P. Zoller Sonic Analog of Gravitational Black Holes in Bose-Einstein Condensates, Phys. Rev. Lett. 85 4643 (2000-11-27), http://dx.doi.org/10.1103/PhysRevLett.85.4643 doi:10.1103/PhysRevLett.85.4643 (ID: 337595) Toggle Abstract
  It is shown that, in dilute-gas Bose-Einstein condensates, there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit a behavior resembling that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states, as in the well-known suggested mechanism for black-hole evaporation. We propose a scheme to generate a stable sonic black hole in a ring trap.
• L. Duan, G. Giedke, J. I. Cirac, P. Zoller Continuous variable entanglement purification and its physical implementation, J. Mod. Opt. 47 2529 (2000-11-20), URL (ID: 337615) Toggle Abstract
  We describe in detail an entanglement purification protocol which generates maximally entangled states with high efficiencies from realistic Gaussian continuous variable entangled states. A physical implementation of this protocol which uses high finesse cavities and cavity enhanced cross-Kerr nonlinearities is analysed.
• L. Duan, A. Sorensen, J. I. Cirac, P. Zoller Squeezing and Entanglement of Atomic Beams, Phys. Rev. Lett. 85 3991 (2000-11-06), http://dx.doi.org/10.1103/PhysRevLett.85.3991 doi:10.1103/PhysRevLett.85.3991 (ID: 337596) Toggle Abstract
  We propose and analyze a scheme for generating entangled atomic beams out of a Bose-Einstein condensate using spin-exchanging collisions. In particular, we show how to create both atomic squeezed states and entangled states of pairs of atoms.
• T. Calarco, H. J. Briegel, D. Jaksch, J. I. Cirac, P. Zoller Quantum Computing with Trapped Particles in Microscopic Potentials, Fortschr. Phys. 48 945 (2000-10-25), http://dx.doi.org/10.1002/1521-3978(200009)48:9/11 doi:10.1002/1521-3978(200009)48:9/11 (ID: 337593) Toggle Abstract
  We review recent proposals for performing entanglement manipulation via controlled interactions between trapped atoms. State-dependent, time-varying microscopic potentials allow one to obtain with high fidelity a conditional phase shift realizing a universal quantum gate. We discuss possible physical implementations with existing experimental techniques, for example optical lattices and magnetic micro-traps.
• T. Calarco, H. J. Briegel, D. Jaksch, J. I. Cirac, P. Zoller Entangling neutral atoms for quantum information processing, J. Mod. Opt. 47 2137 (2000-10-15), URL (ID: 337599) Toggle Abstract
  We review recent proposals for performing entanglement manipulation via cold collisions between neutral atoms. State-dependent, time-varying trapping potentials allow one to control the interaction between atoms, so that conditional phase shifts realizing a universal quantum gate can be obtained with high fidelity. We discuss possible physical implementations with existing experimental techniques, for example optical lattices and magnetic micro-traps.
• D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cote, M. Lukin Fast Quantum Gates for Neutral Atoms, Phys. Rev. Lett. 85 2208 (2000-09-04), http://dx.doi.org/10.1103/PhysRevLett.85.2208 doi:10.1103/PhysRevLett.85.2208 (ID: 337601) Toggle Abstract
  We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.
• L. Santos, G. V. Shlyapnikov, P. Zoller, M. Lewenstein Bose-Einstein Condensation in Trapped Dipolar Gases, Phys. Rev. Lett. 85 1791 (2000-08-28), http://dx.doi.org/10.1103/PhysRevLett.85.1791 doi:10.1103/PhysRevLett.85.1791 (ID: 337602) Toggle Abstract
  We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realizations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.
• L. Duan, G. Giedke, J. I. Cirac, P. Zoller Physical implementation for entanglement purification of Gaussian continuous-variable quantum states, Phys. Rev. A 62 32304 (2000-08-14), http://dx.doi.org/10.1103/PhysRevA.62.032304 doi:10.1103/PhysRevA.62.032304 (ID: 337600) Toggle Abstract
  We give a detailed description of the entanglement purification protocol which generates maximally entangled states with high efficiencies from realistic Gaussian continuous variable entangled states. The physical implementation of this protocol is extensively analyzed using high finesse cavities and cavity enhanced cross Kerr nonlinearities. In particular, we take into account many imperfections in the experimental scheme and calculate their influences. Quantitative requirements are given for the relevant experimental parameters.
• S. Gardiner, D. Jaksch, R. Dumhart, J. I. Cirac, P. Zoller Nonlinear matter wave dynamics with a chaotic potential, Phys. Rev. A 62 023612 (2000-07-20), http://dx.doi.org/10.1103/PhysRevA.62.023612 doi:10.1103/PhysRevA.62.023612 (ID: 337604) Toggle Abstract
  We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential, the one-dimensional delta-kicked harmonic oscillator, and its semiclassical limit, discovering in the process an interesting interference effect, where increasing the strength of the repulsive nonlinearity promotes localization of the wave function. We explore the feasibility of an experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion.
• P. Törmä, P. Zoller Laser Probing of Atomic Cooper Pairs, Phys. Rev. Lett. 85 487 (2000-07-17), http://dx.doi.org/10.1103/PhysRevLett.85.487 doi:10.1103/PhysRevLett.85.487 (ID: 337603) Toggle Abstract
  We consider a gas of attractively interacting cold fermionic atoms which are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length to one with almost no interactions. The process can be viewed as a tunneling of atomic population between the superconducting and the normal states of the gas. It can be used to detect the BCS ground state and to measure the superconducting order parameter.
• C. Saavedra, K. M. Gheri, P. Törmä, J. I. Cirac, P. Zoller Controlled source of entangled photonic qubits, Phys. Rev. A 61 062311 (2000-05-17), http://dx.doi.org/10.1103/PhysRevA.61.062311 doi:10.1103/PhysRevA.61.062311 (ID: 337605) Toggle Abstract
  We consider a general proposal for generating a train of entangled single-photon wavepackets. The photons are created inside a resonator via an interaction with an active medium. In the course of the generation process photons are transferred to the continuum outside the resonator through cavity loss. We show that wave packets generated in this way can be regarded as independent logical qubits. This and the possibility of producing strong entanglement between the qubits suggests many applications in quantum communication. We give a specific example in the context of cavity QED and show that undesired decoherence effects can be efficiently reduced in the considered scheme.
• L. Duan, G. Giedke, J. I. Cirac, P. Zoller Entanglement Purification of Gaussian Continuous Variable Quantum States, Phys. Rev. Lett. 84 4002 (2000-04-24), http://dx.doi.org/10.1103/PhysRevLett.84.4002 doi:10.1103/PhysRevLett.84.4002 (ID: 337607) Toggle Abstract
  We describe an entanglement purification protocol to generate maximally entangled states with high efficiencies from two-mode squeezed states or from mixed Gaussian continuous entangled states. The protocol relies on a local quantum nondemolition measurement of the total excitation number of several continuous variable entangled pairs. We propose an optical scheme to do this kind of measurement using cavity enhanced cross-Kerr interactions.
• J. J. García-Ripoll, J. I. Cirac, J. R. Anglin, V. M. Perez-Garcia, P. Zoller Spin monopoles with Bose-Einstein condensates, Phys. Rev. A 61 053609 (2000-04-17), http://dx.doi.org/10.1103/PhysRevA.61.053609 doi:10.1103/PhysRevA.61.053609 (ID: 337609) Toggle Abstract
  We study the feasibility of preparing a Bose-Einstein condensed sample of atoms in a macroscopic quantum state that resembles a spin monopole. In this state, the atomic internal spins lie in the x-y plane and point along the radial direction. The stability and dynamics of this structure are studied analytically in some cases and numerically in the more general situation. We find these structures to be stable objects giving rise to a nontrivial state of a Bose-Einstein condensate.
• J. I. Cirac, P. Zoller A scalable quantum computer with ions in an array of microtraps, Nature 404 579 (2000-04-06), http://dx.doi.org/10.1038/35007021 doi:10.1038/35007021 (ID: 337611) Toggle Abstract
  Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models—accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).
• P. Zoller Quantum optics: Tricks with a single photon, Nature 404 340 (2000-03-23), http://dx.doi.org/10.1038/35006185 doi:10.1038/35006185 (ID: 337610)
• L. Duan, G. Giedke, J. I. Cirac, P. Zoller Inseparability Criterion for Continuous Variable Systems, Phys. Rev. Lett. 84 2722 (2000-03-20), http://dx.doi.org/10.1103/PhysRevLett.84.2722 doi:10.1103/PhysRevLett.84.2722 (ID: 337606) Toggle Abstract
  An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.
• H. J. Briegel, T. Calarco, D. Jaksch, J. I. Cirac, P. Zoller Quantum computing with neutral atoms, J. Mod. Opt. 47 415 (2000-02-15), http://dx.doi.org/10.1080/095003400148303 doi:10.1080/095003400148303 (ID: 337608) Toggle Abstract
  We develop a method to entangle neutral atoms using cold controlled collisions. We analyse this method in two particular set-ups: optical lattices and magnetic microtraps. Both offer the possibility of performing certain multi-particle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for fault-tolerant computing.
• Gardiner, Crispin, P. Zoller Quantum kinetic theory. V. Quantum kinetic master equation for mutual interaction of condensate and noncondensate, Phys. Rev. A 61 033601 (2000-02-04), http://dx.doi.org/10.1103/PhysRevA.61.033601 doi:10.1103/PhysRevA.61.033601 (ID: 337612) Toggle Abstract
  A detailed quantum kinetic master equation is developed that couples the kinetics of a trapped condensate to the vapor of noncondensed particles. This generalizes previous work that treated the vapor as being undepleted.
• T. Calarco, E. A. Hinds, D. Jaksch, J. Schmiedmayer, J. I. Cirac, P. Zoller Quantum gates with neutral atoms: Controlling collisional interactions in time-dependent traps, Phys. Rev. A 61 022304 (2000-01-10), http://dx.doi.org/10.1103/PhysRevA.61.022304 doi:10.1103/PhysRevA.61.022304 (ID: 337613) Toggle Abstract
  We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.
• D. Jaksch, T. Calarco, P. Zoller Auf dem Weg zum universellen Quantencomputer, Physik in unserer Zeit 31 260 (2000), URL (ID: 337597) Toggle Abstract
  Die Quantenmechanik eröffnet faszinierende Perspektiven für die Kommunikation und die Informationsverarbeitung. Um universell programmierbare Quantenrechner realisieren zu können bedarf es der Implementierung von Konzepten zur Quanteninformationsverarbeitung die sich auf eine große Anzahl von Qubits anwenden lassen.
• J. F. Poyatos, J. I. Cirac, P. Zoller Schemes of Quantum Computations with Trapped Ions, Fortschr. Phys. 48 785 (2000), URL (ID: 337598) Toggle Abstract
  The purpose of this article is to review two complementary schemes for quantum computation with trapped ions. We initially discuss the first proposal of quantum computations with cold trapped ions (J. I. Cirac and P. Zoller; Phys. Rev. Lett. 74, 4091, 1995) which requires, prior to any computation, laser cooling to the motional ground state. This proposal is closely related to the physics of generating and manipulating N-particles entangled states in both ion traps and high-Q cavities (cavity quantum electrodynamics). The second scheme is that of quantum computations with hot trapped ions (J.F. Poyatos, J.I. Cirac and P. Zoller; Phys. Rev. Lett. 81, 1322, 1998) which works at finite temperature and resembles physical ideas found in atom interferometry.

1999

Articles

• G. Morigi, J. Eschner, J. I. Cirac, P. Zoller Laser Cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit, Phys. Rev. A 59 003793 (1999-05-00), http://dx.doi.org/10.1103/PhysRevA.59.3797 doi:10.1103/PhysRevA.59.3797 (ID: 352422) Toggle Abstract
  We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
• H. J. Kimble, J. I. Cirac, P. Zoller Quantum communication with dark photons, Phys. Rev. A 59 002659 (1999-04-00), http://dx.doi.org/10.1103/PhysRevA.59.2659 doi:10.1103/PhysRevA.59.2659 (ID: 352421) Toggle Abstract
  We show that quantum information may be transferred between atoms in different locations by using "phantom" or "dark" photons: the atoms are coupled through electromagnetic fields, but the corresponding field modes do not have to be fully populated. In the case where atoms are placed inside optical cavities, errors in quantum information processing due to photon absorption inside the cavity are diminished in this way. This effect persists up to intercavity distances of about a meter for the current levels of cavity losses, and may be useful for distributed quantum computing.
• G. Giedke, H. J. Briegel, J. I. Cirac, P. Zoller Lower bounds for attainable fidelities in entanglement purification, Phys. Rev. A 59 002641 (1999-04-00), http://dx.doi.org/10.1103/PhysRevA.59.2641 doi:10.1103/PhysRevA.59.2641 (ID: 352423) Toggle Abstract
  We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal completely positive map describing a purification step and the one in the presence of errors. We derive nonlinear maps for a lower bound of the fidelity at each purification step in terms of this parameter.
• D. Jaksch, H. J. Briegel, J. I. Cirac, Gardiner, Crispin, P. Zoller Entanglement of Atoms via Cold Controlled Collisions, Phys. Rev. Lett. 82 001975 (1999-03-01), http://dx.doi.org/10.1103/PhysRevLett.82.1975 doi:10.1103/PhysRevLett.82.1975 (ID: 352425) Toggle Abstract
  We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum gates and efficient creation of highly entangled states of many atoms in optical lattices.
• C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, P. Zoller Creation of entangled states of distant atoms by interference, Phys. Rev. A 59 001025 (1999-02-00), http://dx.doi.org/10.1103/PhysRevA.59.1025 doi:10.1103/PhysRevA.59.1025 (ID: 352426) Toggle Abstract
  We propose a scheme to create distant entangled atomic states. It is based on driving two (or more) atoms with a weak laser pulse, so that the probability that two atoms are excited is negligible. If the subsequent spontaneous emission is detected, the entangled state is created. We have developed a model to analyze the fidelity of the resulting state as a function of the dimensions and location of the detector, and the motional properties of the atoms.
• J. I. Cirac, P. Zoller Engineering Entangled States of Trapped Ions, Physics World 01 (1999-01-00), (ID: 352424)
• W. Dür, H. J. Briegel, J. I. Cirac, P. Zoller Quantum repeaters based on entanglement purification, Phys. Rev. A 59 000169 (1999-01-00), http://dx.doi.org/10.1103/PhysRevA.59.169 doi:10.1103/PhysRevA.59.169 (ID: 352427) Toggle Abstract
  We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
• G. Morigi, J. Eschner, J. I. Cirac, P. Zoller Laser cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit, Phys. Rev. A 59 3797 (1999), (ID: 344243) Toggle Abstract
  We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
• K. M. Gheri, P. Törmä, P. Zoller Quantum state engineering with photonic qubits, Acta Physica Slovaca 49 523 (1999), URL (ID: 352420) Toggle Abstract
  We outline a scheme for the generation of a train of entangled single-photon wavepackets using standard CQED-techniques. The generated photons are transferred to the continuum outside the resonator through cavity loss in the form of wavepackets each of which may be regarded as a logical qubit. We show that undesired decoherence effects can be efficiently reduced in the considered scheme.
• H. J. Briegel, J. I. Cirac, P. Zoller Quantencomputer: Wie sich Verschränkung für die Informationsverarbeitung nutzen lässt, Physikalische Blätter 55 37 (1999), (ID: 537023)

Proceedings

• H. J. Briegel, J. I. Cirac, P. Zoller EPR correlations made useful. A quantum communication perspective, Cybernetics and Systems '98 (1999), URL (ID: 352419) Toggle Abstract
  Maximally entangled states of particles play a key role in quantum communication, for teleportation and cryptography. We discuss the essential steps that are needed to establish EPR-type correlations of high fidelity over a noisy channel such as an optical fiber.
• H. J. Briegel, J. I. Cirac, Gardiner, Crispin, D. Jaksch, P. Zoller Quantum computing in optical lattices, Technical Digest, Summaries of papers presented at the Quantum Electronics and Laser Science Conference Postconference Edition (Wasington-USA) 283-112 (1999), (ID: 383510)
• H. J. Briegel, T. Calarco, D. Jaksch, J. I. Cirac, P. Zoller Quantum optical systems for implementation of quantum information processes, Laser Spectroscopy 14th International Conference 256-65 (1999), (ID: 383517)

1998

Articles

• H. J. Briegel, W. Dür, J. I. Cirac, P. Zoller Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication, Phys. Rev. Lett. 81 5932 (1998-12-26), http://dx.doi.org/10.1103/PhysRevLett.81.5932 doi:10.1103/PhysRevLett.81.5932 (ID: 367760) Toggle Abstract
  In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. Our scheme tolerates general errors on the percent level, it works with a polynomial overhead in time and a logarithmic overhead in the number of particles that need to be controlled locally.
• Gardiner, Crispin, M. D. Lee, R. J. Ballagh, M. J. Davis, P. Zoller Quantum Kinetic Theory of Condensate Growth: Comparison of Experiment and Theory, Phys. Rev. Lett. 81 5266 (1998-12-14), http://dx.doi.org/10.1103/PhysRevLett.81.5266 doi:10.1103/PhysRevLett.81.5266 (ID: 367762) Toggle Abstract
  In a major extension of our previous model [Phys. Rev. Lett. 79, 1793 (1997)] of condensate growth, we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels. We find good agreement with experiment, especially at higher temperatures. We also confirm the picture of the "kinetic" region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient W^+.
• D. Jaksch, C. Bruder, J. I. Cirac, Gardiner, Crispin, P. Zoller Cold Bosonic Atoms in Optical Lattices, Phys. Rev. Lett. 81 3108 (1998-10-12), http://dx.doi.org/10.1103/PhysRevLett.81.3108 doi:10.1103/PhysRevLett.81.3108 (ID: 367764) Toggle Abstract
  The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (“optical crystal”). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
• K. M. Gheri, C. Saavedra, P. Törmä, J. I. Cirac, P. Zoller Entanglement engineering of one-photon wave packets using a single-atom source, Phys. Rev. A 58 R2627 (1998-10-00), http://dx.doi.org/10.1103/PhysRevA.58.R2627 doi:10.1103/PhysRevA.58.R2627 (ID: 367766) Toggle Abstract
  We propose a cavity-QED scheme for the controlled generation of sequences of entangled single-photon wave packets. A photon is created inside a cavity via an active medium, such as an atom, and decays into the continuum of radiation modes outside the cavity. Subsequent wave packets generated in this way behave as independent logical quantum bits (qubits). This and the possibility of producing maximally entangled multiqubit states suggest many applications in quantum communication.
• H. J. Briegel, W. Dür, J. I. Cirac, P. Zoller Quantum communication and the creation of maximally entangled pairs of atoms over a noisy channel, Phil. Trans. R. Soc. Lond. A 356 1841 (1998-08-15), http://dx.doi.org/10.1098/rsta.1998.0252 doi:10.1098/rsta.1998.0252 (ID: 367767) Toggle Abstract
  We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high-Q optical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the 'absorption free channel'. A concatenation protocol using the absorption free channel allows for quantum communication with single qubits over distances much larger than the coherence length of the channel.
• T. Busch, J. R. Anglin, J. I. Cirac, P. Zoller Inhibition of spontaneous emission in Fermi gases, 44 1 (1998-08-10), http://dx.doi.org/10.1209/epl/i1998-00426-2 doi:10.1209/epl/i1998-00426-2 (ID: 367757) Toggle Abstract
  Fermi inhibition is a quantum-statistical analogue for the inhibition of spontaneous emission by an excited atom in a cavity. This is achieved when the relevant motional states are already occupied by a cloud of cold atoms in the internal ground state. We exhibit non-trivial effects at finite temperature and in anisotropic traps, and briefly consider a possible experimental realization.
• J. F. Poyatos, J. I. Cirac, P. Zoller Quantum Gates with “Hot” Trapped Ions, Phys. Rev. Lett. 81 1322 (1998-08-10), http://dx.doi.org/10.1103/PhysRevLett.81.1322 doi:10.1103/PhysRevLett.81.1322 (ID: 367770) Toggle Abstract
  We propose a scheme to perform a fundamental two-qubit gate between two trapped ions using ideas from atom interferometry. As opposed to the scheme considered by J. I. Cirac and P. Zoller, [Phys. Rev. Lett. 74, 4091 (1995)], it does not require laser cooling to the motional ground state.
• D. Jaksch, Gardiner, Crispin, K. M. Gheri, P. Zoller Quantum kinetic theory. IV. Intensity and amplitude fluctuations of a Bose-Einstein condensate at finite temperature including trap loss, Phys. Rev. A 58 1450 (1998-08-00), http://dx.doi.org/10.1103/PhysRevA.58.1450 doi:10.1103/PhysRevA.58.1450 (ID: 367772) Toggle Abstract
  We use the quantum kinetic theory to calculate the steady state and fluctuations of a trapped Bose-Einstein condensate at a finite temperature. The system is divided in a condensate and a noncondensate part. A quantum-mechanical description based on the number-conserving Bogoliubov method is used for describing the condensate part. The noncondensed particles are treated as a classical gas in thermal equilibrium with temperature T and chemical potential μ. We find a master equation for the reduced density operator of the Bose-Einstein condensate, calculate the steady state of the system, and investigate the effect of one-, two-, and three-particle losses on the condensate. Using linearized Ito equations, we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. A Lorentzian line shape is found for the intensity correlation function that is characterized by a time constant γI-1 derived in the paper. For the amplitude correlation function, we find ballistic behavior for time differences smaller than γI-1, and diffusive behavior for larger time differences.
• Gardiner, Crispin, P. Zoller Quantum kinetic theory. III. Quantum kinetic master equation for strongly condensed trapped systems, Phys. Rev. A 58 536 (1998-07-00), http://dx.doi.org/10.1103/PhysRevA.58.536 doi:10.1103/PhysRevA.58.536 (ID: 367769) Toggle Abstract
  We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle-number-conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles—nevertheless, the stationary state exhibits the property of off-diagonal long-range order, to the extent that this concept makes sense in a tightly trapped condensate.
• R. Dumhart, J. I. Cirac, M. Lewenstein, P. Zoller Creation of Dark Solitons and Vortices in Bose-Einstein Condensates, Phys. Rev. Lett. 80 2972 (1998-04-06), http://dx.doi.org/10.1103/PhysRevLett.80.2972 doi:10.1103/PhysRevLett.80.2972 (ID: 367776) Toggle Abstract
  We propose and analyze a scheme to create dark solitons and vortices in Bose-Einstein condensates. This is achieved starting from a condensate in the internal state |a> and transferring the atoms to the internal state |b> via a Raman transition induced by laser light. By scanning adiabatically the Raman detuning, dark solitons and vortices are created.
• G. Morigi, J. I. Cirac, K. Ellinger, P. Zoller Laser cooling of trapped atoms to the ground state: A dark state in position space, Phys. Rev. A 57 2909 (1998-04-00), http://dx.doi.org/10.1103/PhysRevA.57.2909 doi:10.1103/PhysRevA.57.2909 (ID: 367774) Toggle Abstract
  We propose a scheme that allows us to laser cool trapped atoms to the ground state of a one-dimensional confining potential. The scheme is based on the creation of a dark state by designing the laser profile, so that the hottest atoms are coherently pumped to another internal level, and then repumped back. The scheme works beyond the Lamb-Dicke limit. We present results of a full quantum treatment for a one-dimensional model.
• J. I. Cirac, M. Lewenstein, K. Moelmer, P. Zoller Quantum superposition states of Bose-Einstein condensates, Phys. Rev. A 57 1208 (1998-02-00), http://dx.doi.org/10.1103/PhysRevA.57.1208 doi:10.1103/PhysRevA.57.1208 (ID: 367775) Toggle Abstract
  We propose a scheme to create a macroscopic "Schrödinger-cat" state formed by two interacting Bose condensates. In analogy with quantum optics, where the control and engineering of quantum states can be maintained to a large extent, we consider the present scheme to be an example of quantum atom optics at work.
• P. Zoller Photonic Channels for Quantum Communication, Science 279 205 (1998-01-09), http://dx.doi.org/10.1126/science.279.5348.205 doi:10.1126/science.279.5348.205 (ID: 367794) Toggle Abstract
  A general photonic channel for quantum communication is defined. By means of local quantum computing with a few auxiliary atoms, this channel can be reduced to one with effectively less noise. A scheme based on quantum interference is proposed that iteratively improves the fidelity of distant entangled particles.
• N. Lütkenhaus, J. I. Cirac, P. Zoller Mimicking a squeezed-bath interaction: Quantum-reservoir engineering with atoms, 57 548 (1998-01-00), http://dx.doi.org/10.1103/PhysRevA.57.548 doi:10.1103/PhysRevA.57.548 (ID: 367777) Toggle Abstract
  The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a 4 pi squeezed vacuum. In this paper we show how to "engineer" a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum J = 1/2 --> J = 1/2 transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath–atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number N and the squeezing phase phi. We present results of a detailed analytical and numerical study.
• J. I. Cirac, P. Zoller, H. J. Kimble, H. Mabuchi Quantum Communication in a Quantum Network, Physica Scripta T76 223 (1998), URL (ID: 367768) Toggle Abstract
  We propose a physical implementation for quantum communication in quantum networks. Our scheme demonstrates how to transfer quantum information between spatially separated atoms, which are each inside a high-Q optical cavity, and how to establish a distant maximally entangled pair, by sending photons through a general, noisy channel, such as a standard optical fiber.
• K. M. Gheri, K. Ellinger, T. Pellizzari, P. Zoller Photon-Wavepackets as Flying Quantum Bits, Fortschr. Phys. 46 401 (1998), URL (ID: 367773) Toggle Abstract
  A novel description of the interaction of quantum optical systems with a single one-photon wave packet in terms of a generalized master equation is introduced. A corresponding quantum Monte-Carlo wavefunction simulation algorithm can be obtained from the driven system approach [H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993); C. W. Gardiner, ibid. 2269 (1993)].
• J. I. Cirac, P. Zoller Quantenkommunikation und Quantencomputing, Mitteilungsblatt d. Österr. Physikal. Ges. 1 (1998), URL (ID: 367793)
• J. F. Poyatos, J. I. Cirac, P. Zoller Characterization of decoherence processes in quantum computation, Optics Express 2 372 (1998), (ID: 367802)
• P. Zoller, H. J. Kimble, H. Mabuchi Transmission of quantum information in a quantum network: A quantum optical implementation, Fortschr. Phys. 46 689 (1998), URL (ID: 367803) Toggle Abstract
  We show how to transmit quantum communication reliably between the nodes of a quantum network. The nodes are represented by atoms, stored in a trap. The communication is accomplished via photons, which are coupled to the atoms by a high-Q cavity. We discuss the effects of decoherence and ways to correct for the corresponding errors.

Proceedings

• H. J. Briegel, J. I. Cirac, P. Zoller Creation of Maximally Entangled Pairs of Atoms over a noisy channel: a finite-means approach, Proceedings of the 5th International Wigner Symposium (Vienna-Austria, 1997-08-25) 422 (1998), (ID: 383525)
• H. J. Briegel, W. Dür, J. I. Cirac, P. Zoller Quantum Communication and Computation, Proceedings of the International Conference on Atomic Physics (Canada, 1998-08-08) (1998), (ID: 411701)

1997

Articles

• S. van Enk, J. I. Cirac, P. Zoller Purifying Two-Bit Quantum Gates and Joint Measurements in Cavity QED, Phys. Rev. Lett. 79 5178 (1997-12-22), http://dx.doi.org/10.1103/PhysRevLett.79.5178 doi:10.1103/PhysRevLett.79.5178 (ID: 367806) Toggle Abstract
  Using a cavity QED setup we show how to implement a particular joint measurement on two atoms in a fault tolerant way. Based on this scheme, we illustrate how to realize quantum communication over a noisy channel when local operations are subject to errors. We also present a scheme to perform and purify a fundamental two-bit gate.
• S. Gardiner, J. I. Cirac, P. Zoller Quantum Chaos in an Ion Trap: The Delta-Kicked Harmonic Oscillator, Phys. Rev. Lett. 79 4790 (1997-12-15), http://dx.doi.org/10.1103/PhysRevLett.79.4790 doi:10.1103/PhysRevLett.79.4790 (ID: 367800) Toggle Abstract
  We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.
• T. Busch, J. I. Cirac, V. M. Perez-Garcia, P. Zoller Stability and collective excitations of a two-component Bose-Einstein condensed gas: A moment approach, Phys. Rev. A 56 2978 (1997-10-04), http://dx.doi.org/10.1103/PhysRevA.56.2978 doi:10.1103/PhysRevA.56.2978 (ID: 367807) Toggle Abstract
  The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative s-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.
• J. I. Cirac, P. Zoller, H. J. Kimble, H. Mabuchi Quantum state transfer in a quantum network: a quantum-optical implementation, J. Mod. Opt. 44 1727 (1997-10-01), http://dx.doi.org/10.1080/095003497152762 doi:10.1080/095003497152762 (ID: 367805) Toggle Abstract
  We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. We also propose a method to correct errors during transmission.
• Gardiner, Crispin, P. Zoller, R. J. Ballagh, M. J. Davis Kinetics of Bose-Einstein Condensation in a Trap, Phys. Rev. Lett. 79 1793 (1997-09-08), http://dx.doi.org/10.1103/PhysRevLett.79.1793 doi:10.1103/PhysRevLett.79.1793 (ID: 367808) Toggle Abstract
  The formation process of a Bose-Einstein condensate in a trap is described using a master equation based on quantum kinetic theory, which can be well approximated by a description using only the condensate mode in interaction with a thermalized bath of noncondensate atoms. A rate equation of the form n-dot = 2W+(n)[(1–exp((µn–µ)/kT))n + 1] is derived, in which the difference between the condensate chemical potential µn and the bath chemical potential µ gives the essential behavior. Solutions of this equation give a characteristic latency period for condensate formation and appear to be consistent with the observed behavior of both rubidium and sodium condensate formation.
• V. M. Perez-Garcia, H. Michinel, J. I. Cirac, M. Lewenstein, P. Zoller Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations, Phys. Rev. A 56 1424 (1997-08-00), http://dx.doi.org/10.1103/PhysRevA.56.1424 doi:10.1103/PhysRevA.56.1424 (ID: 367809) Toggle Abstract
  A variational technique is applied to solve the time-dependent nonlinear Schrödinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schrödinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.
• D. Jaksch, Gardiner, Crispin, P. Zoller Quantum kinetic theory. II. Simulation of the quantum Boltzmann master equation, Phys. Rev. A 56 575 (1997-07-00), http://dx.doi.org/10.1103/PhysRevA.56.575 doi:10.1103/PhysRevA.56.575 (ID: 367810) Toggle Abstract
  We present results of simulations of a quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equation derived in previous work. We consider two cases of trapping potentials: a three-dimensional square-well potential with periodic boundary conditions and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.
• S. van Enk, J. I. Cirac, P. Zoller Ideal Quantum Communication over Noisy Channels: A Quantum Optical Implementation, Phys. Rev. Lett. 78 4293 (1997-06-02), http://dx.doi.org/10.1103/PhysRevLett.78.4293 doi:10.1103/PhysRevLett.78.4293 (ID: 367812) Toggle Abstract
  We consider transmission of a quantum state between two distant atoms via photons. Based on a quantum-optical realistic model, we define a noisy quantum channel which includes systematic errors as well as errors due to coupling to the environment. We present a protocol that allows one to accomplish ideal transmission by repeating the transfer operation as many times as needed.
• G. Morigi, J. I. Cirac, M. Lewenstein, P. Zoller Ground-state laser cooling beyond the Lamb-Dicke limit, 39 13 (1997-05-26), http://dx.doi.org/10.1209/epl/i1997-00306-3 doi:10.1209/epl/i1997-00306-3 (ID: 367813) Toggle Abstract
  We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state |0>. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.
• J. I. Cirac, P. Zoller, H. J. Kimble, H. Mabuchi Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Phys. Rev. Lett. 78 3221 (1997-04-21), http://dx.doi.org/10.1103/PhysRevLett.78.3221 doi:10.1103/PhysRevLett.78.3221 (ID: 367814) Toggle Abstract
  We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. The transmission protocol employs special laser pulses that excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wave packet that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.
• Gardiner, Crispin, P. Zoller Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential, Phys. Rev. A 55 2902 (1997-04-00), http://dx.doi.org/10.1103/PhysRevA.55.2902 doi:10.1103/PhysRevA.55.2902 (ID: 367811) Toggle Abstract
  A quantum kinetic master equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.
• S. Gardiner, J. I. Cirac, P. Zoller Nonclassical states and measurement of general motional observables of a trapped ion, Phys. Rev. A 55 1683 (1997-03-00), http://dx.doi.org/10.1103/PhysRevA.55.1683 doi:10.1103/PhysRevA.55.1683 (ID: 367815) Toggle Abstract
  We describe a method to perform a single quantum measurement of an arbitrary motional observable of a single ion moving in a harmonic potential. We illustrate the measurement procedure with explicit examples, namely the position and phase observables. A necessary tool for this is the ability to synthesize an arbitrary motional state. In addition, we show how to generalize this to higher dimensions, and show explicit examples of how to engineer states in two spatial dimensions, including a proposed experimental configuration.
• J. F. Poyatos, J. I. Cirac, P. Zoller Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate, Phys. Rev. Lett. 78 390 (1997-01-13), http://dx.doi.org/10.1103/PhysRevLett.78.390 doi:10.1103/PhysRevLett.78.390 (ID: 367817) Toggle Abstract
  We show how to fully characterize a quantum process in an open quantum system. We particularize the procedure to the case of a universal two-qubit gate in a quantum computer. We illustrate the method with a numerical simulation of a quantum gate in the ion trap quantum computer.
• H. Stecher, H. Ritsch, P. Zoller, F. Sander, T. Esslinger, T. W. Hänsch All-optical gray lattice for atoms, Phys. Rev. A 55 545 (1997-01-00), http://dx.doi.org/10.1103/PhysRevA.55.545 doi:10.1103/PhysRevA.55.545 (ID: 367816) Toggle Abstract
  We create a gray optical lattice structure using a blue detuned laser field coupling an atomic ground state of angular momentum J simultaneously to two excited states with angular momenta J and J – 1. The atoms are cooled and trapped at locations of purely circular polarization. The cooling process efficiently accumulates almost half of the atomic population in the lowest-energy band, which is only weakly coupled to the light field. Very low kinetic temperatures are obtained by adiabatically reducing the optical potential. The dynamics of this process is analyzed using a full quantum Monte Carlo simulation. The calculations explicitly show the mapping of the band populations on the corresponding momentum intervals of the free atom. In an experiment with subrecoil momentum resolution we measure the band populations and find excellent absolute agreement with the theoretical calculations.

Proceeding

• J. I. Cirac, T. Pellizzari, J. F. Poyatos, P. Zoller Quantum Computing and Decoherence in Quantum Optical Systems, Quantum Communication, Computing, and Measurement Quantum Communications and Measurement Conference (Shizuoka, Japan, 1996-09-25) (1997), URL (ID: 305713) Toggle Abstract
  We present recent theoretical results in the context of quantum computing and error correction. In particular, a short review of the ion trap quantum computer is given. Moreover, we present a novel scheme for quantum gate error correction in the ion trap model system. Finally, a method for a tomographic characterization of quantum gates is presented.

1996

Articles

• M. Naraschewski, H. Wallis, A. Schenzle, J. I. Cirac, P. Zoller Interference of Bose condensates, Phys. Rev. A 54 2185–2196 (1996), http://dx.doi.org/10.1103/PhysRevA.54.2185 doi:10.1103/PhysRevA.54.2185 (ID: 305682) Toggle Abstract
  We investigate the prospects of atomic interference using samples of Bose condensed atoms. First we show the ability of two independent Bose condensates to create an interference pattern. This holds even if both condensates are described by Fock states. Thus, the existence of an experimental signature for a broken gauge symmetry, seen in a single run of the experiment, is not necessarily reflected by a broken symmetry on the level of the quantum mechanical state vector. Based on these results, we simulate numerically a recent experiment with two independent Bose condensates [K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995)]. The existence of interference fringes is predicted based on the nonlinear Schrödinger equation. Finally we study theoretically the influence of finite temperatures on the visibility of the interference in a double pinhole configuration.
• R. Walser, J. I. Cirac, P. Zoller Magnetic Tomography of a Cavity State, Phys. Rev. Lett. 77 002658 (1996), http://dx.doi.org/10.1103/PhysRevLett.77.2658 doi:10.1103/PhysRevLett.77.2658 (ID: 305684) Toggle Abstract
  A method to determine the state of a single quantized cavity mode is proposed. By adiabatic passage, the quantum state of the field is transferred completely onto an internal Zeeman submanifold of an atom. Utilizing a method of Newton and Young [Ann. Phys. 49, 393 (1968)], we can determine this angular momentum state uniquely, by a finite number of magnetic dipole measurements with Stern-Gerlach analyzers. An example illustrates the influence of dissipation.
• J. I. Cirac, Gardiner, Crispin, M. Naraschewski, P. Zoller Continuous observation of interference fringes from Bose condensates, Phys. Rev. A 54 R3714–R3717 (1996), http://dx.doi.org/10.1103/PhysRevA.54.R3714 doi:10.1103/PhysRevA.54.R3714 (ID: 305685) Toggle Abstract
  We use continuous measurement theory to describe the evolution of two Bose condensates in an interference experiment. It is shown how in a single run the system evolves into a state with a fixed relative phase, without violating particle number conservation.
• J. F. Poyatos, R. Walser, J. I. Cirac, P. Zoller Motion tomography of a single trapped ion, Phys. Rev. A 53 R1966–R1969 (1996), http://dx.doi.org/10.1103/PhysRevA.53.R1966 doi:10.1103/PhysRevA.53.R1966 (ID: 305687) Toggle Abstract
  A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground-state population of the trap after a sudden change of the trapping potential. In particular, we show how the Q( alpha ) function and the quadrature distribution P(x, theta ) can be measured directly. In an example we demonstrate the principle and analyze the sensitivity of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions.
• J. F. Poyatos, J. I. Cirac, P. Zoller Quantum Reservoir Engineering with Laser Cooled Trapped Ions, Phys. Rev. Lett. 77 004728 (1996), http://dx.doi.org/10.1103/PhysRevLett.77.4728 doi:10.1103/PhysRevLett.77.4728 (ID: 305700) Toggle Abstract
  We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.
• V. M. Perez-Garcia, H. Michinel, J. I. Cirac, M. Lewenstein, P. Zoller Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis, Phys. Rev. Lett. 77 005320 (1996), http://dx.doi.org/10.1103/PhysRevLett.77.5320 doi:10.1103/PhysRevLett.77.5320 (ID: 305704) Toggle Abstract
  We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.
• R. Blatt, P. Zoller Quantengatter für Quantenrechner, Physikalische Blätter 52 205 (1996), (ID: 344248)
• J. F. Poyatos, J. I. Cirac, R. Blatt, P. Zoller Trapped ions in the strong excitation regime: ion interferometry and non-classical states, Phys. Rev. A 54 1532 (1996), (ID: 344249)
• J. F. Poyatos, R. Walser, J. I. Cirac, R. Blatt, P. Zoller Motion tomography of a single trapped ion, Phys. Rev. A 53 R1966 (1996), (ID: 344250)
• J. I. Cirac, A. S. Parkins, R. Blatt, P. Zoller Non-Classical States of Motion in Ion Traps, Adv. Atom. Molec. and Opt. Physics 37 238-296 (1996), (ID: 619592)

Proceedings

• T. Pellizzari, J. F. Poyatos, J. I. Cirac, P. Zoller Quantum Computing and Decoherence in Quantum Optical Systems, Proceedings of the Third International Conference on Quantum Communication and Measurement Plenum Press 1997 (Shizuoka, Japan, 1996-09-30) 159 (1996), (ID: 411705)
• J. I. Cirac, S. Gardiner, T. Pellizzari, J. F. Poyatos, P. Zoller Synthesis of Entangled States and Quantum Computing, . Fifteenth International Conference on Atomic Physics (Amsterdam, The Netherlands, 1996-08-09) (1996), (ID: 413458)
• R. Blatt, J. F. Poyatos, J. I. Cirac, P. Zoller Quantum motion of a trapped ion: Schrödinger cats, ion interferometry and quantum tomography, Proceedings of the 5th Symposium on Frequency Standards and Metrology 20 (1996), (ID: 629057)

1995

Articles

• L. You, J. Cooper, P. Zoller Quantum-classical correspondences for atomic operators: a positive presentation approach, JOSA B 12 1774 (1995), URL (ID: 303476)
• T. Pellizzari, P. Marte, P. Zoller Laser cooling to a single quantum state in a trap: One-dimensional results, Phys. Rev. A 52 4709–4718 (1995), http://dx.doi.org/10.1103/PhysRevA.52.4709 doi:10.1103/PhysRevA.52.4709 (ID: 303487) Toggle Abstract
  Laser cooling in a trap is investigated for laser and trapping configurations which allow the existence of approximate ``dark states´´ of the combined atom-plus-trap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a one-dimensional (1D) free-particle dark state in angular momentum Jg=1 to Je=1 transitions and in two counterpropagating laser fields survives as an approximate dark state in a ``flat-bottom´´ trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonic-oscillator potentials. In the latter configuration we are able to provide analytical results.
• T. Pellizzari, S. Gardiner, J. I. Cirac, P. Zoller Decoherence, continuous observation, and quantum computing: a cavity qed model, Phys. Rev. Lett. 75 3788–3791 (1995), http://dx.doi.org/10.1103/PhysRevLett.75.3788 doi:10.1103/PhysRevLett.75.3788 (ID: 303489) Toggle Abstract
  We use the theory of continuous measurement to analyze the effects of decoherence on a realistic model of a quantum computer based on cavity QED. We show how decoherence affects the computation, and methods to prevent it.
• A. S. Parkins, P. Marte, P. Zoller, O. Carnal, H. J. Kimble Quantum-state mapping between multilevel atoms and cavity light fields, Phys. Rev. A 51 1578–1596 (1995), http://dx.doi.org/10.1103/PhysRevA.51.1578 doi:10.1103/PhysRevA.51.1578 (ID: 303497) Toggle Abstract
  A scheme for the preparation of Fock states and general superposition states of the electromagnetic field in a cavity is studied in detail. The scheme uses adiabatic passage in a strongly coupled atom-cavity system to ``map´´ atomic ground-state Zeeman coherence onto the cavity-mode field. We model photon-counting and homodyne measurements of the field exiting the cavity and demonstrate the possibility of generating and detecting highly nonclassical states of the field parameter values close to currently realizable experimental values. The adiabatic passage process is also reversible, enabling cavity-mode fields to be mapped onto atomic ground-state Zeeman coherence. Application of this property to the measurement of cavity fields is discussed, with particular consideration given to a possible scheme for quantum measurements of the intracavity photon number.
• S. Marksteiner, R. Walser, P. Marte, P. Zoller Localization of atoms in light fields: Optical molasses, adiabatic compression and squeezing, Appl. Phys. B Las. Opt. 60 145 - 153 (1995), http://dx.doi.org/10.1007/BF01135856 doi:10.1007/BF01135856 (ID: 303542) Toggle Abstract
  We present a theoretical study of the localization1 of atoms with an angular momentumJ g=3 toJ e=4 transition (e.g., chromium atoms) in quantized optical molasses created by two counterpropagating linearly polarized laser beams. We study the localization as a function of the potential depth, the angle between the polarizations and the interaction time with the molasses in the low-intensity limit, and discuss the possibility of adiabatic compression and squeezing of the atomic distribution.
• M. Lewenstein, J. I. Cirac, P. Zoller Master equation for sympathetic cooling of trapped particles, Phys. Rev. A 51 4617–4627 (1995), http://dx.doi.org/10.1103/PhysRevA.51.4617 doi:10.1103/PhysRevA.51.4617 (ID: 305613) Toggle Abstract
  A model for cooling a system of bosons in a harmonic trap via their interactions with a thermal bath of other particles is studied. The master equation describing the evolution of the system is derived for an arbitrary number of spatial dimensions. This equation is characterized by transition rates between trap levels. We present an analytic approximation for these rates and compare it with exact formulas, derived for the case of an even number of spatial dimensions. Analytic expressions show very good agreement with the exact ones for a wide range of parameters. We also discuss the cooling dynamics in terms of the approximated rates.
• J. I. Cirac, P. Zoller Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. 74 4091–4094 (1995), http://dx.doi.org/10.1103/PhysRevLett.74.4091 doi:10.1103/PhysRevLett.74.4091 (ID: 305614) Toggle Abstract
  A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. Quantum gates involving any pair, triplet, or subset of ions can be realized by coupling the ions through the collective quantized motion. In this system decoherence is negligible, and the measurement (readout of the quantum register) can be carried out with a high efficiency.
• J. I. Cirac, M. Lewenstein, P. Zoller Generalized Bose-Einstein distributions and multistability of a laser-cooled gas, Phys. Rev. A 51 2899–2907 (1995), http://dx.doi.org/10.1103/PhysRevA.51.2899 doi:10.1103/PhysRevA.51.2899 (ID: 305618) Toggle Abstract
  We study the dynamics of a system of atoms undergoing laser cooling in a microtrap. Using a simple model, we show that the stationary state of the system can be different from the standard Bose-Einstein distribution. In particular, it can exhibit infinite sequences of phase transitions as a function of laser detuning, as well as multistable behavior. This is due to the combination of quantum statistical phenomena and other effects related to the laser-cooling process.
• J. I. Cirac, M. Lewenstein, P. Zoller Laser cooling a trapped atom in a cavity: Bad-cavity limit, Phys. Rev. A 51 1650–1655 (1995), http://dx.doi.org/10.1103/PhysRevA.51.1650 doi:10.1103/PhysRevA.51.1650 (ID: 305621) Toggle Abstract
  We analyze theoretically a one-dimensional model of laser cooling of an atom or ion trapped in a cavity. We assume that the cavity loss rate is much larger than the atom-cavity coupling (bad-cavity limit) and that the atomic excited state is weakly occupied (low saturation limit). After elimination of the cavity mode and the atomic excited state, we derive rate equations for the populations of the trap states. We find that in the Lamb-Dicke limit the atom can be cooled to the ground state of the trap even in the strong confinement limit. This result is interpreted in terms of quantum interferences between different cooling and heating processes involving spontaneous emission in the cavity.
• R. Blatt, J. I. Cirac, P. Zoller Trapping states of motion with cold ions, Phys. Rev. A 52 518–524 (1995), http://dx.doi.org/10.1103/PhysRevA.52.518 doi:10.1103/PhysRevA.52.518 (ID: 305623) Toggle Abstract
  We describe a simple technique to prepare Fock states of the motion of an atom trapped in a harmonic potential. The method is based on using two lasers which interact with a weak and strong transition of the atom successively. Application of a well-defined pulse length on the weak transition leaves the population of some states out of the oscillator manifold unchanged (trapping states). Interaction on the strong transition with a second laser is used to repopulate one of these states via a third intermediate level.
• R. Blatt, J. I. Cirac, A. S. Parkins, P. Zoller Quantum motion of trapped ions, Physica Scripta T59 294 (1995), (ID: 305661)

Proceeding

• P. Zoller, Gardiner, Crispin Les Houches, (1995-07-28) Quantum noise in quantum optics, the Stochastic Schrödinger Equation (1995), (ID: 413469)

1994

Articles

• J. Lawall, M. Prentiss, L. S. Goldner, C. Gerz, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, P. Zoller Pushing atoms with darkness, Adiabatic momentum transfer, Optics and Photonic News (1994-12-28), (ID: 375176)
• R. Dumhart, P. Marte, T. Pellizzari, P. Zoller Laser Cooling to a Single Quantum State in a Trap, Phys. Rev. Lett. 73 2829–2832 (1994-11-21), http://dx.doi.org/10.1103/PhysRevLett.73.2829 doi:10.1103/PhysRevLett.73.2829 (ID: 375181) Toggle Abstract
  Laser cooling in a trap is investigated for configurations which allow the existence of "dark states" of the combined atom-plus-trap system, i.e., states which are decoupled from the laser light by quantum interference. Two examples of approximate dark states in a 1D flat bottom and 2D harmonic trap for angular momentum 1 to 1 transitions are discussed. A wave function simulation of the quantum master equation predicts that a significant fraction of the atoms are transferred to a single trap state. ©1994 The American Physical Society
• R. Walser, J. Cooper, P. Zoller Saturated absorption spectroscopy using diode-laser phase noise, Phys. Lett. A 50 4303–4309 (1994-11-05), http://dx.doi.org/10.1103/PhysRevA.50.4303 doi:10.1103/PhysRevA.50.4303 (ID: 375171) Toggle Abstract
  We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.
• J. I. Cirac, P. Zoller Preparation of macroscopic superpositions in many-atom systems, Phys. Rev. A 50 R2799–R2802 (1994-10-04), http://dx.doi.org/10.1103/PhysRevA.50.R2799 doi:10.1103/PhysRevA.50.R2799 (ID: 375182) Toggle Abstract
  We propose a technique to prepare two or more atoms in certain entangled states, based on the interaction of the atoms with a cavity mode. After the atomic state is prepared, the cavity mode is left in the vacuum state, so dissipation does not affect the generated entangled states. These states could be used for improved tests that challenge local realistic theories, and to examine related phenomena, which, thus far, have been realized only with photons. ©1994 The American Physical Society
• S. Marksteiner, C. M. Savage, P. Zoller, S. L. Rolston Coherent atomic waveguides from hollow optical fibers: Quantized atomic motion, Phys. Rev. A 50 2680–2690 (1994-09-03), http://dx.doi.org/10.1103/PhysRevA.50.2680 doi:10.1103/PhysRevA.50.2680 (ID: 375173) Toggle Abstract
  We present a theoretical analysis of coherent atomic motion through a straight atomic waveguide constructed from a hollow optical fiber. Atoms are guided by the evanescent light field at the fiber’s interior glass-vacuum interface. The atoms’ internal structure is modeled by a Jg=0 to Je=1 transition. The atomic wave functions are determined and the loss rates due to spontaneous emission, tunneling to the wall, and nonadiabatic transitions are estimated. The influence of Casimir-Polder forces is considered. We conclude with a discussion of the feasibility of the proposed waveguides. ©1994 The American Physical Society
• R. Walser, P. Zoller Laser-noise-induced polarization fluctuations as a spectroscopic tool, Phys. Rev. A 49 5067–5077 (1994-06-06), http://dx.doi.org/10.1103/PhysRevA.49.5067 doi:10.1103/PhysRevA.49.5067 (ID: 375170) Toggle Abstract
  We have investigated theoretically the possibility of employing noisy laser fields for spectroscopic purposes. The basis for this spectroscopy is a modification of the statistic of the fluctuations caused by the nonlinear interaction. All atomic resonances within the range of several bandwidths can be observed in the power spectrum, even in case of large inhomogeneous broadening. We have derived analytical, nonperturbative results for a real Gaussian, a complex Gaussian, and a phase-diffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for two-level systems. Without modification, we can apply our results also to other transition schemes. As an example, the power spectrum of the D2 transition of 133Cs driven by a phase-diffusing field is calculated. For this four-level system we find qualitative agreement with experimental results by Yabuzaki et al. [Phys. Rev. Lett. 67, 2453 (1991)].
• R. Taïeb, R. Dumhart, J. I. Cirac, P. Marte, P. Zoller Cooling and localization of atoms in laser-induced potential wells, Phys. Rev. A 49 4876–4887 (1994-06-06), http://dx.doi.org/10.1103/PhysRevA.49.4876 doi:10.1103/PhysRevA.49.4876 (ID: 375172) Toggle Abstract
  We discuss theoretically the cooling and localization of atoms in deep potentials induced by a far-off-resonant standing-wave laser. For a two-level atom cooling occurs via a Sisyphus mechanism. For a Λ system we discuss a Raman cooling scheme similar to the one proposed for laser cooling in ion traps. ©1994 The American Physical Society
• P. Marte, R. Dumhart, R. Taïeb, P. Zoller, M. S. Shahriar, M. Prentiss Polarization-gradient-assisted subrecoil cooling: Quantum calculations in one dimension, Phys. Rev. A 49 4826–4836 (1994-06-06), http://dx.doi.org/10.1103/PhysRevA.49.4826 doi:10.1103/PhysRevA.49.4826 (ID: 375174) Toggle Abstract
  We present a fully quantum-mechanical analysis of laser cooling of an angular momentum Jg=1 to Je=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ‘‘precooling’’ of the initial momentum distribution and (ii) in the long-time limit ‘‘confinement of velocities.’’ This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms. ©1994 The American Physical Society
• J. I. Cirac, M. Lewenstein, P. Zoller Quantum statistics of a laser cooled ideal gas, Phys. Rev. Lett. 72 2977–2980 (1994-05-09), http://dx.doi.org/10.1103/PhysRevLett.72.2977 doi:10.1103/PhysRevLett.72.2977 (ID: 375183) Toggle Abstract
  We study the dynamics of a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We show that the stationary state can be described by a Bose-Einstein or Fermi-Dirac distribution, respectively. Fluorescence from the system reflects quantum statistical properties. ©1994 The American Physical Society
• K. Ellinger, J. Cooper, P. Zoller Light-pressure force in N-atom systems, Phys. Rev. A 49 3909–3933 (1994-05-05), http://dx.doi.org/10.1103/PhysRevA.49.3909 doi:10.1103/PhysRevA.49.3909 (ID: 375180) Toggle Abstract
  An analytical description of long-range collisions between atoms in a laser cooling field is developed. We begin by considering an N-atom master equation. In the regime of low atomic densities (i.e., where the mean distance between two atoms is much larger than the laser wavelength) it is possible to treat the atom-atom interactions in perturbation theory. Furthermore we assume temperatures which allow a semiclassical treatment of the cooling process. The effect of the presence of other atoms can be separated analytically into two parts; an attenuation force due to the absorption of the laser beams in the atomic cloud similar to the results of Dalibard [Opt. Commun. 68, 203 (1988)], which tends to compress the atomic cloud, and a two-atom force due to photon emission and absorption cycles between different atoms. This force proves to be repulsive for the configurations studied and prevents the cloud from collapsing. The result for the first-order perturbation expansion in collision strength generalizes the model proposed by Walker, Sesko, and Wieman [J. Opt. Soc. B 8, 946 (1991)] by including additional terms, such as those associated with Raman couplings. ©1994 The American Physical Society
• J. I. Cirac, R. Blatt, P. Zoller Nonclassical states of motion in a three-dimensional ion trap by adiabatic passage, Phys. Rev. A 49 R3174–R3177 (1994-05-05), http://dx.doi.org/10.1103/PhysRevA.49.R3174 doi:10.1103/PhysRevA.49.R3174 (ID: 375186) Toggle Abstract
  A scheme for the preparation of nonclassical states of motion in a three-dimensional harmonic ion trap is proposed. The technique is based on adiabatic passage along dressed energy levels of the strongly coupled ion-trap system by varying the laser frequency. ©1994 The American Physical Society
• I. Marzoli, J. I. Cirac, R. Blatt, P. Zoller Laser cooling of trapped three-level ions: Designing two-level systems for sideband cooling, Phys. Rev. A 49 2771–2779 (1994-04-04), http://dx.doi.org/10.1103/PhysRevA.49.2771 doi:10.1103/PhysRevA.49.2771 (ID: 375175) Toggle Abstract
  Laser cooling of three-level ions of the cascade, vee, and lambda configuration is considered with simultaneous excitation on a weak and strong transition. Choosing appropriate parameters for the Rabi frequencies and the respective detunings allows one to eliminate adiabatically one of the levels. The thus designed two-level ion can acquire decay rates Γ’ smaller than the trap frequency ν such that sideband cooling becomes possible and accordingly allows cooling of the ion to its lowest oscillator state 〈n〉=0 in the trap. Explicit expressions for the detunings and the Rabi frequencies for sideband cooling of the effective two-level system are derived. ©1994 The American Physical Society
• J. I. Cirac, A. Schenzle, P. Zoller Inhibition of quantum tunneling of an atom due to the continuous observation of light scattering, 27 123 (1994-03-02), (ID: 375184)
• L. S. Goldner, C. Gerz, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, P. Zoller Momentum transfer in laser-cooled cesium by adiabatic passage in a light field, Phys. Rev. Lett. 97 997–1000 (1994-02-07), http://dx.doi.org/10.1103/PhysRevLett.72.997 doi:10.1103/PhysRevLett.72.997 (ID: 375179) Toggle Abstract
  We have observed transfer of momentum and ground state population in laser-cooled cesium by adiabatic following of a slowly evolving light field. In this new technique for mechanical manipulation of atoms, spontaneous emission is suppressed since the atoms evolve in a ‘‘dark’’ state that follows the light field. This means that the phase coherence of the atom is preserved so that this technique is useful in the realization of coherent atomic beam splitters and mirrors. Our experimental results are in good agreement with optical Bloch equation calculations. ©1994 The American Physical Society
• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Quantum collapse and revival in the motion of a single trapped ion, Phys. Rev. A 49 1202–1207 (1994-02-02), http://dx.doi.org/10.1103/PhysRevA.49.1202 doi:10.1103/PhysRevA.49.1202 (ID: 375187) Toggle Abstract
  Within certain limits, the dynamics of a single trapped ion oscillating about the node of a standing-wave light field is described by the Jaynes-Cummings model, which is routinely used for cavity-QED experiments. We propose a technique to measure quantum collapse and revival in the population inversion of a single trapped ion, and show that this method is uniquely suited for the measurement of final temperatures of the trapped ion as well as for the analysis of nonclassical states of the ion motion, such as Fock and squeezed states. The results are discussed with particular consideration given to the effects of a finite laser bandwidth. ©1994 The American Physical Society
• J. I. Cirac, L. J. Garay, R. Blatt, A. S. Parkins, P. Zoller Laser cooling of trapped ions: The influence of micromotion, Phys. Rev. A 49 421–432 (1994-01-01), http://dx.doi.org/10.1103/PhysRevA.49.421 doi:10.1103/PhysRevA.49.421 (ID: 375185) Toggle Abstract
  Laser cooling of a single trapped ion in a Paul trap is discussed theoretically in the Lamb-Dicke limit, with full consideration of the time dependence of the trapping potential. Resulting mean kinetic energies are defined as time averages over one period of the micromotion and are compared with final temperatures expected from the laser-cooling treatment with harmonic traps. For laser-atom detunings close to the micromotion frequency the results differ significantly from those expected for a harmonic trap potential. A physical interpretation is given and simple formulas are derived for the strong confinement case. ©1994 The American Physical Society
• M. Lewenstein, J. I. Cirac, P. Zoller Quantum dynamics of a laser-cooled ideal gas, Phys. Rev. A 50 3409–3422 (1994), http://dx.doi.org/10.1103/PhysRevA.50.3409 doi:10.1103/PhysRevA.50.3409 (ID: 305615) Toggle Abstract
  We study a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We derive a master equation governing the evolution of such a system, and show that the stationary state can be described by Bose-Einstein or Fermi-Dirac distributions. The quantum-statistical character of the atoms exhibits itself in the dynamical behavior of the system and in the statistical properties of fluorescence photons emitted in the stationary state.

Proceeding

• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Nonclassical states of motion and quantum collapse and revival in an ion trap, Quantum Optics VI in Springer Proceedings in Physics 77 112 (1994), (ID: 628469)

1993

Articles

• A. S. Parkins, P. Marte, P. Zoller, H. J. Kimble Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence, Phys. Rev. Lett. 71 3095–3098 (1993-11-08), http://dx.doi.org/10.1103/PhysRevLett.71.3095 doi:10.1103/PhysRevLett.71.3095 (ID: 375413) Toggle Abstract
  A scheme for the preparation of general coherent superpositions of photon-number states is proposed. By strongly coupling an atom to a cavity field, atomic ground-state Zeeman coherence can be transferred by (coherent) adiabatic passage to the cavity mode and a general field state can be generated without atomic projection noise. ©1993 The American Physical Society
• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Spectrum of resonance fluorescence from a single trapped ion, Phys. Rev. A 48 2169–2181 (1993-09-03), http://dx.doi.org/10.1103/PhysRevA.48.2169 doi:10.1103/PhysRevA.48.2169 (ID: 375421) Toggle Abstract
  The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation. ©1993 The American Physical Society
• P. Marte, R. Dumhart, R. Taïeb, P. D. Lett, P. Zoller Quantum wave function simulation of the resonance fluorescence spectrum from one-dimensional optical molasses, Phys. Rev. Lett. 71 1335–1338 (1993-08-09), http://dx.doi.org/10.1103/PhysRevLett.71.1335 doi:10.1103/PhysRevLett.71.1335 (ID: 375416) Toggle Abstract
  Using recently developed quantum wave function techniques, we have performed a simulation of 85Rb atoms in a one-dimensional optical molasses, formed from counterpropagating laser beams with orthogonal linear polarizations. Both internal and external degrees of freedom are treated quantum mechanically in one dimension and the spectrum of resonance fluorescence is calculated and compared to recent experiments. Excellent agreement is obtained for the spectrum and additional insight is gained into the experimental evidence for quantized motion in the optical potentials. ©1993 The American Physical Society
• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Laser cooling of trapped ions with polarization gradients, Phys. Rev. A 48 1434–1445 (1993-08-02), http://dx.doi.org/10.1103/PhysRevA.48.1434 doi:10.1103/PhysRevA.48.1434 (ID: 375420) Toggle Abstract
  Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is Jg=1/2→Je=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser. ©1993 The American Physical Society
• H. R. Xia, J. I. Cirac, S. Swartz, B. Kohler, D. Elliott, J. Hall, P. Zoller Phase shifts and intensity dependence in frequency-modulation spectroscopy, JOSA B 11 721 (1993-06-06), URL (ID: 375387) Toggle Abstract
  Phase shifts and intensity dependence in frequency-modulation spectroscopy
• R. Taïeb, P. Marte, R. Dumhart, P. Zoller Spectrum of resonance fluorescence and cooling dynamics in quantized one-dimensional molasses: Effects of laser configuration, Phys. Rev. A 47 4986–4993 (1993-06-06), http://dx.doi.org/10.1103/PhysRevA.47.4986 doi:10.1103/PhysRevA.47.4986 (ID: 375409) Toggle Abstract
  We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a Jg=1→Je=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle θ between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors. ©1993 The American Physical Society
• M. H. Anderson, G. Vemuri, J. Cooper, P. Zoller, S. Smith Experimental study of absorption and gain by two-level atoms in a time-delayed non-Markovian optical field, Phys. Rev. A 47 3202–3209 (1993-04-04), http://dx.doi.org/10.1103/PhysRevA.47.3202 doi:10.1103/PhysRevA.47.3202 (ID: 375423) Toggle Abstract
  We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3s1/2(F=2,mF=2)→3p3/2(F=3,mF=3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state. ©1993 The American Physical Society
• J. I. Cirac, A. S. Parkins, R. Blatt, P. Zoller Cooling of a trapped ion coupled strongly to a quantized cavity mode, Opt. Com. 97 353-359 (1993-04-01), http://dx.doi.org/10.1016/0030-4018(93)90502-V doi:10.1016/0030-4018(93)90502-V (ID: 375419) Toggle Abstract
  The interaction of a trapped two-level ion, confined in a harmonic potential, with a quantized cavity mode of the radiation field is studied theoretically. The ion is considered to be spatially localized on the scale of the optical wavelength (Lamb-Dicke limit), and the ion-cavity-mode coupling is assumed to be larger than or comparable to the spontaneous emission and cavity-mode loss rates. With broadband thermal light driving the cavity mode, we show that the cooling rates and final temperatures of the trapped-ion motion reflect the Jaynes-Cummings energy spectrum of the strongly-coupled ion-cavity system. 1 Present address: Departamento de Fisica Aplicada, Facultad de Ciencias, Paseo Universidad 4, 13071 Ciudad Real, Spain. 2 Permanent address: I. Institut für Laserphysik, Jungiusstr. 9, W-2000 Hamburg 36, Germany.
• J. I. Cirac, P. Zoller Laser cooling of trapped ions in a squeezed vacuum, Phys. Rev. A 47 2191–2195 (1993-03-03), http://dx.doi.org/10.1103/PhysRevA.47.2191 doi:10.1103/PhysRevA.47.2191 (ID: 375417) Toggle Abstract
  Laser cooling a trapped ion damped by an electromagnetic reservoir in a squeezed-vacuum state is investigated. The cooling rate and the final temperature are given for the case in which the ion is located at the node of a laser standing wave, on resonance with its internal transition. In particular, we find that the ion can have final temperatures below the Dopper limit. ©1993 The American Physical Society
• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Preparation of Fock states by observation of quantum jumps in an ion trap, Phys. Rev. Lett. 70 762–765 (1993-02-06), http://dx.doi.org/10.1103/PhysRevLett.70.762 doi:10.1103/PhysRevLett.70.762 (ID: 375422) Toggle Abstract
  We propose a technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single two-level atomic transition based on the observation of quantum jumps. Examples are taken from the fields of cavity QED and ion trapping, where photon number states and number states of the quantized atomic motion may be prepared, respectively. ©1993 The American Physical Society
• P. Marte, R. Dumhart, R. Taïeb, P. Zoller Resonance fluorescence from quantized one-dimensional molasses, Phys. Rev. A 47 1378–1390 (1993-02-02), http://dx.doi.org/10.1103/PhysRevA.47.1378 doi:10.1103/PhysRevA.47.1378 (ID: 375414) Toggle Abstract
  We study theoretically the spectrum of resonance fluoresence from one-dimensional molasses consisting of two-level atoms with Zeeman substructure. The center-of-mass motion of the atom is treated fully quantum mechanically. The spectrum shows sidebands due to transitions between vibrational levels in optical potentials generated by the laser light. Detailed results are presented for the Jg=1/2→Je=3/2 atomic transition in a laser configuration with two counterpropagating waves with orthogonal polarizations. We have solved the corresponding quantum master equation and calculated the relevant autocorrelation function of the atomic dipole using (i) a direct numerical solution of the master equation, (ii) a wave-function simulation of the master equation and correlation function employing periodic time-dependent Bloch wave functions, and (iii) a semiclassical bipotential calculation for the spectrum including a simple quantum correction. ©1993 The American Physical Society
• J. I. Cirac, A. S. Parkins, R. Blatt, P. Zoller ‘‘Dark’’ squeezed states of the motion of a trapped ion, Phys. Rev. Lett. 70 556–559 (1993-02-01), http://dx.doi.org/10.1103/PhysRevLett.70.556 doi:10.1103/PhysRevLett.70.556 (ID: 375418) Toggle Abstract
  We propose a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a ‘‘dark resonance’’ in the fluorescence emitted by the ion. ©1993 The American Physical Society
• A. S. Parkins, P. Zoller, H. J. Carmichael Spectral linewidth narrowing in a strongly coupled atom-cavity system via squeezed-light excitation of a ‘‘vacuum’’ Rabi resonance, Phys. Rev. A 48 758–763 (1993-01-07), http://dx.doi.org/10.1103/PhysRevA.48.758 doi:10.1103/PhysRevA.48.758 (ID: 375410) Toggle Abstract
  The system consisting of a two-level atom coupled strongly to a cavity mode behaves as a two-state system when excited near one of the ‘‘vacuum’’ Rabi resonances. With finite-bandwidth squeezed light incident upon the cavity and tuned to one of these resonances, we show that it is possible to realize a two-state system coupled to a squeezed vacuum. This system exhibits subnatural linewidths in the emitted spectra, as described by Gardiner [Phys. Rev. Lett. 56, 1917 (1986)] in a study of spontaneous emission of a two-level atom in a squeezed vacuum, but requires that only a single cavity mode be subject to squeezing rather than the entire three-dimensional vacuum. ©1993 The American Physical Society

Proceeding

• J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Non-classical states of motion in an ion trap, Fundamentals of Quantum Optics III 156 (1993), (ID: 628470)

1992

Articles

• Gardiner, Crispin, A. S. Parkins, P. Zoller Wave-function quantum stochastic differential equations and quantum-jump simulation methods, Phys. Rev. A 46 4363–4381 (1992-10-01), http://dx.doi.org/10.1103/PhysRevA.46.4363 doi:10.1103/PhysRevA.46.4363 (ID: 375890) Toggle Abstract
  The quantum-stochastic-differential-equation formulation of driven quantum-optical systems is carried out in the interaction picture, and quantum stochastic differential equations for wave functions are derived on the basis of physical principles. The Ito form is shown to be the most practical, since it already contains all the radiation reaction terms. The connection between this formulation and the master equation is shown to be very straightforward. In particular, a direct connection is made to the theory of continuous measurements, which leads directly to the method of quantum-jump simulations of solutions of the master equation. It is also shown that all conceivable spectral and correlation-function information in output fields is accessible by means of an augmentation of the simulation process. Finally, the question of the reality of the jumps used in the simulations is posed. ©1992 The American Physical Society
• R. Dumhart, A. S. Parkins, P. Zoller, Gardiner, Crispin Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs, Phys. Rev. A 46 4382–4396 (1992-10-01), http://dx.doi.org/10.1103/PhysRevA.46.4382 doi:10.1103/PhysRevA.46.4382 (ID: 375893) Toggle Abstract
  Wave-function simulation of the master equation in terms of quantum jumps is illustrated for vacuum, thermal, and squeezed reservoirs. We discuss simulation techniques for (i) atomic density matrices, and resonance fluoresence and weak-field absorption spectra of atoms, (ii) decay of a two-level system in a squeezed vacuum, and (iii) a strongly coupled atom-cavity system driven by thermal light. ©1992 The American Physical Society
• J. I. Cirac, R. Blatt, P. Zoller, W. D. Phillips Laser cooling of trapped ions in a standing wave, Phys. Rev. A 46 2668–2681 (1992-09-01), http://dx.doi.org/10.1103/PhysRevA.46.2668 doi:10.1103/PhysRevA.46.2668 (ID: 375895) Toggle Abstract
  Laser cooling of trapped ions in a standing- and running-wave configuration is discussed theoretically. The ions are assumed to be spatially localized on the scale provided by the wavelength of the laser (Lamb-Dicke limit). A master equation for the center-of-mass distribution of the ion is derived for a multilevel system, and explicit results are presented for two- and three-level systems and harmonic trapping potentials. For the two-level system located at the node of the standing wave, we find final temperatures that are a factor of 2 lower than the limit for a running wave and cooling rates that do not saturate with the laser intensity. At the point of maximum gradient of the standing wave, blue detuned cooling is found that is analogous to the Sisyphus cooling of free atoms. For a three-level system we compare our results with those of Wineland, Dalibard, and Cohen-Tannoudji [J. Opt. Soc. Am. B 9, 32 (1992)]. ©1992 The American Physical Society
• A. S. Parkins, P. Zoller Laser cooling of atoms with broadband real Gaussian laser fields, Phys. Rev. A 45 6522–6538 (1992-05-01), http://dx.doi.org/10.1103/PhysRevA.45.6522 doi:10.1103/PhysRevA.45.6522 (ID: 375592) Toggle Abstract
  We describe a theoretical approach to laser cooling with broadband real Gaussian laser fields that is based on adiabatic elimination methods and the Fokker-Planck equation for the Wigner function. This approach is used to model the recent broadband cooling experiment of Zhu, Oates, and Hall [Phys. Rev. Lett. 67, 46 (1991)] and gives correct order-of-magnitude results. The theory is then applied to J=0→J=1 and J=1→J=2 transitions in a σ+-σ- optical molasses configuration with correlated broadband laser fields. An instability in the cooling scheme at zero velocity is found for red laser detunings, and sub-Doppler-width velocity distributions are predicted for J=1→J=2 transitions with both red and blue laser detunings. ©1992 The American Physical Society
• A. S. Parkins, P. Zoller σ+-σ- laser-cooling configuration with broadband laser fields: Instability at zero velocity, Phys. Rev. A 45 R6161–R6164 (1992-05-01), http://dx.doi.org/10.1103/PhysRevA.45.R6161 doi:10.1103/PhysRevA.45.R6161 (ID: 375596) Toggle Abstract
  We investigate theoretically laser cooling with broadband σ+-σ- lasers acting on J=0→J=1 and J=1→J=2 transitions. For cross-correlated laser fluctuations an instability in the friction force at zero velocity is predicted for red laser detunings. The dependence of this instability on the cross-correlation and spectral line shape is investigated. ©1992 The American Physical Society
• M. Marte, P. Zoller Localization of atoms in light fields: Optical molasses, adiabatic compression and squeezing, 54/5 477 - 485 (1992-05-01), http://dx.doi.org/10.1007/BF00325394 doi:10.1007/BF00325394 (ID: 375719) Toggle Abstract
  It is demonstrated that one can measure the distribution of the transverse position of an atom crossing one or more optical cavities by monitoring the phase of the standing wave fields in the cavities. For the atom-field interaction the Kapitza-Dirac regime is assumed; it is shown that in this regime the method represents a quantum nondemolition measurement of the atomic position. On the other hand it can be applied to prepare narrow distributions of the transverse atomic position. In order to show this, a numerical simulation is performed, which illustrates the collapse of a broad initial Gaussian wavepacket, which can be coherent or incoherent, to a distribution with narrow peaks. Preparing the cavity fields in a squeezed state, one can greatly enhance the impact of the cavity field measurements on the atomic density matrix.
• R. Graham, D. Walls, P. Zoller Emission from atoms in linear superpositions of center-of-mass wave packets, Phys. Rev. A 45 5018–5030 (1992-04-01), http://dx.doi.org/10.1103/PhysRevA.45.5018 doi:10.1103/PhysRevA.45.5018 (ID: 375865) Toggle Abstract
  We study theoretically the electromagnetic field emitted by atoms prepared in linear superpositions of several internal states, each of which is attached to a different center-of-mass wave packet by the preparation process. It is shown that the motion and mutual separation of the wave packets can be monitored either by observing the coherent spontaneous emission in a heterodyne experiment or by measuring the energy-absorption rate from a weak probe-laser beam. We also show that a three-level system involving three wave packets coherently emits photons, forming a linear superposition of states of opposite wave vectors. A heterodyne scheme for detecting the photons in this state is proposed. ©1992 The American Physical Society
• R. Dumhart, P. Zoller, H. Ritsch Monte Carlo simulation of the atomic master equation for spontaneous emission, Phys. Rev. A 45 4879–4887 (1992-04-01), http://dx.doi.org/10.1103/PhysRevA.45.4879 doi:10.1103/PhysRevA.45.4879 (ID: 375891) Toggle Abstract
  A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow’s pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically. ©1992 The American Physical Society
• R. Walser, H. Ritsch, P. Zoller, J. Cooper Laser-noise-induced population fluctuations in two-level systems: Complex and real Gaussian driving fields, Phys. Rev. A 45 468–476 (1992-02-01), http://dx.doi.org/10.1103/PhysRevA.45.468 doi:10.1103/PhysRevA.45.468 (ID: 375428) Toggle Abstract
  The nonlinear dynamics of a sample of two-level systems exposed to noisy laser light is investigated. As stochastic models we treat the chaotic field and the real Gaussian field. Based on the method of marginal characteristic functions, we deduce analytical solutions for the mean values and variances of the atomic populations in terms of matrix continued fractions. We find significantly enhanced on-resonance fluctuations for a real Gaussian field compared to a chaotic field of the same bandwidth and intensity. Furthermore, in contrast to phase-noise models, the fluctuations in the fluorescence intensity do not decrease to zero in the limit of slow fluctuations. ©1992 The American Physical Society
• H. Ritsch, P. Zoller Dynamic quantum-noise reduction in multilevel-laser systems, Phys. Rev. A 45 1881–1892 (1992-02-01), http://dx.doi.org/10.1103/PhysRevA.45.1881 doi:10.1103/PhysRevA.45.1881 (ID: 375590) Toggle Abstract
  Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m≥3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity. ©1992 The American Physical Society
• R. Graham, M. Schlautmann, P. Zoller Dynamical localization of atomic-beam deflection by a modulated standing light wave, Mod. Phys. Lett. A 45 R19–R22 (1992-01-01), http://dx.doi.org/10.1103/PhysRevA.45.R19 doi:10.1103/PhysRevA.45.R19 (ID: 375870) Toggle Abstract
  The deflection of an atomic beam passing a standing-wave laser field in front of an oscillating mirror occurs by chaotic diffusive momentum transfer in a classical description and, as we show, is limited by dynamical localization quantum mechanically. An experiment to observe this quantum effect in an atomic beam is proposed. ©1992 The American Physical Society
• H. Ritsch, P. Zoller Quantum noise reduction in Raman lasers, 19 7 (1992), (ID: 375591) Toggle Abstract
  Quantum noise reduction in Raman lasers

1991

Articles

• M. Marte, J. I. Cirac, P. Zoller Deflection of Atoms by Circularly Polarized Light Beams in Triple Laue Configuration, J. Mod. Opt. 38/11 2265 - 2280 (1991-11-11), URL (ID: 376278) Toggle Abstract
  A new type of atomic interferometer is discussed, in which atoms with two ground-state Zeeman sub-levels m = - 1 , and an excited state with m = 0 , pass through three laser interaction zones-each comprising two counter-propagating waves of opposite circular polarization with a large detuning from resonance. By means of Raman-type transitions between the two ground-state levels, which convey a recoil of two photon momenta, the atomic wave function is split up into two coherent spatially separated branches, and subsequently recombined. In this system, conservation of energy and momentum leads to a strong correlation between the external centre of mass motion and internal magnetic degrees of freedom. As a consequence, the paths within the interferometer are tagged by the internal quantum number m . As an example, we calculate the position and momentum distribution function of a helium atom on its way through the interferometer.
• P. Marte, P. Zoller, J. Hall Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems, Phys. Rev. A 44 R4118–R4121 (1991-10-01), http://dx.doi.org/10.1103/PhysRevA.44.R4118 doi:10.1103/PhysRevA.44.R4118 (ID: 376268) Toggle Abstract
  We study atomic-beam deflection by adiabatic passage between Zeeman ground levels via Raman transitions induced by counterpropagating σ±-polarized lasers. We show that complete population transfer between the ground states can be achieved, which corresponds to the scattering of the atomic wave packet into a single final momentum state by absorption and induced emission of laser photons. Although the lasers can be resonant, the excited state(s) are never populated during the adiabatic transfer, which suppresses the effects of spontaneous emission and preserves the coherence of the atomic wave function. This scheme has attractive features as a beam splitter and mirror for atomic interferometry. ©1991 The American Physical Society
• J. I. Cirac, H. Ritsch, P. Zoller Two-level system interacting with a finite-bandwidth thermal cavity mode, Phys. Rev. A 44 4541–4551 (1991-10-01), http://dx.doi.org/10.1103/PhysRevA.44.4541 doi:10.1103/PhysRevA.44.4541 (ID: 376271) Toggle Abstract
  The interaction of a two-level system with a single quantized mode of the radiation field of finite bandwidth in a thermal state and coupled to background vacuum modes is considered theoretically. A hierarchy of equations for atom-field moments is derived and solved in terms of continued fractions. The population inversion, the spectrum of resonance fluorescence, and the photon statistics of the cavity mode are calculated. ©1991 The American Physical Society
• H. Ritsch, P. Zoller, Gardiner, Crispin, D. Walls Sub-Poissonian laser light by dynamic pump-noise suppression, Phys. Rev. A 44 3361–3364 (1991-09-01), http://dx.doi.org/10.1103/PhysRevA.44.3361 doi:10.1103/PhysRevA.44.3361 (ID: 376267) Toggle Abstract
  We identify a mechanism of dynamical pump-noise suppression in lasers. It is based on the recycling of the active laser electron from the lower to the upper laser level by a sequence of incoherent step processes. Although each of these steps corresponds to a Poisson process, i.e., is stochastic, the combination of many incoherent steps leads to a regular (deterministic) recycling of the laser electron and, correspondingly, a pump-noise suppression in the laser. The mechanism predicts sub-Poissonian laser output and intensity fluctuations beyond the shot-noise limit for incoherently pumped systems. ©1991 The American Physical Society
• P. Marte, P. Zoller Hydrogen in intense laser fields: Radiative close-coupling equations and quantum-defect parametrization, Phys. Rev. A 43 1512–1522 (1991-02-01), http://dx.doi.org/10.1103/PhysRevA.43.1512 doi:10.1103/PhysRevA.43.1512 (ID: 376269) Toggle Abstract
  A system of radiative close-coupling equations for a hydrogen atom in a circularly polarized intense laser field is derived. The radiative scattering matrix is parametrized within a multichannel quantum-defect formalism. The quasienergy spectrum corresponding to nonperturbative shifts and ionization widths of the bound atomic states is computed from the poles of the radiative scattering matrix. For an intensity range up to α0≊1.5a0 (with α0 the oscillation amplitude of the free electron in the laser and a0 the Bohr radius), numerical results are presented in the frequency regime where two-photon ionization and above-threshold ionization of the ground state is possible. For one-photon transitions a stabilization of the atomic states for strong fields is predicted. ©1991 The American Physical Society
• G. Alber, P. Zoller Laser excitation of electronic wave packets in rydberg atoms, Physics Reports 199(5) 231-280 (1991-01-05), http://dx.doi.org/10.1016/0370-1573(91)90058-T doi:10.1016/0370-1573(91)90058-T (ID: 376488) Toggle Abstract
  We review recent theoretical and experimental work on laser-induced excitation of atomic Rydberg wave packets. Studying the motion of these wave packets provides a bridge between quantum mechanics and the classical concept of the trajectory of an electron and corresponds to real-time observations of atomic dynamics in a Coulomb, and possibly static external field. We discuss generation and detection of wave packets by short and/or intense laser pulses. On the theoretical side our emphasis is on quantum defect theory and semiclassical methods.
• K. M. Gheri, M. Marte, P. Zoller Atomic absorption in cross-correlated time-delayed stochastic laser fields, JOSA B 8 1559 (1991), URL (ID: 376281) Toggle Abstract
  Atomic absorption in cross-correlated time-delayed stochastic laser fields
• K. Ellinger, H. Gratl, P. Zoller New aspects in laser excitation of Rydberg wavepackets, Physica Scripta T34 60 (1991), (ID: 376491) Toggle Abstract
  New aspects in laser excitation of Rydberg wavepackets
• G. Alber, P. Zoller Laser induced excitation of electronic Rydberg wave packets, Contemp. Phys. 32 185 (1991), (ID: 376525) Toggle Abstract
  Laser induced excitation of electronic Rydberg wave packets

1990

Articles

• M. H. Anderson, R. Jones, J. Cooper, S. Smith, D. Elliott, H. Ritsch, P. Zoller Variance and spectra of fluorescence-intensity fluctuations from two-level atoms in a phase-diffusing field, Phys. Rev. A 42 6690–6703 (1990-12-01), http://dx.doi.org/10.1103/PhysRevA.42.6690 doi:10.1103/PhysRevA.42.6690 (ID: 376546) Toggle Abstract
  We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself. ©1990 The American Physical Society
• H. Ritsch, P. Zoller, J. Cooper Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms, Phys. Rev. A 41 2653–2667 (1990-05-01), http://dx.doi.org/10.1103/PhysRevA.41.2653 doi:10.1103/PhysRevA.41.2653 (ID: 376539) Toggle Abstract
  Variances and power spectra of the resonance fluorescence intensity induced by laser noise in two-level systems are studied theoretically. The effects of amplitude and phase noise fluctuations of a single-mode laser are investigated. Correlations of amplitude and phase fluctuations, as is relevant for excitation with diode lasers, are shown to lead to pronounced asymmetries in variance spectra. ©1990 The American Physical Society
• M. H. Anderson, R. Jones, J. Cooper, S. Smith, D. Elliott, H. Ritsch, P. Zoller Observation of population fluctuations in two-level atoms driven by a phase diffusing field, Phys. Rev. Lett. 64 1346–1349 (1990-03-12), http://dx.doi.org/10.1103/PhysRevLett.64.1346 doi:10.1103/PhysRevLett.64.1346 (ID: 376550) Toggle Abstract
  We have measured the variance in fluorescence intensity as a phase diffusing laser is scanned through resonance with a beam of two-level atoms. For laser intensities below saturation, our results are in quantitative agreement with recent theoretical predictions provided Doppler effects are treated. Above saturation, the agreement is somewhat less quantitative primarily due to the sensitivity of the predictions to the laser intensity profile and the experimental uncertainty in measuring it. ©1990 The American Physical Society
• P. Zoller Sub-Poissonian laser output due to optical pumping by squeezed light, Quant. Opt. 2 229-235 (1990), http://dx.doi.org/10.1088/0954-8998/2/3/004 doi:10.1088/0954-8998/2/3/004 (ID: 376545) Toggle Abstract
  A recent analysis of the influence of the pump statistics on the laser output fluctuations is applied to the experimentally feasible case of a laser being pumped by light coming from a separate pump field cavity that is driven by a broad-band squeezed vacuum plus a coherent driving field. In contrast to the 'squeezed-reservoir laser', where a reservoir of squeezed modes coming from all directions coupled to the dipole moment of the lasing transition and leads to atomic phase decay inhibition and phase locking of the laser field, here the squeezed light merely pumps the gain atoms, that is gives rise to inversion of the laser transition. In analogy to photodetection theory the photon statistics of the laser output is calculated as a function of the photon statistics of the absorbed squeezed pump light. For the case of a squeezed pump field chosen to display sub-Poissonian statistics, it is demonstrated that the Mandel Q-parameter of the laser cavity output can theoretically reach the optimum value of Q=-1/2, similar to the case of a deterministic pumping mechanism.

1989

Articles

• M. Marte, P. Zoller Lasers with sub-Poissonian pump, Phys. Rev. A 40 5774–5782 (1989-11-10), http://dx.doi.org/10.1103/PhysRevA.40.5774 doi:10.1103/PhysRevA.40.5774 (ID: 376796) Toggle Abstract
  It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit. ©1989 The American Physical Society
• H. Gratl, G. Alber, P. Zoller Near-threshold behaviour of multiphoton ionisation probabilities, J. Phys. B: At. Mol. Opt. Phys. 22 L547-L551 (1989-10-14), http://dx.doi.org/10.1088/0953-4075/22/19/002 doi:10.1088/0953-4075/22/19/002 (ID: 376799) Toggle Abstract
  The near-threshold behaviour of four-photon ionisation is studied in an energy region where the third laser photon crosses the Rydberg threshold. Particular emphasis is given to the role played by the Stark shift (raising of the ionisation potential) in a Gaussian laser pulse. As a function of the laser frequency the ionisation probability shows (i) a region where individual Rydberg resonances are well resolved, followed by (ii) a smoothly decreasing ionisation probability in the bound-state region, and (iii) an almost energy-independent above-threshold ionisation signal.
• M. J. Fink, P. Zoller Quantum-defect parametrization of perturbative two-photon ionization cross sections, Phys. Rev. A 39 2933–2947 (1989-03-06), http://dx.doi.org/10.1103/PhysRevA.39.2933 doi:10.1103/PhysRevA.39.2933 (ID: 376800) Toggle Abstract
  A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization (2PI) of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed. The rapid energy variation of such amplitudes is extracted in terms of elementary functions of energy and a set of MQDT parameters, which are ‘‘smooth’’ functions of energy. As an example, results of numerical computations of MQDT parameters for 2PI of atomic hydrogen (1s, 2s, and 3s) by circularly polarized light are presented. MQDT parameters for the many-channel case are derived, and an analysis of their energy dependence across Rydberg thresholds is given. The two-channel case is analyzed using phase-shifted Coulomb functions, and simple analytic formulas are given for the energy dependence of the amplitude as a function of a small set of physical parameters. ©1989 The American Physical Society

1988

Articles

• G. Alber, T. Haslwanter, P. Zoller One-photon resonant two-photon excitation of Rydberg series close to threshold, JOSA B 5 2439 (1988-12-12), URL (ID: 376892) Toggle Abstract
  One-photon resonant two-photon excitation of Rydberg series close to threshold
• T. Haslwanter, H. Ritsch, J. Cooper, P. Zoller Laser-noise-induced population fluctuations in two- and three-level systems, Phys. Rev. A 38 5652–5659 (1988-12-01), http://dx.doi.org/10.1103/PhysRevA.38.5652 doi:10.1103/PhysRevA.38.5652 (ID: 376816) Toggle Abstract
  Significant fluctuations, above the shot-noise limit, have been observed in the intensity of fluorescent light scattered from atoms excited by an intense noisy laser, where a central role is played by the nonlinearity of the atom-field interaction. By considering the variance of the atomic populations, we show that ‘‘noise spectroscopy’’ is sensitive to the field statistics of the laser. We specifically consider the cases of resonance fluorescence (analogous in the weak-field limit to analysis by a Fabry-Pérot interferometer), two-photon excitation, and double optical resonance for variable laser intensity and bandwidth. We show that large differences in the ‘‘noise’’ spectra can occur between lasers characterized by a phase-diffusion or a phase-jump model, although these models would give the same values for the mean atomic populations. We believe that observation of population fluctuations can become a useful method for characterizing laser noise. ©1988 The American Physical Society
• H. Ritsch, P. Zoller Systems driven by colored squeezed noise: The atomic absorption spectrum, Phys. Rev. A 38 4657–4668 (1988-11-01), http://dx.doi.org/10.1103/PhysRevA.38.4657 doi:10.1103/PhysRevA.38.4657 (ID: 376803) Toggle Abstract
  We derive stochastic density-matrix equations for an atom strongly driven by finite-bandwidth squeezed light. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. Saturation properties and the weak-field absorption spectrum of a two-level atom embedded in finite-bandwidth squeezed light and driven by a coherent field are calculated. We discuss the effect of finite bandwidth of the squeezed light in obtaining subnatural linewidth in the atomic absorption spectra, based on nonperturbative solutions of the stochastic optical Bloch equations. ©1988 The American Physical Society
• R. Blatt, P. Zoller Quantum jumps in atomic systems, European Journal of Physics 9 250-256 (1988-10-04), http://dx.doi.org/10.1088/0143-0807/9/4/002 doi:10.1088/0143-0807/9/4/002 (ID: 376844) Toggle Abstract
  The authors summarise the principal aspects of the recent discussion regarding the observation of Bohr's quantum jumps in resonance fluorescence from three-level systems. The experimental results are reviewed and possible applications are given.
• H. Ritsch, P. Zoller Atomic Transitions in Finite-Bandwidth Squeezed Light, Phys. Rev. Lett. 61 1097–1100 (1988-08-09), http://dx.doi.org/10.1103/PhysRevLett.61.1097 doi:10.1103/PhysRevLett.61.1097 (ID: 376814) Toggle Abstract
  A stochastic density-matrix equation for an atom strongly driven by finite-bandwidth squeezed light is derived. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. The possibility of obtaining reduced atomic linewidths in the absorption spectrum of the atom embedded in colored squeezed light is discussed, based on nonperturbative solutions of stochastic optical Bloch equations. ©1988 The American Physical Society
• G. Alber, P. Zoller Near-threshold excitation of Rydberg series by strong laser fields, Phys. Rev. A 37 377–389 (1988-01-02), http://dx.doi.org/10.1103/PhysRevA.37.377 doi:10.1103/PhysRevA.37.377 (ID: 376893) Toggle Abstract
  We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core. ©1988 The American Physical Society

1987

Articles

• A. Giusti-Suzor, P. Zoller Rydberg electrons in laser fields: A finite-range-interaction problem, Phys. Rev. A 36 5178–5188 (1987-12-01), http://dx.doi.org/10.1103/PhysRevA.36.5178 doi:10.1103/PhysRevA.36.5178 (ID: 376903) Toggle Abstract
  A theory of Rydberg and continuum states in intense laser fields is developed based on the observation that the effect of laser radiation can be described in a scattering formulation as a finite-volume interaction coupling Coulomb-type fragmentation channels. In particular, laser-induced couplings may be incorporated in a multichannel quantum-defect treatment, in which a set of dressed channels corresponding to different photon numbers is defined, with intensity-dependent quantum defects and mixing angles. These quantities may be obtained by solving a system of close-coupling equations for the electron wave function, in a frame where the asymptotic electron oscillations are transformed away. This allows us to read off at a finite distance a radiative reaction matrix, which is a smooth function of energy for an energy range small compared with the photon frequency, and contains the net effect of radiative couplings. Calculations are presented for ionization of hydrogen s states in circularly polarized laser light, with allowance for above-threshold photon absorption. ©1987 The American Physical Society
• W. Henle, H. Ritsch, P. Zoller Rydberg wave packets in many-electron atoms excited by short laser pulses, Phys. Rev. A 36 683–692 (1987-07-02), http://dx.doi.org/10.1103/PhysRevA.36.683 doi:10.1103/PhysRevA.36.683 (ID: 376900) Toggle Abstract
  An atomic electron excited to a coherent superposition of Rydberg states by a short laser pulse corresponds to a wave packet moving on a radial Kepler orbit. The dynamics of the motion of the wave packet can be observed in a two-photon process where a first laser pulse excites the wave packet, which at a later time is probed by a second pulse. In a many-electron atom a single valence electron excited to the Rydberg wave packet can exchange energy with the atomic ion core (electron correlation), whenever the Rydberg wave packet passes through the atomic core region. We can view this orbiting of the wave packet as a succession of below-threshold inelastic scattering events from the atomic ion core. A theory of two-photon absorption with time-delayed short laser pulses is developed which is based on a ‘‘smooth’’ multichannel quantum-defect Green function. ©1987 The American Physical Society
• M. Hamilton, K. Arnett, S. Smith, D. Elliott, M. Dziemballa, P. Zoller Saturation of an optical transition by a phase-diffusing laser field, Phys. Rev. A 36 178–188 (1987-07-01), http://dx.doi.org/10.1103/PhysRevA.36.178 doi:10.1103/PhysRevA.36.178 (ID: 376901) Toggle Abstract
  The dependence of the optical Autler-Townes effect on laser field phase fluctuations describable by a two-dimensional Markovian process (phase-diffusion model with a non-Lorentzian line shape) is investigated experimentally in atomic sodium. An intense cw laser tuned to near resonance with the 3S1/2(F=2,MF=2)→3P3/2(F=3,MF=3) transition was frequency modulated to generate phase fluctuations with the desired characteristics. A weak probe laser coupling to the 4D5/2(F=4, MF=4) state was used to obtain the double-peaked optical Autler-Townes absorption profiles in order to investigate their dependencies on band shape, bandwidth, intensity, and detuning of the intense fluctuating laser field. Reversals of the peak-height asymmetry and reversion to normal asymmetry with increased detuning were observed and measured. Quantitative studies of the spectral widths and splittings of the peaks are also reported. Measured absorption profiles are in excellent agreement with calculations based on previous theoretical work. ©1987 The American Physical Society
• P. Zoller, M. Marte, D. Walls Quantum jumps in atomic systems, Phys. Rev. A 35 198–207 (1987-01-01), http://dx.doi.org/10.1103/PhysRevA.35.198 doi:10.1103/PhysRevA.35.198 (ID: 376897) Toggle Abstract
  We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density p[0,t)(t1,t2,..., tn) which gives us the probability density that exactly n photons are emitted at times t1,t2,...,tn by the atom in the time interval [0,t). We show that p[0,t) essentially factorizes into products of conditional densities c̃(τ) that, given a photon is emitted at time zero, the next photon emission occurs at time τ. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ‘‘quantum jumps.’’ ©1987 The American Physical Society
• W. Henle, P. Zoller Multichannel quantum defect parametrisation of resonant multiphoton ionisation, J. Phys. B: At. Mol. Opt. Phys. 20 4007-4025 (1987), http://dx.doi.org/10.1088/0022-3700/20/16/013 doi:10.1088/0022-3700/20/16/013 (ID: 376899) Toggle Abstract
  A theory of resonant multiphoton ionisation with perturbed Rydberg series as intermediate states is developed which parametrises the atomic density matrix equations with the help of multichannel quantum defect theory. The authors apply the theory to stepwise three-photon ionisation of Ba near the 5d7d 1D2 state.

1986

Articles

• R. Blatt, W. Ertmer, P. Zoller, J. Hall Atomic-beam cooling: A simulation approach, Phys. Rev. A 34 3022–3033 (1986-10-04), http://dx.doi.org/10.1103/PhysRevA.34.3022 doi:10.1103/PhysRevA.34.3022 (ID: 377060) Toggle Abstract
  Laser cooling af atoms in an atomic beam is studied theoretically by using a simulation approach derived from a pure-state analysis of resonant radiation pressure. Detailed numerical results are presented discussing the form of the atomic velocity distribution (and its minimum achievable width) and effects due to the spatial (focusing) and frequency variation of a Gaussian laser beam. A comparison of these results with recent experiments is given. ©1986 The American Physical Society
• G. Alber, H. Ritsch, P. Zoller Generation and detection of Rydberg wave packets by short laser pulses, Phys. Rev. A 34 1058–1064 (1986-08-02), http://dx.doi.org/10.1103/PhysRevA.34.1058 doi:10.1103/PhysRevA.34.1058 (ID: 377061) Toggle Abstract
  We discuss the generation and detection of wave packets of Rydberg states by exciting electrons from a low-lying atomic state with a short pulse to a Rydberg series. To observe the motion of the wave packet, we analyze a time-delayed two-photon experiment, where the first laser pulse generates a wave packet, which is then probed by a second short pulse. The two-photon transition probability shows peaks when the time delay between the pulses is a multiple of the classical orbit time. A semiclassical formalism is developed to describe the motion of the wave packet and to analyze the time-delayed two-photon process. ©1986 The American Physical Society
• R. Blatt, P. Zoller, G. Holzmüller, I. Siemers Brownian motion of a parametric oscillator: A model for ion confinement in radio frequency traps, Zeitschrift für Physik D; Atoms, Molecules and Clusters 4 121 - 126 (1986-06-01), http://dx.doi.org/10.1007/BF01437349 doi:10.1007/BF01437349 (ID: 376916) Toggle Abstract
  The distribution function for Brownian motion of a parametric oscillator is calculated exactly with the help of continued fraction expansions in the long time limit. We derive expressions for the energy and the widths of the spatial and velocity distribution. Our results are relevant to understand confinement of particles in radio frequency ion traps.

1985

Articles

• M. J. Fink, P. Zoller One- and two-photon detachment of negative hydrogen ions: a hyperspherical adiabatic approach, J. Phys. B: At. Mol. Opt. Phys. 18 L373-L377 (1985), http://dx.doi.org/10.1088/0022-3700/18/12/005 doi:10.1088/0022-3700/18/12/005 (ID: 377066) Toggle Abstract
  The authors report results on one- and two-photon detachment cross sections of negative hydrogen ions from the 1Se ground state in lowest-order perturbation theory using an adiabatic hyperspherical approximation.
• F. Trombetta, G. Ferrante, K. Wodkiewicz, P. Zoller Field correlation effects in laser-assisted electron scattering: the phase diffusion model, J. Phys. B: At. Mol. Opt. Phys. 18 2915-2930 (1985), http://dx.doi.org/10.1088/0022-3700/18/14/016 doi:10.1088/0022-3700/18/14/016 (ID: 377072) Toggle Abstract
  The authors present a theory of the potential scattering in the presence of a laser field taken with a well stabilised amplitude and a randomly fluctuating phase (phase diffusion model, PDM), and investigate the structure of the scattering lineshapes in the weak- and strong-field limits. The field, with its statistics, enters the theoretical treatment in a non-perturbative way. This gives the possibility of obtaining new information on the role of the statistical properties of the radiation fields in highly non-linear domains of the matter-field interaction, which complements in a significant way what is presently known. The PDM results are compared with those relative to a chaotic field (multimode laser field with a large number of uncorrelated modes). The broadening of the scattering lines is found to be controlled in an essential way by several parameters (field bandwidth, strength of the particle-field coupling, field intensity and so on); among them, the multiplicity of the exchanged photons becomes the most important only in the limit of weak coupling. In the strong-coupling limit, a chaotic field (i.e. a field undergoing amplitude and phase fluctuations) is found to broaden the scattering lines in a more effective way than a PDM field.

1984

Articles

• M. Collett, D. Walls, P. Zoller Spectrum of squeezing in resonance fluorescence, 52 145-149 (1984-11-15), http://dx.doi.org/10.1016/0030-4018(84)90300-6 doi:10.1016/0030-4018(84)90300-6 (ID: 377119) Toggle Abstract
  The spectral squeezing in resonance fluorescence from a two-level atom is calculated. It is shown that for resonance excitation optimum squeezing is obtained for near resonant frequencies of the fluorescent light. An operational definition of the spectrum of squeezing is given based on a discussion of possible experimental configurations.
• H. Klar, P. Zoller, M. Fedorov Laser-induced collective binding in two-electron systems, Phys. Rev. A 30 658–660 (1984-07-01), http://dx.doi.org/10.1103/PhysRevA.30.658 doi:10.1103/PhysRevA.30.658 (ID: 377073) Toggle Abstract
  Doubly excited states of atoms in an intense laser field can be described approximately within the framework of an adiabatic separation method with the use of hyperspherical coordinates. Under suitable conditions, depending on the zero-field atomic spectrum and on the laser field, new laser-induced two-electron resonances appear. ©1984 The American Physical Society
• G. Alber, P. Zoller Structure of autoionizing Rydberg series in strong laser fields: A multichannel-quantum-defect-theory approach, Phys. Rev. A 29 2290–2293 (1984-04-04), http://dx.doi.org/10.1103/PhysRevA.29.2290 doi:10.1103/PhysRevA.29.2290 (ID: 377126) Toggle Abstract
  We study one-photon resonant two-photon ionization into an autoionizing Rydberg series for the case of a weak excitation from the ground state to a resonant intermediate state, followed by a strong-field transition to a structured continuum. The dipole strength for the transition into the autoionizing series is thereby modeled by a multichannel-quantum-defect-theory expression taking into account the infinite number of autoionizing Rydberg states. Analytical expressions are derived for the total ionization rate in the limit of extremely overlapping resonances. ©1984 The American Physical Society
• M. Helm, P. Zoller On the model dependence of laser temporal coherence effects in multiphoton transitions, 49 324-328 (1984-04-01), http://dx.doi.org/10.1016/0030-4018(84)90242-6 doi:10.1016/0030-4018(84)90242-6 (ID: 377075) Toggle Abstract
  Theoretical predictions for laser temporal coherence effects in strongly driven multiphoton transitions are generally based on the assumption of specific stochastic light models. In this paper we discuss the model dependence of these calculations by studying the double optical resonance spectrum in an intense real gaussian and jumplike Markov field. We have found in this context that laser fluctuations can induce line splittings in atomic spectra, which provides a sensitive testing ground for comparing the predictions of different light models. We demonstrate that the results are - at least qualitatively insensitive to the model assumptions.
• J. Cooper, P. Zoller Radiative transfer equations in broad-band, time-varying fields, The Astrophysical Journal 277 813 (1984), http://dx.doi.org/10.1086/161751 doi:10.1086/161751 (ID: 377081) Toggle Abstract
  A derivation of the equation of transfer is obtained by starting with Maxwell's equations in the 'slowly varying envelope' form. Particular attention is paid to characterizing the intensity that is 'seen' by the atom (which is found to be related to a Wigner distribution of the electric field). The equation of transfer is found to be valid for 'broad-band' slowly varying radiation fields.

1983

Articles

• P. Zoller, J. Cooper Nonlinear noise fields and strongly driven atomic transitions, Phys. Rev. A 28 2310–2317 (1983-10-04), URL (ID: 377127) Toggle Abstract
  A theory of the interaction of an atom with an intense nonlinear (non-Gaussian) noise field is developed, with emphasis on the connection with the underlying physics of laser coherence. We point out the possibility of obtaining exact solutions for the stochastically averaged atomic density matrix in terms of (matrix) continued fractions for a large class of nonlinear noise fields by generalizing the techniques developed by Risken and co-workers to solve nonlinear Fokker-Planck equations. As an example we discuss the absorption sepctrum of an atom strongly driven by noisy phase-locked radiation. ©1983 The American Physical Society
• E. Matthias, P. Zoller, D. Elliott, N. Piltch, S. Smith, G. Leuchs Influence of Configuration Mixing in Intermediate States on Resonant Multiphoton Ionization, Phys. Rev. Lett. 50 1914–1917 (1983-06-23), http://dx.doi.org/10.1103/PhysRevLett.50.1914 doi:10.1103/PhysRevLett.50.1914 (ID: 377377) Toggle Abstract
  Resonant three-photon ionization of Ba to a structureless continuum via 6snd Rydberg states was performed in the range 19<~n<~30. It is shown that state mixing in the Rydberg states strongly affects the photoion and photoelectron yields as well as the angular distributions of photoelectrons. The experimental results are explained on the basis of a three-channel quantum-defect theory for the perturbed Rydberg series. ©1983 The American Physical Society
• G. Alber, P. Zoller Spin polarization by selective laser-induced interference, Phys. Rev. A 27 1713–1716 (1983-03-03), http://dx.doi.org/10.1103/PhysRevA.27.1713 doi:10.1103/PhysRevA.27.1713 (ID: 377380) Toggle Abstract
  States behaving like autoionizing states can be selectively induced by laser radiation into one of the continuum spin channels in the photoionization of polarized excited alkaki atoms. As a result of destructive or constructive interference between the direct ionization channel and those introduced by the dressing laser radiation, the cross section of this specific spin component is completely suppressed or enhanced, while leaving the other spin channel unaffected. The q parameter which determines the line shape of the Fano-type resonance can be resonantly tuned as a function of the dressing laser frequency. ©1983 The American Physical Society
• G. Alber, P. Zoller Harmonic generation and multiphoton ionization near an autoionizing resonance, Phys. Rev. A 27 1373–1388 (1983-03-03), http://dx.doi.org/10.1103/PhysRevA.27.1373 doi:10.1103/PhysRevA.27.1373 (ID: 377390) Toggle Abstract
  We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses. ©1982 The American Physical Society
• C. Parigger, P. Zoller, D. Walls Effect of Stark shift on two photon optical tristability, 44 213-218 (1983-01-01), http://dx.doi.org/10.1016/0030-4018(83)90203-1 doi:10.1016/0030-4018(83)90203-1 (ID: 377120) Toggle Abstract
  The effect of Stark shifts on two photon two mode optical multistability is investigated. We find that realistic Stark shifts produce significant changes in the state equations and their stability. Self oscillations, period doubling and optical chaos may occur.
• P. Zoller Stark shifts and resonant multiphoton ionisation in multimode laser fields, J. Phys. B: At. Mol. Opt. Phys. 15 2911 (1983), http://dx.doi.org/10.1088/0022-3700/15/17/023 doi:10.1088/0022-3700/15/17/023 (ID: 377128) Toggle Abstract
  The author presents a theory of resonant multiphoton ionisation by multimode laser light. He investigates N photon resonant N+1 photon ionisation for a high order bound-bound transition with the resonance dominated by the Stark shift. Two aspects of the problem are considered. He studies the bandwidth dependence for the resonant ionisation probability, approximating the multimode laser light by a chaotic field. Secondly, he investigates the effects of finite mode numbers of the multimode laser. Finally, the theory is compared with the recent experimental results of Lompre et al (1981).
• T. Poston, D. Walls, P. Zoller Multiple Bifurcations in Coherent n-photon Processes, J. Mod. Opt. 29 1691 - 1704 (1983), URL (ID: 377133) Toggle Abstract
  We consider a new class of bifurcations that may arise in multiphoton processes inside a coherently driven optical cavity involving more than one mode of the radiation field. For a non-saturable, non-linear medium, a single bifurcation point exists where the symmetric solution bifurcates into a number of non-symmetric solutions. The nature of the bifurcation ranges from a simple pitchfork bifurcation, in the case of four-wave mixing, to more complicated phenomena in higher-order processes. A saturable non-linear medium exhibits similar behaviour for low-input intensities; however, as the input intensity is increased the medium saturates, and at a second bifurcation point the symmetric branch regains its stability. The presence of fluctuations assures the accessibility of the symmetric branch. Thus, for example, for a two-photon absorbing medium we have the possibility of optical tristability involving one symmetric solution and two non-symmetric solutions.
• M. Lewenstein, P. Zoller, J. Mostowski Path integration method applied to (N-1)-resonant N-photon ionisation, J. Phys. B: At. Mol. Opt. Phys. 16 563-568 (1983), http://dx.doi.org/10.1088/0022-3700/16/4/010 doi:10.1088/0022-3700/16/4/010 (ID: 377379) Toggle Abstract
  The authors investigate the problem (N-1) resonant N-photon ionisation of an atom driven by a stochastic field. The authors compare ionisation rates in the presence of a phase-diffusing laser field and light undergoing Gaussian amplitude fluctuations (chaotic field). In the case of the chaotic field the authors obtain exact results with the help of the functional integration method. They also present numerical results for the case of three-resonant four-photon ionisation.

1981

Articles

• D. Walls, P. Zoller Enhanced sensitivity of a gravitational wave detector, Phys. Lett. A 85 118-120 (1981-09-14), http://dx.doi.org/10.1016/0375-9601(81)90238-3 doi:10.1016/0375-9601(81)90238-3 (ID: 377459) Toggle Abstract
  We calculate the change in energy absorbed and the power spectrum in a coherently driven antenna induced by interaction with gravitational radiation. The coherent driving field prepares the antenna in a correlated state which enhances the sensitivity of the detector as proposed in a recent paper by Weber.
• D. Walls, P. Zoller Reduced Quantum Fluctuations in Resonance Fluorescence, Phys. Rev. A 47 709–711 (1981-09-07), http://dx.doi.org/10.1103/PhysRevLett.47.709 doi:10.1103/PhysRevLett.47.709 (ID: 377456) Toggle Abstract
  We demonstrate that reduced quantum fluctuations or squeezing are present in both the atomic observables and the radiation field produced by a two-level atom undergoing resonance fluorescence. ©1981 The American Physical Society
• P. Zoller, G. Alber, R. Salvador ac Stark splitting in intense stochastic driving fields with Gaussian statistics and non-Lorentzian line shape, Phys. Rev. A 24 398–410 (1981-07-01), http://dx.doi.org/10.1103/PhysRevA.24.398 doi:10.1103/PhysRevA.24.398 (ID: 377422) Toggle Abstract
  Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser. ©1981 The American Physical Society
• D. Walls, C. Kunasz, P. Drummond, P. Zoller Bifurcations and multistability in two-photon processes, Phys. Rev. A 24 627–630 (1981-07-01), http://dx.doi.org/10.1103/PhysRevA.24.627 doi:10.1103/PhysRevA.24.627 (ID: 377462) Toggle Abstract
  We consider an intracavity nonlinear medium interacting with two modes of the electromagnetic field via a two-photon process. The cavity is coherently driven at the frequencies of the two modes. We consider as the intracavity medium (a) a two-photon absorber, and (b) N three-level atoms. These systems display a new class of bifurcations, and, in the case of the two-photon absorber, optical tristability is possible. ©1981 The American Physical Society
• P. Lambropoulos, P. Zoller Autoionizing states in strong laser fields, Phys. Rev. A 24 379–397 (1981-07-01), http://dx.doi.org/10.1103/PhysRevA.24.379 doi:10.1103/PhysRevA.24.379 (ID: 377465) Toggle Abstract
  A formalism is developed for the study of autoionizing states under the influence of strong lasers. It is cast in both a semiclassical as well as a fully quantum-mechanical form. A set of integrodifferential equations is derived and solutions are obtained for certain special cases. It is demonstrated that the strong field causes significant distortion of the line profile and that new effects appear in double optical resonance when autoionizing states are involved. ©1981 The American Physical Society
• S. N. Dixit, P. Lambropoulos, P. Zoller Spin polarization of electrons in two-photon resonant three-photon ionization, Phys. Rev. A 24 318–325 (1981-07-01), http://dx.doi.org/10.1103/PhysRevA.24.318 doi:10.1103/PhysRevA.24.318 (ID: 377470) Toggle Abstract
  We present a theory of spin polarization of electrons ejected from atoms by two-photon resonant three-photon ionization. Our treatment includes saturation effects and pays proper attention to the finite rise time of the laser pulse and the non-Lorentzian wings of the laser spectrum. Numerical results for the cesium atoms indicate that due to saturation effects the spin polarization is generally less than its value predicted by perturbation theory. The different saturation behavior of the ionization channels causes a saturation dip to develop in the degree of spin polarization. ©1981 The American Physical Society
• D. Wals, P. Zoller, M. Steyn-Ross Optical bistability from three-level atoms, Quantum Electronics, IEEE Journal 17 380- 384 (1981-03-01), URL (ID: 377454) Toggle Abstract
  A novel mechanism is proposed for optical bistability utilizing the population trapping which may occur in a coherent superposition of sublevels in a three-level system. The resulting bistability does not require atomic saturation and is insensitive to Doppler and laser bandwidth effects.

1980

Articles

• D. Walls, P. Zoller A coherent nonlinear mechanism for optical bistability from three level atoms, 34 260-264 (1980-08-01), http://dx.doi.org/10.1016/0030-4018(80)90029-2 doi:10.1016/0030-4018(80)90029-2 (ID: 377685) Toggle Abstract
  A novel scheme for optical bistability in a coherently driven three level atomic system is proposed. The scheme utilizes the non absorption resonance which occurs due to a population trapping in a coherent superposition of the ground state sublevels. The resulting optical bistability occurs for a lower threshold power than for a two level system and is insensitive to Doppler and laser bandwidth effects.
• S. N. Dixit, P. Zoller, P. Lambropoulos Non-Lorentzian laser line shapes and the reversed peak asymmetry in double optical resonance, Phys. Rev. A 21 1289–1296 (1980-04-04), http://dx.doi.org/10.1103/PhysRevA.21.1289 doi:10.1103/PhysRevA.21.1289 (ID: 377688) Toggle Abstract
  The interaction of an atomic system with a laser having phase fluctuations is studied within the phase-diffusion model, with the finite correlation time of the time derivative of the phase taken into account. This finite correlation time introduces a line shape which is Lorentzian near the center and falls off faster than the Lorentzian at its wings. The authors apply this model to calculate the spectrum of double optical resonance for excitation by a laser having this non-Lorentzian line shape. It is observed that the reversed peak asymmetry reverts to normal far off resonance owing to the cutoff of the laser spectrum, in agreement with recent experiments. Numerical results are presented. ©1980 The American Physical Society
• P. Zoller Laser photon correlation effects in electron scattering, J. Phys. B: At. Mol. Opt. Phys. 13 L249-L252 (1980), http://dx.doi.org/10.1088/0022-3700/13/8/001 doi:10.1088/0022-3700/13/8/001 (ID: 377471) Toggle Abstract
  Photon correlation effects are investigated on account of the multimode structure of laser radiation in electron scattering in the presence of an intense laser field. Appreciable deviations from the Kroll-Watson formula (1973) are found.
• P. Zoller, P. Lambropoulos Laser temporal coherence effects in two-photon resonant three-photon ionisation, J. Phys. B: At. Mol. Opt. Phys. 13 69-83 (1980), http://dx.doi.org/10.1088/0022-3700/13/1/015 doi:10.1088/0022-3700/13/1/015 (ID: 377472) Toggle Abstract
  Presents a theoretical analysis of the effect of laser light statistics on two-photon resonant three-photon ionisation of sodium. The ionisation probability and the population of the atom in the resonant state are compared in the presence of an intensity stabilised laser with a diffusing phase (phase diffusion model) and light undergoing Gaussian amplitude fluctuations (chaotic field). In the limit of large bandwidth fields the resonant two-photon excitation is statistically decoupled from the following ionisation step. A decrease of the bandwidth results in a partial correlation between these two steps manifesting itself in an enhancement of the ionisation probability in the chaotic field. With increasing intensity and the onset of saturation of the bound-bound transition, the ionisation probability and resonant excited-state population in the chaotic field may become smaller than the one in the phase diffusing light. In the large-bandwidth limit the Stark shift in the chaotic field is enhanced, which has a pronounced effect on the effective power-law dependence of the ionisation probability.
• C. Leubner, P. Zoller Gauge invariant interpretation of multiphoton transition probabilities, J. Phys. B: At. Mol. Opt. Phys. 13 3613-3617 (1980), http://dx.doi.org/10.1088/0022-3700/13/18/013 doi:10.1088/0022-3700/13/18/013 (ID: 377686) Toggle Abstract
  It is shown by an elementary discussion that the proper discrimination between the energy operator of the system in a specified gauge and the so-called unperturbed Hamiltonian, as recently emphasised by Yang (1976), resolves apparent difficulties with the gauge invariant interpretation of multiphoton transition probabilities in some of the current literature. In particular, conditions more general than those usually quoted are established, under which either of the interactions -qx.E and -qA.p/m gives the same transition probabilities with the same unperturbed wavefunctions.
• S. N. Dixit, A. Georges, P. Lambropoulos, P. Zoller Comments on the short-time behaviour of multiphoton ionisation, J. Phys. B: At. Mol. Opt. Phys. 13 L157-L158 (1980), http://dx.doi.org/10.1088/0022-3700/13/5/007 doi:10.1088/0022-3700/13/5/007 (ID: 377689) Toggle Abstract
  Some questions regarding the applicability of theoretical results (1977, 1978) for the short-time behaviour of the multiphoton ionisation to the experiments are discussed. It is argued that the relevant conditions could not have been satisfied in the experiments concerned.
• G. Alber, P. Zoller Light statistical dependence of saturated two-photon transitions, J. Phys. B: At. Mol. Opt. Phys. 13 4567-4576 (1980), http://dx.doi.org/10.1088/0022-3700/13/23/014 doi:10.1088/0022-3700/13/23/014 (ID: 377690) Toggle Abstract
  The light statistical dependence of stationary saturated two-photon transitions is discussed. While at low intensities, in comparison with light having a stable amplitude, Gaussian amplitude fluctuations of the exciting radiation are more effective in populating the excited resonant state, light with amplitude fluctuations is less effective in saturating a two-photon transition. The amplitude fluctuations are shown to wash out the resonance curves. While at low intensities the effective Stark shift (i.e. the maximum of the dispersion curve) is larger by a factor of three in light with Gaussian amplitude fluctuations compared with radiation of constant amplitude, this enhancement factor becomes intensity dependent with increasing intensity.

1979

Articles

• P. Zoller Saturation of two-level atoms in chaotic fields, Phys. Rev. A 20 2420–2423 (1979-12-06), http://dx.doi.org/10.1103/PhysRevA.20.2420 doi:10.1103/PhysRevA.20.2420 (ID: 377475) Toggle Abstract
  Exact solutions are presented for the equations describing the stationary population of a two-level atom in a nonmonochromatic ideal chaotic field. The dependence of the excited-state population on the Rabi frequency, bandwidth of the field, spontaneous decay, and detuning is studied and compared with the results obtained for phase-diffusing laser light. The validity of the decorrelation approximation is also investigated. ©1979 The American Physical Society
• P. Zoller Resonant multiphoton ionization by finite-bandwidth chaotic fields, Phys. Rev. A 20 1295 (1979-09-03), http://dx.doi.org/10.1103/PhysRevA.20.1295 doi:10.1103/PhysRevA.20.1295 (ID: 377476) Toggle Abstract
  Resonant multiphoton ionization by finite-bandwidth chaotic fields. ©1979 The American Physical Society
• P. Zoller Ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic chaotic field, Phys. Rev. A 20 1019–1031 (1979-09-03), http://dx.doi.org/10.1103/PhysRevA.20.1019 doi:10.1103/PhysRevA.20.1019 (ID: 377692) Toggle Abstract
  A detailed theoretical analysis of ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic complex chaotic field is presented. It is shown that a one-photon transition undergoes Stark splitting, which is strongly affected by the intensity fluctuations of the chaotic light. On resonance, the lines in the doublet structure of double optical resonance and the sidebands of the triplet structure in resonance fluorescence are broadened by the intensity fluctuations and tend to copy the Rayleigh distribution of the field amplitude. Off resonance, the asymmetry of the doublet in double optical resonance is reversed and a sideband asymmetry appears in resonance fluorescence for finite bandwidth of the incident light. While on resonance the splitting is always reduced, off resonance the intensity fluctuations may lead to an enhancement of the splitting in comparison to phase-diffusing light. ©1979 The American Physical Society
• A. Georges, P. Lambropoulos, P. Zoller Saturation and Stark Splitting of Resonant Transitions in Strong Chaotic Fields of Arbitrary Bandwidth, Phys. Rev. Lett. 42 1609–1613 (1979-06-11), http://dx.doi.org/10.1103/PhysRevLett.42.1609 doi:10.1103/PhysRevLett.42.1609 (ID: 377687) Toggle Abstract
  We report the solution of the problem of saturation and ac Stark splitting of a resonant transition in a strong chaotic field of arbitrary bandwidth. We present results for double optical resonance and resonance fluorescence and compare them to those obtained for a phase-diffusion field. ©1979 The American Physical Society
• P. Zoller, P. Lambropoulos Non-Lorentzian laser lineshapes in intense field-atom interaction, J. Phys. B: At. Mol. Opt. Phys. 12 L547-L551 (1979), http://dx.doi.org/10.1088/0022-3700/12/18/003 doi:10.1088/0022-3700/12/18/003 (ID: 377691) Toggle Abstract
  The effect of a cut off of the Lorentzian laser lineshape (as predicted by the phase-diffusion model of ideal laser theory) on the laser-atom interaction is investigated. The damping terms in the averaged density matrix equation of the atom, arising from the finite laser bandwidth are shown to be multiplied by a detuning-dependent cut-off. For detunings of the laser well within the Lorentzian part of the spectrum, the authors recover the previously derived results, while these damping terms are seen to drop out for detuning larger than the cut-off. Within their model, therefore, a laser with a lineshape falling faster than a Lorentzian, and for large detunings, appears monochromatic to the atom. In particular, the authors obtain qualitative agreement with recent experiments in which the reversed peak asymmetry in the doublet of double optical resonance persists only within a certain range of detuning from resonance.

1978

Articles

• P. Zoller, F. Ehlotzky Resonance fluorescence in phase-frequency modulated laser fields, Zeitschrift für Physik A 285 245 - 247 (1978-09-00), http://dx.doi.org/10.1007/BF01408234 doi:10.1007/BF01408234 (ID: 377744) Toggle Abstract
  Recently we have formulated a generalization of Mollow's theory of the resonant dynamic Stark effect by adding a stochastic description of the laser light fluctuations according to a model due to Burshtein et al. In this paper we apply our theory to the case of simultaneous phase-frequency modulated incident light and compare the results with our foregoing predictions for pure phase modulation. In case of detuning we find the asymmetry of the triplet to be less marked than in our previous work. The financial support of this work by the Österreichische Fonds zur Förderung der wissenschaftlichen Forschung under contract number 2097 is gratefully acknowledged.
• P. Zoller Atomic relaxation and resonance fluorescence in intensity and phase-fluctuating laser light, J. Phys. B: At. Mol. Opt. Phys. 11 2825-2832 (1978), http://dx.doi.org/10.1088/0022-3700/11/16/010 doi:10.1088/0022-3700/11/16/010 (ID: 377755) Toggle Abstract
  The relaxation process and resonance fluorescence of a two-level atom strongly driven by stochastically fluctuating laser light is studied. A laser with small intensity fluctuations about a constant mean value and a diffusing phase is assumed. Depending on the relative time scales of the intensity fluctuations and the atomic response to these fluctuations, the time decay of the atomic population is found to be non-exponential. The broadening of the sidebands in the triplet spectrum of resonance fluorescence is shown to be non-Lorentzian.
• P. Zoller Emission spectra of atoms strongly driven by finite bandwidth laser light, J. Phys. B: At. Mol. Opt. Phys. 11 805-810 (1978), http://dx.doi.org/10.1088/0022-3700/11/5/014 doi:10.1088/0022-3700/11/5/014 (ID: 377758) Toggle Abstract
  Assuming a phase diffusion model for the laser light, two-time atomic correlation functions for strongly driven atoms are calculated via the quantum regression theorem. This formalism is applied to the determination of the emission spectrum of a two-level atom for transition to or from a third unperturbed level. In comparison with the purely radiatively damped atom marked modifications of the asymmetry of the doublet are predicted.

1977

Articles

• P. Zoller, F. Ehlotzky Resonance fluorescence in modulated laser fields, J. Phys. B: At. Mol. Opt. Phys. 10 3023-3032 (1977), http://dx.doi.org/10.1088/0022-3700/10/15/013 doi:10.1088/0022-3700/10/15/013 (ID: 377764) Toggle Abstract
  On the basis of a stochastic model of Burshtein et al. (1967) which assumes the phases, frequencies and/or amplitudes of the radiation field to constitute a randomly time-varying jump-like Markoff process, a generalisation of Mollow's theory (1975) of the dynamic Stark effect is formulated leading to predictions for the resonant scattering spectrum for a two-level atom quite similar to those published in the work of Agarwal (1976), of Eberly (1976) and of Kimble et al. (1977) who use a different approach. Apparently, the general form of the resonant scattering spectrum in a modulated radiation field depends less strongly on the particular stochastic model of the laser light than might be expected.
• P. Zoller Fokker-Planck equation treatment of atomic relaxation and resonance fluorescence in phase-modulated laser light, J. Phys. B: At. Mol. Opt. Phys. 10 L321-L324 (1977), http://dx.doi.org/10.1088/0022-3700/10/8/012 doi:10.1088/0022-3700/10/8/012 (ID: 377769) Toggle Abstract
  The phase-diffusion laser models is coupled to a multi-level system. Equations of motion for the density matrix elements and for the spectral emission rate are derived using Fokker-Planck equation techniques. As an illustrative example a two-level system is considered. The results are found to agree with those of Agarwal (1976).