
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 (20241017),
http://dx.doi.org/10.1103/PhysRevLett.133.163403 doi:10.1103/PhysRevLett.133.163403 (ID: 721233)
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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 periodicallydriven (Floquet) system of either spins or hardcore 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, nearestneighbor, free boson model, we find evidence  from both a coupled wire analysis and largescale 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 Halperin221 fractional quantum Hall state at 1/6 filling (on a honeycomb lattice). At 1/2 filling on the square lattice, timereversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an opticallatticebased 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 Manybody entropies and entanglement from polynomiallymany local measurements,
Phys. Rev. X 14 31035 (20240826),
http://dx.doi.org/10.1103/PhysRevX.14.031035 doi:10.1103/PhysRevX.14.031035 (ID: 721143)
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Randomized measurements (RMs) provide a practical scheme to probe complex manybody 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 postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixedstate entanglement via partialtransposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on onedimensional 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 polynomiallymany measurements and postprocessing operations. We prove that the AFCs hold for finitedepth quantumcircuit states and translationinvariant matrixproduct density operators, and provide numerical evidence that they are satisfied in more general, physicallyinteresting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixedstate 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 (20240701),
http://dx.doi.org/10.1103/PhysRevLett.133.010402 doi:10.1103/PhysRevLett.133.010402 (ID: 721174)
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The nonequilibrium physics of manybody 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 trappedion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed 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 (20240507),
http://dx.doi.org/10.1103/PhysRevLett.132.190001 doi:10.1103/PhysRevLett.132.190001 (ID: 721252)
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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 manybody 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 longterm 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 faulttolerant 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 (20240226),
http://dx.doi.org/10.1088/20589565/ad2986 doi:10.1088/20589565/ad2986 (ID: 720821)
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With today's quantum processors venturing into regimes beyond the capabilities of classical devices [13], 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 [68], 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, proofofprinciple experiment a verification protocol using only classical means on a small trappedion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gatelevel 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 scaledup version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on postquantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaledup 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 (20240118),
http://dx.doi.org/10.1103/PhysRevA.109.012422 doi:10.1103/PhysRevA.109.012422 (ID: 720958)
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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 loworder moments of the partially transposed reduced density matrix and show that this ratio takes welldefined 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 mixedstate randomness, in quantum states formed in quantum computers and programmable quantum simulators.

R. Ott, T. Zache, N. Maskara, M. Lukin, P. Zoller, H. Pichler Probing topological entanglement on large scales,
(20240822),
arXiv:2408.12645 arXiv:2408.12645 (ID: 721272)
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Topologically ordered quantum matter exhibits intriguing longrange 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 longrange topological entanglement from measurements on small subsystems of finite size, trading an exponential number of measurements against a polynomialtime evolution. Our protocol is general and readily applicable to various quantum simulation architectures. We apply our method to various stringnet models representing both abelian and nonabelian 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 spincats as biased qubits,
(20240808),
arXiv:2408.04421v1 arXiv:2408.04421v1 (ID: 721274)
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We present a biased atomic qubit, universally implementable across all atomic platforms, encoded as a `spincat' 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 `spincat', leading to the designation `dark spincat'. We demonstrate that under strong Rabi drive and for large Fg, the `dark spincat' is autonomously stabilized against common noise sources and encodes a qubit with significantly biased noise. Specifically, the bitflip error rate decreases exponentially with Fg relative to the dephasing rate. We provide an analysis of dark spincats, their robustness to noise, and discuss biaspreserving single qubit and entangling gates, exemplified on a Rydberg tweezer platform.

A. Chu, V. MartinezLahuerta, M. Miklos, K. Kim, P. Zoller, K. Hammerer, J. Ye, A. M. Rey Exploring the interplay between massenergy equivalence, interactions and entanglement in an optical lattice clock,
(20240606),
arXiv:2406.03804v1 arXiv:2406.03804v1 (ID: 721260)
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We propose protocols that probe manifestations of the massenergy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the massenergy 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 photonmediated 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 weaklydissipative quantum manybody systems,
(20240510),
arXiv:2405.06768 arXiv:2405.06768 (ID: 721275)
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We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from nonequilibrium quench dynamics in the limit of weakly dissipative manybody 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 postprocessing, 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,
(20240422),
arXiv:2404.14194 arXiv:2404.14194 (ID: 721276)
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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 GreenbergerHorneZeilinger statebased interferometer, renowned for achieving the Heisenberg limit in singleparameter 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 lowdepth quantum circuits approaching the optimal sensing performance in the manyrepetition 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 trappedion 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.

R. Ott, T. Zache, M. Prüfer, S. Erne, M. Tajik, H. Pichler, J. Schmiedmayer, P. Zoller Hamiltonian Learning in Quantum Field Theories,
(20240102),
arXiv:2401.01308 arXiv:2401.01308 (ID: 721175)
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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.

M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring LargeScale Entanglement in Quantum Simulation,
Nature 624 539 (20231129),
http://dx.doi.org/10.1038/s41586023067680 doi:10.1038/s41586023067680 (ID: 721080)
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Entanglement is a distinguishing feature of quantum manybody 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 51ion programmable quantum simulator and perform sampleefficient `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 spatiallyvarying temperature profile as a signature of entanglement. Our results also show the transition from area to volumelaw 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 wideranging applicability to revealing and understanding entanglement in manybody problems with local interactions including higher spatial dimensions.

T. Zache, D. Gonzalez Cuadra, P. Zoller Quantum and classical spin network algorithms for qdeformed KogutSusskind gauge theories,
Phys. Rev. Lett. 131 171902 (20231024),
http://dx.doi.org/10.1103/PhysRevLett.131.171902 doi:10.1103/PhysRevLett.131.171902 (ID: 721075)
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Treating the infinitedimensional Hilbert space of nonabelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce qdeformed KogutSusskind 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 infinitedimensional local Hilbert space while preserving essential symmetryrelated properties. This enables the development of both quantum as well as quantuminspired classical Spin Network Algorithms for qdeformed 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) KogutSusskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational groundstate 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 realtime evolution by analytically diagonalizing the SU(2)k plaquette interactions. Our work gives a new perspective for the application of tensor network methods to highenergy physics and paves the way for quantum simulations of nonabelian gauge theories far from equilibrium where no other methods are currently available.

T. Zache, D. GonzálezCuadra, P. Zoller Fermionqudit quantum processors for simulating lattice gauge theories with matter,
Quantum 7 1140 (20231016),
http://dx.doi.org/10.22331/q202310161140 doi:10.22331/q202310161140 (ID: 721067)
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Simulating the realtime 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 Rydbergbased architecture, codesigned to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardwareefficient manner. Ref. [1] showed how a qudit processor, where nonabelian gauge fields are locally encoded and timeevolved, considerably reduces the required simulation resources compared to standard qubitbased 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 gaugematter interactions. We exemplify the flexibility of such a fermionqudit processor by focusing on two paradigmatic highenergy phenomena. First, we present a resourceefficient protocol to simulate the AbelianHiggs 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 nonabelian 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 experimentallyrelevant quantities in particle physics.

D. GonzálezCuadra, 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 (20230822),
http://dx.doi.org/10.1073/pnas.2304294120 doi:10.1073/pnas.2304294120 (ID: 721066)
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Simulating the properties of manybody fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubitbased quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on nearterm architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardwareefficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydbergmediated 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 fermionqubit 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 (20230807),
http://dx.doi.org/10.1103/PhysRevLett.131.060601 doi:10.1103/PhysRevLett.131.060601 (ID: 720886)
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We provide a measurement protocol to estimate 2 and 4point fermionic correlations in ultracold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with highresolution 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 faulttolerant quantum computation with squeezed cat qubits,
npj Quantum Information 9 (20230803),
http://dx.doi.org/10.1038/s41534023007460 doi:10.1038/s41534023007460 (ID: 720895)
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We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuousvariable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a twocomponent SC while autonomously correcting the errors. The implementation of such dissipation only requires loworder 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 trappedion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the biaspreserving 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 discretevariable code. The surfaceSC 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 repetitionSC 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 MultiParameter Quantum Metrology and Vector Field Sensing,
PRX Quantum 4 20333 (20230601),
http://dx.doi.org/10.1103/PRXQuantum.4.020333 doi:10.1103/PRXQuantum.4.020333 (ID: 721056)
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We study multiparameter 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 Natom 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 multiparameter 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.

A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller Highdimensional SO(4)symmetric Rydberg manifolds for quantum simulation,
Quantum Sci. Technol. 8 (20221219),
http://dx.doi.org/10.1088/20589565/aca996 doi:10.1088/20589565/aca996 (ID: 720885)
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We develop a toolbox for manipulating arrays of Rydberg atoms prepared in highdimensional hydrogenlike 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 wellstructured manifolds of states with principal quantum number n. This enables us to construct generalized largespin Heisenberg models for which we develop statepreparation 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 sineGordon and massive Schwinger models. Moreover, these highdimensional manifolds also offer the opportunity to perform quantum information processing operations for quditbased quantum computing, which we exemplify with an entangling gate and a statetransfer 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 (20221202),
http://dx.doi.org/10.1038/s42254022005352 doi:10.1038/s42254022005352 (ID: 720824)
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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 manyqubit 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 (20221130),
http://dx.doi.org/10.1103/PRXQuantum.3.040324 doi:10.1103/PRXQuantum.3.040324 (ID: 720833)
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Twodimensional p+ip superconductors and superfluids are systems that feature chiral behavior emerging from the Cooper pairing of electrons or neutral fermionic atoms with nonzero 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 twodimensional trappedion crystals in a Penning trap to simulate the dynamical phases of twodimensional p+ip superfluids. This is accomplished by mapping the presence or absence of a Cooper pair into an effective spin1/2 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 meanfield 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 GonzálezCuadra , T. Zache, J. Carrasco, Barbara Kraus, Peter Zoller Hardware efficient quantum simulation of nonabelian gauge theories with qudits on Rydberg platforms,
Phys. Rev. Lett. 129 160501 (20221013),
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 (20220830),
http://dx.doi.org/10.1088/20589565/ac88f5 doi:10.1088/20589565/ac88f5 (ID: 720858)
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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 manybody 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 longrange 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 faulttolerant 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 (20220819),
http://dx.doi.org/10.1088/17518121/ac8087 doi:10.1088/17518121/ac8087 (ID: 720859)
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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 fewbody 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 loworder 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 manybody 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 (20220818),
http://dx.doi.org/10.1103/PRXQuantum.3.030324 doi:10.1103/PRXQuantum.3.030324 (ID: 720828)
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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 timeindependent, 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 orderbyorder 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 stateoftheart 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 nonunitary 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 (20220727),
http://dx.doi.org/10.1038/s41586022049406 doi:10.1038/s41586022049406 (ID: 720857)
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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 shortterm 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, highenergy physics and quantum chemistry. This would impact several important realworld 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 faulttolerant digital quantum computers but also already today through specialpurpose 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 faulttolerant hardware. Hybrid digital–analogue devices that exist today already promise substantial flexibility in nearterm applications.

M. Di Liberto, A. Kruckenhauser, P. Zoller, M. Baranov Topological phonons in arrays of ultracold dipolar particles,
Quantum 6 731 (20220531),
http://dx.doi.org/10.22331/q20220607731 doi:10.22331/q20220607731 (ID: 720680)
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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 faulttolerant applications. We discuss how to design and study a large variety of topologyrelated phenomena for phononlike 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 longrange interactions dominate over singleparticle 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 LiHaldane Conjecture in Topological Quantum Matter,
Quantum 6 702 (20220427),
http://dx.doi.org/10.22331/q20220427702 doi:10.22331/q20220427702 (ID: 720692)
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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 quasilocal 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 noninteracting 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 manybody systems.

V. Kuzmin, T. Zache, L. Pastori, A. Celi, M. Baranov, P. Zoller Probing infinite manybody quantum systems with finite size quantum simulators,
PRX Quantum 3 20304 (20220406),
http://dx.doi.org/10.1103/PRXQuantum.3.020304 doi:10.1103/PRXQuantum.3.020304 (ID: 720681)
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Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finitesize 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 translationinvariant infinitesized 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 quasiparticle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a nonintegrable extended SuSchriefferHeeger 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 Symmetryresolved dynamical purification in synthetic quantum matter,
SciPost Phys. 12 106 (20220325),
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, symmetryresolved 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 logvolume and logarea 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 symmetryresolved 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 manybody dynamics in open quantum systems, and, in particular, in noisyintermediate 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 (20220323),
http://dx.doi.org/10.1038/s41586022044354 doi:10.1038/s41586022044354 (ID: 720667)
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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 lowdepth, variational quantum circuits searching for optimal input states and measurement operators in a trapped ion platform. We perform entanglementenhanced 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 quantumclassical feedback optimization to `selfcalibrate' 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 manybody quantum chaos with quantum simulators,
Phys. Rev. X (20220127),
http://dx.doi.org/10.1103/PhysRevX.12.011018 doi:10.1103/PhysRevX.12.011018 (ID: 720665)
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The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of manybody quantum chaos. In addition, partial spectral form factors (pSFFs) can be defined which refer to subsystems of the manybody system. They provide unique insights into energy eigenstate statistics of manybody 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 manybody spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum manybody 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 manybody quantum chaotic behavior, thermalization and manybody localization in closed quantum systems which we illustrate with simulations for Hamiltonian and Floquet manybody spinsystems.

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 (20211206),
http://dx.doi.org/10.1103/PhysRevX.11.041045 doi:10.1103/PhysRevX.11.041045 (ID: 720629)
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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 oneaxis 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 longterm instability. Remarkably, even lowdepth 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 (20211111),
http://dx.doi.org/10.1103/PhysRevLett.127.200503 doi:10.1103/PhysRevLett.127.200503 (ID: 720632)
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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 machinelearning and tensor networks using partial information on the quantum state. In present experimental settings of engineered manybody 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 (20211022),
http://dx.doi.org/10.1103/PhysRevLett.127.170501 doi:10.1103/PhysRevLett.127.170501 (ID: 720649)
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Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum manybody states in analog quantum simulation. We describe a protocol where spatial deformations of the manybody 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 FermiHubbard models in quasi1D geometries, finding excellent agreement of the EH with BisognanoWichmann predictions. Subsequent ondevice 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 Symmetryresolved entanglement detection using partial transpose moments,
npj Quantum Information 7 (20211020),
http://dx.doi.org/10.1038/s4153402100487y doi:10.1038/s4153402100487y (ID: 720635)
Toggle Abstract
We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The kth condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the PeresHorodecki 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. nonidentical, 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 (20210825),
http://dx.doi.org/10.1103/PRXQuantum.2.030334 doi:10.1103/PRXQuantum.2.030334 (ID: 720526)
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Quantum computing is in its greatest upswing, with socalled noisyintermediatescalequantum 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 fundamentalparticle interactions. On the way to their fullfledged quantum simulations, the challenge of limited resources on nearterm quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study groundstate properties in twodimensional 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 lowenergy observable quantities, e.g., the hadron spectrum, in the continuum theory. By including both dynamical matter and a nonminimal gaugefield truncation, we provide the novel opportunity to observe 2D effects on presentday quantum hardware. More specifically, we present two variationalquantumeigensolver (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 qubitbased 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. (20210624),
http://dx.doi.org/10.1038/s4156702101260w doi:10.1038/s4156702101260w (ID: 720530)
Toggle Abstract
Entanglement is the crucial ingredient of quantum manybody 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 fewbody 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 BisognanoWichmann 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 longrange 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 Symmetryresolved dynamical purification in synthetic quantum matter,
SciPost Phys. 12 (20210325),
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 (20210303),
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 crossdevice 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 Manybody Chern number from statistical correlations of randomized measurements,
Phys. Rev. Lett. 126 50501 (20210201),
http://dx.doi.org/10.1103/PhysRevLett.126.050501 doi:10.1103/PhysRevLett.126.050501 (ID: 720496)
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One of the main topological invariants that characterizes several topologicallyordered phases is the manybody 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 linearresponse 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 ancillafree 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 disklike geometries that are more amenable to current quantum simulator architectures.

A. Elben, R. Kueng, H. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, B. Vermersch Mixedstate entanglement from local randomized measurements,
Phys. Rev. Lett. 125 (20201111),
http://dx.doi.org/10.1103/PhysRevLett.125.200501 doi:10.1103/PhysRevLett.125.200501 (ID: 720525)
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We propose a method for detecting bipartite entanglement in a manybody 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 postprocessing using the classical shadows framework. Our method can be applied to any quantum system with singlequbit 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 (20201106),
http://dx.doi.org/10.1103/PRXQuantum.1.020311 doi:10.1103/PRXQuantum.1.020311 (ID: 720652)
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Quantum annealing aims at solving optimization problems efficiently by preparing the ground state of an Ising spinHamiltonian quantum mechanically. A prerequisite of building a quantum annealer is the implementation of programmable longrange two, three, or multispin Ising interactions. We discuss an architecture, where the required spin interactions are implemented via twoport 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 threedimensional (3D) character of atomic platforms, including atoms in optical lattices and Rydberg tweezer arrays. The realization only requires engineering onsite terms and twobody interactions between nearest neighboring qubits. The locally coupled spin model on a 3D cubic lattice is sufficient to effectively produce arbitrary alltoall coupled Ising Hamiltonians. We illustrate the approach for fewspin devices solving MaxCut and prime factorization problems, and discuss the potential scaling to large atombased systems.

J. ArgüelloLuengo, . GonzálezTudela, T. Shi, P. Zoller, J. I. Cirac Quantum Simulation of 2D Quantum Chemistry in Optical Lattices,
Phys. Rev. Research 2 (20201016),
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 NonDemolition Couplings to Atomic Clock Qubits,
PRX Quantum 1 (20201009),
http://dx.doi.org/10.1103/PRXQuantum.1.020302 doi:10.1103/PRXQuantum.1.020302 (ID: 720493)
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We discuss monitoring the time evolution of an analog quantum simulator via a quantum nondemolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum manybody 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 manybody systems, where the aim is to identify signatures of ergodic vs. nonergodic 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 (20200826),
http://dx.doi.org/10.1103/PRXQuantum.1.020316 doi:10.1103/PRXQuantum.1.020316 (ID: 720527)
Toggle Abstract
Trappedion quantum computers have demonstrated highperformance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long onedimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubitqubit 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 manybody physics with ultracold polar molecules: Nanostructured potential barriers and interactions,
Phys. Rev. A 102 23320 (20200819),
http://dx.doi.org/10.1103/PhysRevA.102.023320 doi:10.1103/PhysRevA.102.023320 (ID: 720474)
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We design dipolar quantum manybody 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 singlebody potential barriers and twobody 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 manybody systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standingwave optical light fields exploiting optical nonlinearities. In the second, static electricfield 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 (20200804),
http://dx.doi.org/10.1140/epjd/e20201005718 doi:10.1140/epjd/e20201005718 (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 longterm 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 nonAbelian 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 proofofprinciple 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 (20200616),
http://dx.doi.org/10.1103/PhysRevX.10.021057 doi:10.1103/PhysRevX.10.021057 (ID: 720355)
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Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from highenergy physics to condensed matter. On a lattice, gauge invariance and gauge invariant (plaquette) interactions involve (at least) fourbody 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 RokhsarKivelson Hamiltonian a 2D U(1) lattice gauge theory that describes quantum dimer and spinice 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 RokhsarKivelson Hamiltonian adiabatically, and probe them and their quench dynamics by onsite 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 Manybody topological invariants from randomized measurements,
Sci. Adv. 6 (20200410),
http://dx.doi.org/10.1126/sciadv.aaz3666 doi:10.1126/sciadv.aaz3666 (ID: 720289)
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The classification of symmetryprotected 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 manybody topological invariants, which are quantized nonlocal correlators for the manybody wavefunction. While SPT phases can now be realized in interacting synthethic quantum systems, the direct measurement of quantized manybody topological invariants has remained so far elusive. Here, we propose measurement protocols for manybody topological invariants for all types of protecting symmetries of onedimensional interacting bosonic systems. Our approach relies on randomized measurements implemented with local random unitaries, and can be applied to any spin system with singlesite 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 OnChip Photonic Interface for Superconducting Circuits,
npj Quantum Information 6 (20200327),
http://dx.doi.org/10.1038/s4153402002619 doi:10.1038/s4153402002619 (ID: 720478)
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We propose and analyze a passive architecture for realizing onchip, 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 manybody 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 Nondemolition Measurement of a ManyBody Hamiltonian,
Nat. Commun. 11 (20200207),
http://dx.doi.org/10.1038/s41467020144895 doi:10.1038/s41467020144895 (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 nondemolition (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 manybody 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 manybody observable. Here, we describe how a QND measurement of the Hamiltonian of an interacting manybody system can be implemented in a trappedion analog quantum simulator. Through a single shot measurement, the manybody 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 nonequilibrium 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 trappedion quantum simulator with tunable range interactions,
Phys. Rev. Lett. 124 240505 (20200107),
http://dx.doi.org/10.1103/PhysRevLett.124.240505 doi:10.1103/PhysRevLett.124.240505 (ID: 720436)
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In ergodic manybody 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 manybody dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10qubit trappedion quantum simulator representing a tunable longrange interacting spin system, by estimating outoftime 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 CrossPlatform Verification of Intermediate Scale Quantum Devices,
Phys. Rev. Lett. 124 10504 (20200106),
http://dx.doi.org/10.1103/PhysRevLett.124.010504 doi:10.1103/PhysRevLett.124.010504 (ID: 720357)
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We describe a protocol for crossplatform 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 (mixedstate) 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 proofofprinciple, we present the measurement of experimenttheory fidelities for entangled 10qubit quantum states in a trapped ion quantum simulator.

S. Barbarino, J. Yu, P. Zoller, J. Budich Preparing Atomic Topological Quantum Matter by Adiabatic NonUnitary Dynamics,
Phys. Rev. Lett. 124 10401 (20200102),
http://dx.doi.org/10.1103/PhysRevLett.124.010401 doi:10.1103/PhysRevLett.124.010401 (ID: 720390)
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Motivated by the outstanding challenge of realizing lowtemperature 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 (nonsymmetry 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 spindependent hexagonal optical lattice.

R. Belyansky, J. Young, P. Bienias, Z. Eldredge, A. Kaufman, P. Zoller, A. V. Gorshkov Nondestructive cooling of an atomic quantum register via stateinsensitive Rydberg interactions,
Phys. Rev. Lett. 123 213603 (20191120),
http://dx.doi.org/10.1103/PhysRevLett.123.213603 doi:10.1103/PhysRevLett.123.213603 (ID: 720326)
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We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing stateinsensitive Rydberg interactions between the datacarrying 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 stateinsensitive interactions between the data and the auxiliary atoms but tunable and nontrivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spinmodel.

J. ArgüelloLuengo, A. GonzalezTudela, T. Shi, P. Zoller, J. I. Cirac Analog quantum chemistry simulation,
Nature 574 218 (20191009),
http://dx.doi.org/10.1038/s4158601916144 doi:10.1038/s4158601916144 (ID: 720043)
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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 wellestablished technologies, namely, ultracold 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 (20190920),
http://dx.doi.org/10.1038/s4153401901925 doi:10.1038/s4153401901925 (ID: 720105)
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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 trappedion quantum simulators which implement DQS of alltoall interacting spin1/2 systems. These platforms thus enable indepth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of outoftimeordered correlators.

M. Lacki, P. Zoller, M. Baranov Stroboscopic painting of optical potentials for atoms with subwavelength resolution,
Phys. Rev. A 100 (20190911),
http://dx.doi.org/10.1103/PhysRevA.100.033610 doi:10.1103/PhysRevA.100.033610 (ID: 720290)
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We propose and discuss a method to engineer stroboscopically arbitrary onedimensional 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 comblike 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 timeaveraged potentials. In contrast to usual stroboscopic engineering which becomes increasingly accurate with increasing the stroboscopic frequency, the presence of the bright states of the \Lambdasystem 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 timeaveraged potential fails. For frequencies below this bound, the lowest Bloch band of quasienergies contains several avoidedcrossing 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 spinsqueezing algorithms on programmable quantum sensors,
Phys. Rev. Lett. 123 260505 (20190822),
http://dx.doi.org/10.1103/PhysRevLett.123.260505 doi:10.1103/PhysRevLett.123.260505 (ID: 720356)
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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 ondemand 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 spinsqueezed states on Sr atom tweezer arrays, where finiterange 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 (20190627),
http://dx.doi.org/10.1103/PhysRevX.9.021061 doi:10.1103/PhysRevX.9.021061 (ID: 720042)
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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 manybody systems. Our protocol, which does not require reversing time evolution or auxiliary degrees of freedom, can be realized in stateoftheart 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 (20190627),
http://dx.doi.org/10.1103/PhysRevB.99.241302 doi:10.1103/PhysRevB.99.241302 (ID: 720058)
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We propose and analyze a setup based on (solidstate) qubits coupled to a common multimode transmission line, which allows for coherent spinspin interactions over macroscopic onchip distances, without any groundstate 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 (longrange) 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 Selfverifying variational quantum simulation of lattice models,
Nature 569 360 (20190515),
http://dx.doi.org/10.1038/s4158601911774 doi:10.1038/s4158601911774 (ID: 720076)
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Hybrid classicalquantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum coprocessor, while benefitting from quantum resources. Here we present experiments demonstrating selfverifying, hybrid, variational quantum simulation of lattice models in condensed matter and highenergy 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 coprocessor is a programmable, trappedion 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 longstanding 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 manybody quantum states,
Phys. Rev. A 99 52323 (20190515),
http://dx.doi.org/10.1103/PhysRevA.99.052323 doi:10.1103/PhysRevA.99.052323 (ID: 720100)
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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 trappedion 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 (20190419),
http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034)
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Entanglement is the key feature of manybody 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 trappedion 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 (20190412),
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 manybody system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localizationby constraining the time evolution through quantum interferencestrongly bounds these errors for local observables. Consequently, for generic quantum manybody 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 manybody 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 timeevolution 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 (20190401),
http://dx.doi.org/10.1038/s4158601910701 doi:10.1038/s4158601910701 (ID: 720062)
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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 realtime dynamics in isolated, nonequilibrium 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 KibbleZurek mechanism (QKZM) for an Isingtype 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 (20190305),
http://dx.doi.org/10.1103/PhysRevLett.122.093601 doi:10.1103/PhysRevLett.122.093601 (ID: 720126)
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We study collective “freespace” radiation properties of two distant singlelayer arrays of quantum emitters as twolevel atoms. We show that this system can support a longlived 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 (20190222),
http://dx.doi.org/10.1088/20589565/ab042d doi:10.1088/20589565/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 kickstart a continentwide quantumdriven industry and accelerate market takeup, 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 rampup 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 knowledgebased industrial and technological leader in this innovative field.

A. Grankin, D. Vasilyev, P. Guimond, B. Vermersch, P. Zoller Freespace photonic quantum link and chiral quantum optics,
Phys. Rev. A 98 3825 (20181012),
http://dx.doi.org/10.1103/PhysRevA.98.043825 doi:10.1103/PhysRevA.98.043825 (ID: 719980)
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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 laserassisted process to an atomic array acting as a quantum phasedarray antenna. This provides a basic building block for quantum networks in free space, i.e., without requiring cavities or nanostructures, which we illustrate with highfidelity quantum state transfer protocols. Our setup can be implemented with neutral atoms using Rydbergdressed interactions.

D. Yang, D. Vasilyev, C. Laflamme, M. Baranov, P. Zoller Quantum Scanning Microscope for Cold Atoms,
Phys. Rev. A 98 23852 (20180827),
http://dx.doi.org/10.1103/PhysRevA.98.023852 doi:10.1103/PhysRevA.98.023852 (ID: 720027)
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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 superresolution 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 (20180521),
http://dx.doi.org/10.1038/s4156701801517 doi:10.1038/s4156701801517 (ID: 720028)
Toggle Abstract
The properties of a strongly correlated manybody 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 manybody 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 (20180405),
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 stateoftheart quantum simulation experiments with ultracold atoms in an optical lattice. First, we demonstrate that our model shares characteristic manybody features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of fewbody bound states. Then we show that in the onedimensional 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 nonAbelian 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 (20180330),
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 subwavelength spatial structure,
Phys. Rev. Lett. 120 83601 (20180220),
http://dx.doi.org/10.1103/PhysRevLett.120.083601 doi:10.1103/PhysRevLett.120.083601 (ID: 719917)
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We report on the experimental realization of a conservative optical lattice for cold atoms with subwavelength spatial structure. The potential is based on the nonlinear optical response of threelevel atoms in laserdressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a 1D array of ultranarrow barriers with widths less than 10~nm, well below the wavelength of the lattice light, physically realizing a KronigPenney 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 subwavelength 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 (20180202),
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 timedependent 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 twodimensional spin models or the entanglement growth in manybody localized systems.
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B. Vermersch, A. Elben, M. Dalmonte, J. I. Cirac, P. Zoller Unitary ndesigns via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies,
Phys. Rev. A 97 23604 (20180202),
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 ndesigns, 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 indepth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with manybody quantum chaos.
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J. Perczel, J. Borregaard, D. Chang, H. Pichler, S. F. Yelin, P. Zoller, M. Lukin Photonic band structure of twodimensional atomic lattices,
Phys. Rev. A 96 63801 (20171204),
http://dx.doi.org/10.1103/PhysRevA.96.063801 doi:10.1103/PhysRevA.96.063801 (ID: 719916)
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Twodimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation, and longlived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including longrange interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such longrange interactions for arbitrary twodimensional 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 (20171128),
http://dx.doi.org/10.1038/s41467017018955 doi:10.1038/s41467017018955 (ID: 719766)
Toggle Abstract
Quantumenhanced measurements hold the promise to improve highprecision 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 trappedion qubit. In our approach, alwayson 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 selfcorrecting 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 (20171020),
http://dx.doi.org/10.1088/13672630/aa89ab doi:10.1088/13672630/aa89ab (ID: 719936)
Toggle Abstract
Lattice gauge theories describe fundamental phenomena in nature, but calculating their realtime 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 longrange interactions between the matter fields. Trappedion 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 nearfuture experiments can reach regimes where finitesize 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 timedelayed feedback,
PNAS 114 (20171017),
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 twodimensional photonic cluster states using a single quantum emitter via timedelayed quantum feedback. As a physical implementation, we consider a single atom or atomlike 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 manybody 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 (20171010),
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 manybody 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 (20170920),
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 lightmatter 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 nonlinear quantum spin lenses: in a nonlinear lens, repulsive spinspin 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 (20170908),
http://dx.doi.org/10.1088/20589565/aa7f03 doi:10.1088/20589565/aa7f03 (ID: 719814)
Toggle Abstract
We study the scattering of photons propagating in a semiinfinite 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 twophoton 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 lowpower 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 (20170818),
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 timeperiodic 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 drivefrequency 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 nonlinear with respect to the strength of the driving field and it explicitly involves interband 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 nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized effect revealed in this work designates depletionrate 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 TwoDimensional Atomic Arrays,
Phys. Rev. Lett. 119 23603 (20170714),
http://dx.doi.org/10.1103/PhysRevLett.119.023603 doi:10.1103/PhysRevLett.119.023603 (ID: 719767)
Toggle Abstract
We demonstrate that twodimensional 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 timereversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers. Such a system displays topologically protected bound states and unidirectional emission by individual atoms into longlived 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 (20170622),
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 welldeveloped quantum simulation toolbox for Rydberg atoms with the recently proposed LechnerHaukeZoller~(LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with alltoall Ising interactions and, therefore, a novel platform for quantum annealing. In LHZ a infiniterange spinglass is mapped onto the low energy subspace of a spin1/2 lattice gauge model with quasilocal 4body parity constraints. This spin model can be emulated in a natural way with Rubidium and Cesium atoms in a bipartite optical lattice involving laserdressed RydbergRydberg 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 stateoftheart atomic physics experiments.
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F. Iemini, L. Mazza, L. Fallani, P. Zoller, R. Fazio, M. Dalmonte Majorana QuasiParticles Protected by Z 2 Angular Momentum Conservation,
Phys. Rev. Lett. 118 200404 (20170519),
http://dx.doi.org/10.1103/PhysRevLett.118.200404 doi:10.1103/PhysRevLett.118.200404 (ID: 719762)
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We show how angular momentum conservation can stabilise a symmetryprotected quasitopological phase of matter supporting Majorana quasiparticles as edge modes in onedimensional cold atom gases. We investigate a numberconserving fourspecies Hubbard model in the presence of spinorbit 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 densitymatrixrenormalizationgroup simulations. Our results pave the way toward the observation of Majorana edge modes with alkalineearthlike fermions in optical lattices, where all basic ingredients for our recipe  spinorbit coupling and strong interorbital 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 (20170428),
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 manybody 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 backaction. 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 manybody 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 (20170424),
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 doublewires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e.~the HarperHofstadter model and the two leg flux ladder, respectively. We present both an indepth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous HarperHofstadter model accessible with cold atom experiments. For the minimal setup of a doublewire, we explore how a subwavelength 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 manybody 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 LaguerreGauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar 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 (20170327),
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 (20170307),
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 spinmomentum 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 (20170126),
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 (20170105),
http://dx.doi.org/10.1088/20589565/2/1/015001 doi:10.1088/20589565/2/1/015001 (ID: 719597)
Toggle Abstract
We show how to realize quantum state transfer between distant qubits using the chiral edge states of a twodimensional 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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M. Leib, P. Zoller, W. Lechner A Transmon Quantum Annealer: Decomposing ManyBody Ising Constraints Into Pair Interactions,
Quantum Sci. Technol. 1 15008 (20161216),
http://dx.doi.org/10.1088/20589565/1/1/015008 doi:10.1088/20589565/1/1/015008 (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 4body 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 NanoScale `Dark State' Optical Potentials for Cold Atoms,
Phys. Rev. Lett. 117 233001 (20161130),
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 nonadiabatic corrections to BornOppenheimer 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 offresonant optical lattice, and discuss bound states of pairs of atoms interacting via magnetic dipolar interactions. The subwavelength optical barriers represent an optical `KronigPenney' potential. We present a detailed study of the bandstructure in optical `KronigPenney' 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 (20161116),
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 pseudospins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating latticeregularized quantum electrodynamics (QED) in (1+1) spacetime dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finitesize 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 microtraps. 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 smallscale 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 falsevacuum 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 NonTopological States,
Phys. Rev. Lett. 117 126803 (20160916),
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 twodimensional system initialized in a topologically trivial state before its Hamiltonian is ramped into a Cherninsulator phase. Under coherent dynamics, the nonequilibrium 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 LandauZener 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 nontrivial, 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 Vlevel atoms and coherent quantum feedback,
Phys. Rev. A 94 33829 (20160916),
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 Vlevel configuration driven by lasers and coupled to a semiinfinite 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 timedelay 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 singleatom analogue of the quantum dimer, where a pair of laserdriven twolevel atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current stateoftheart experiments. Second, we extend our study to nonMarkovian regimes and investigate the effect of the feedback retardation on the steadystate.
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C. Laflamme, J. Budich, P. Zoller, M. Dalmonte Nonequilibrium 8π Josephson Effect in Atomic Kitaev Wires,
Nat. Commun. 7 12280 (20160802),
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, nonequlibrium 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 timedependent simulations including the effects of dephasing and particle losses. Our findings provide a novel signature of Majorana quasiparticles which is qualitatively different form the behavior of a conventional superconductor, and can be experimentally verified in cold atom systems using alkalineearthlike 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 Realtime dynamics of lattice gauge theories with a fewqubit quantum computer,
Nature 534 519 (20160622),
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 realtime 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 quantummechanical 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+1dimensional quantum electrodynamics (Schwinger model) on a fewqubit trappedion quantum computer. We are interested in the realtime evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electronpositron 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 longrange interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particleantiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the realtime 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 highenergy theories with atomic physics experiments, the longterm vision being the extension to realtime quantum simulations of nonAbelian lattice gauge theories.

B. Vermersch, T. Ramos, P. Hauke, P. Zoller Implementation of Chiral Quantum Optics with Rydberg and Trappedion Setups,
Phys. Rev. A 93 63830 (20160617),
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 twolevel 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 spinorbit coupling in the dipoledipole interactions, while for the trapped ions it is obtained by engineered sideband transitions. We take longrange 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 stateoftheart technology, such as the drivendissipative formation of entangled dimer states.
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T. Ramos, B. Vermersch, P. Hauke, H. Pichler, P. Zoller NonMarkovian Dynamics in Chiral Quantum Networks with Spins and Photons,
Phys. Rev. A 93 62104 (20160602),
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 twolevel 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 XXspin chains representing a spin waveguide. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a BornMarkov approximation to obtain a master equation for the nodes, we are interested in nonMarkovian dynamics. This arises from the nonlinear character of the dispersion with bandedge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the nonMarkovian 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 timedependent density matrix renormalization group techniques. We illustrate our approach showing nonMarkovian effects in the drivendissipative 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 (20160525),
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 (20160517),
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 manybody quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum manybody 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 manybody 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) BoseHubbard 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. MejiaDiaz, W. Bietenholz, U. Wiese, P. Zoller CP(N1) Quantum Field Theories with AlkalineEarth Atoms in Optical Lattices,
Ann. Phys. 370 127 (20160423),
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(N1) 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(N1) 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 alkalineearth 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 realtime evolution of a false θvacuum state after a quench, and we propose experiments to unravel the phase diagram at nonzero 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 BoseHubbard Models with Ultracold Magnetic Atoms,
Science 352 205 (20160408),
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 longrange interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended BoseHubbard model for an ultracold gas of strongly magnetic erbium atoms in a threedimensional 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 superfluidtoMott insulator quantum phase transition. Moreover, we observe nearestneighbor interaction, which is a genuine consequence of the longrange nature of dipolar interactions. Our results lay the groundwork for future studies of novel exotic manybody quantum phases.
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P. Hauke, M. Heyl, L. Tagliacozzo, P. Zoller Measuring multipartite entanglement via dynamic susceptibilities,
Nature Phys. 12 778 (20160321),
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 manyparticle 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 condensedmatter
experiments. This moreover establishes a fundamental connection between multipartite entanglement
and manybody 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 opticallattice experiments.
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T. Pichler, M. Dalmonte, E. Rico Ortega, P. Zoller, S. Montangero Realtime Dynamics in U(1) Lattice Gauge Theories with Tensor Networks,
Phys. Rev. X 6 11023 (20160303),
http://dx.doi.org/10.1103/PhysRevX.6.011023 doi:10.1103/PhysRevX.6.011023 (ID: 719259)
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Tensor networks algorithms provide a suitable route to tackle realtime dependent problems in lattice gauge theories, enabling the investigation of outofequilibrium 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 quantumelectrodynamics in onedimension, which displays stringbreaking: the confining string between charges can spontaneously break during quench exper iments, giving rise to chargeanticharge pairs according to the Schwinger mechanism. We study the realtime 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 timescales 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 realtime 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 realtime 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 (20160303),
http://dx.doi.org/10.1103/PhysRevLett.116.093601 doi:10.1103/PhysRevLett.116.093601 (ID: 719362)
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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 nonMarkovian 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. AlDossary, J. Budich, P. Zoller Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices,
Phys. Rev. A 93 13604 (20160107),
http://dx.doi.org/10.1103/PhysRevA.93.013604 doi:10.1103/PhysRevA.93.013604 (ID: 719282)
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We propose and study various realizations of a HofstadterHubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by counterpropagating LaguerreGauss 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 LaguerreGauss beams then induces a Ramanhopping 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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J. Budich, C. Laflamme, F. Tschirsich, S. Montangero, P. Zoller Synthetic Helical Liquids with Ultracold Atoms in Optical Lattices,
Phys. Rev. B 92 245121 (20151214),
http://dx.doi.org/10.1103/PhysRevB.92.245121 doi:10.1103/PhysRevB.92.245121 (ID: 719243)
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We develop a new platform for the synthetic realization of helical Tomonaga Luttinger liquids (HTLLs) with ultracold fermionic atoms in onedimensional 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 onedimensional FermiHubbard 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 twodimensional topological insulators, is reflected in the present synthetic scenario.
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W. Lechner, P. Hauke, P. Zoller A quantum annealing architecture with alltoall connectivity from local interactions,
Sci. Adv. 1 e1500838 (20151023),
http://dx.doi.org/10.1126/sciadv.1500838 doi:10.1126/sciadv.1500838 (ID: 719363)
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Quantum annealers are physical devices that aim at solving NPcomplete 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 alltoall connectivity and the quasilocality 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 longrange interactions are mediated by gauge constraints. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NVcenters, 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 (20151016),
http://dx.doi.org/10.1103/PhysRevB.92.165118 doi:10.1103/PhysRevB.92.165118 (ID: 719277)
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Robustness of edge states and nonAbelian 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 timedependent 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 quasistatic 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 longlived quantum correlations in presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and nontopological 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 (20150925),
http://dx.doi.org/10.1126/science.aaa8736 doi:10.1126/science.aaa8736 (ID: 719172)
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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 bulkedge coupling, and observe the edgecyclotron 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 nonAbelian 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 (20150918),
http://dx.doi.org/10.1103/PhysRevLett.115.125301 doi:10.1103/PhysRevLett.115.125301 (ID: 719185)
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The collective excitations in ensembles of dissipative, laser driven ultracold atoms exhibit crystallike patterns, a manybody effect of the Rydberg blockade mechanism. These crystalline structure are revealed in experiment from a postselection of configurations with fixed numbers of excitations. Here, we show that these subensemble 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. SchmidtKaler, R. Gerritsma Hexagonal Plaquette Spinspin Interactions and Quantum Magnetism in a Twodimensional Ion Crystal,
New J. Phys. 17 065018 (20150625),
http://dx.doi.org/10.1088/13672630/17/6/065018 doi:10.1088/13672630/17/6/065018 (ID: 719216)
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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 spinspin interactions in a 2D ion crystal. For this, the phononmode spectrum of the crystal is engineered by standingwave optical potentials or by using Rydberg excited ions, thus generating localized phononmodes around a hexagon of ions selected out of the entire twodimensional crystal. These tailored modes can mediate spinspin interactions between ionqubits on a hexagonal plaquette when subject to statedependent optical dipole forces. We discuss how these interactions can be employed to emulate a generalized BalentsFisherGirvin 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 gaugeinvariant background using the twoplaquettes trapped ions spinsystem. 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 LaserDressed Rydberg Atoms,
Phys. Rev. Lett. 114 173002 (20150428),
http://dx.doi.org/10.1103/PhysRevLett.114.173002 doi:10.1103/PhysRevLett.114.173002 (ID: 719027)
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We show how a broad class of lattice spin1/2 models with angular and distancedependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin1/2 is represented by a pair of atomic ground states, and spinspin interactions are obtained by admixing van der Waals interactions between finestructure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flipflop", and "flipflip" and "flopflop" 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 timescales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within stateoftheart 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 (20150422),
http://dx.doi.org/10.1088/13672630/17/4/043044 doi:10.1088/13672630/17/4/043044 (ID: 719098)
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We propose and investigate a hybrid optomechanical system consisting of a micromechanical 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 highfrequency 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 groundstate 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 (20150414),
http://dx.doi.org/10.1103/PhysRevA.91.042117 doi:10.1103/PhysRevA.91.042117 (ID: 719006)
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Engineered dissipation can be employed to efficiently prepare interesting quantum many body states in a nonequilibrium 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 nonzero Chern number as the unique steady state by means of shortrange 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 nonequilibrium 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 (20150414),
http://dx.doi.org/10.1103/PhysRevA.91.042116 doi:10.1103/PhysRevA.91.042116 (ID: 719040)
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We study the drivendissipative dynamics of a network of spin1/2 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 manybody 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 spinorbit coupled BoseEinstein 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 BoseFermi mixture,
Phys. Rev. Lett. 114 125303 (20150327),
http://dx.doi.org/10.1103/PhysRevLett.114.125303 doi:10.1103/PhysRevLett.114.125303 (ID: 718957)
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We study a mixture of spin1 bosonic and spin1/2 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 noncoplanar spin orders. The phase diagram is mapped out with varying boson tunneling and BoseFermi interactions. Most significantly, in one noncoplanar 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 (20150211),
http://dx.doi.org/10.1103/PhysRevA.91.023411 doi:10.1103/PhysRevA.91.023411 (ID: 719085)
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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 magneticfield. We show, in particular, the existence of magic distances corresponding to the laserexcitation 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 (20150113),
http://dx.doi.org/10.1103/PhysRevB.92.174507 doi:10.1103/PhysRevB.92.174507 (ID: 719116)
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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 onedimensional geometries. We illustrate the potential offered by these systems in the context of dimerized MajumdarGhoshtype phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder and decoherence, and could be observed within stateoftheart experiments.
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B. Vermersch, M. Punk, A. Glätzle, C. Gross, P. Zoller Dynamical preparation of laserexcited anisotropic Rydberg crystals in 2D optical lattices,
New J. Phys. 17 013008 (20150109),
http://dx.doi.org/10.1088/13672630/17/1/013008 doi:10.1088/13672630/17/1/013008 (ID: 718969)
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We describe the dynamical preparation of anisotropic crystalline
phases obtained by laserexciting ultracold Alkali atoms to Rydberg pstates
where they interact via anisotropic van derWaals interactions. We develop a timedependent
variational mean field ansatz to model large, but finite twodimensional
systems in experimentally accessible parameter regimes, and we present numerical
simulations to illustrate the dynamical formation of anisotropic Rydberg crystals.
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T. Ramos, H. Pichler, A. J. Daley, P. Zoller Quantum SpinDimers from Chiral Dissipation in Cold Atom Chains,
Phys. Rev. Lett. 113 237203 (20141203),
http://dx.doi.org/10.1103/PhysRevLett.113.237203 doi:10.1103/PhysRevLett.113.237203 (ID: 718977)
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We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a 1D bosonic bath, and its atomic implementation with a twospecies mixture of cold quantum gases. The reservoir is represented by a spinorbit coupled 1D quasicondensate 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 twolevel emitters coupled to photonic waveguides.
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D. Marcos, P. Widmer, E. Rico Ortega, M. Hafezi, P. Rabl, U. Wiese, P. Zoller Twodimensional Lattice Gauge Theories with Superconducting Quantum Circuits,
Ann. Phys. 351 654 (20140910),
http://dx.doi.org/10.1016/j.aop.2014.09.011 doi:10.1016/j.aop.2014.09.011 (ID: 718973)
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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 realtime dynamics of quantum phase transitions are accessible as well. Here we show how stateoftheart superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong nonlinear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ringexchange and fourbody 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 (20140904),
http://dx.doi.org/10.1103/PhysRevB.90.115110 doi:10.1103/PhysRevB.90.115110 (ID: 718935)
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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 onedimensional 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 (20140821),
http://dx.doi.org/10.1126/science.1254978 doi:10.1126/science.1254978 (ID: 718864)
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Symmetries play a fundamental role in the laws of nature. SU(N) symmetry can emerge in a quantum system with N singleparticle spin states when the spin degree of freedom is decoupled from interactions. Such a system is anticipated to exhibit large degeneracy and exotic manybody behaviors. Owing to the strong decoupling between electronicorbital and nuclearspin degrees of freedom, alkalineearth 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 stateoftheart measurement precision offered by an ultrastable 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 nonequilibrium twoorbital 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 shortrange interactions, our system shows two key differences: the lattice is spanned by energy eigenvalues and the underlying interactions are longrange and nuclear spin independent. To elucidate the microscopic mechanism for SU(N) orbital physics, we model the spinorbital dynamics and determine all relevant interaction parameters with an analytic relation between s and pwave scattering lengths. This work prepares for using AEAs as testbeds 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 manybody system,
Nature 511 202 (20140710),
http://dx.doi.org/10.1038/nature13461 doi:10.1038/nature13461 (ID: 718717)
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The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around manybody 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 onedimensional manybody 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 manybody system. Second, for longrange interactions we observe the divergence of quasiparticle velocity and breakdown of the lightcone picture that is valid for shortrange 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 quantumoptical regime with ondemand quasiparticles with tunable nonlinear 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 (20140625),
http://dx.doi.org/10.1103/PhysRevLett.112.255301 doi:10.1103/PhysRevLett.112.255301 (ID: 718725)
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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 OptoNanomechanics Strongly Coupled to a Rydberg Superatom: Coherent vs. Incoherent Dynamics,
New J. Phys. 16 063042 (20140619),
http://dx.doi.org/10.1088/13672630/16/6/063042 doi:10.1088/13672630/16/6/063042 (ID: 718701)
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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 vanderWaals interaction between the atoms, the ensemble forms an effective twolevel system, a Rydberg superatom, with a collectively enhanced atomlight 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 nonclassical state preparation. As an illustration, we show that a thermally occupied membrane can be prepared in a nonclassical 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 (20140523),
http://dx.doi.org/10.1103/PhysRevLett.112.201601 doi:10.1103/PhysRevLett.112.201601 (ID: 718702)
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We show that gauge invariant quantum link models, Abelian and nonAbelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between highenergy to cold atom physics, as they can be used in coldatoms 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 nonzero 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 (20140421),
http://dx.doi.org/10.1103/PhysRevX.4.041037 doi:10.1103/PhysRevX.4.041037 (ID: 718901)
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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 pstates together with the possibility of designing steplike 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 pRydberg states in exotic geometries, e.g. on a 48 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 nonAbelian lattice gauge theories with cold atoms,
Phys. Rev. Lett. 112 120406 (20140326),
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 manybody 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, quasilocal constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and nonAbelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, nonlocal 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 (20140214),
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 onedimensional 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, wellcontrolled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient nondestructive protocol to check for errors in the mapping.
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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 (20131122),
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 onedimensional quantum electrodynamics. Relying on the rich quantumsimulation toolbox available in stateoftheart trappedion experiments, we show how one can engineer an effectively gaugeinvariant dynamics by imposing energetic constraints, provided by strong Isinglike interactions. Applying exact diagonalization to groundstate and timedependent 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 chargesymmetry breaking, as well as falsevacuum 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 manybody problem. The proposal opens a new route for analog quantum simulation of highenergy and condensedmatter 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 DeutschJosza Algorithm,
Phys. Rev. Lett. 111 203001 (20131111),
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 DeutschJosza algorithm.
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W. Lechner, P. Zoller From Classical to Quantum Glasses with Ultracold Polar Molecules,
Phys. Rev. Lett. 111 185306 (20131030),
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 twodimensional crystals. We find that the defects assemble into linear strings that propagate through the crystal in a succession of rapid onedimensional gliding phases and rare rotations, during which the direction of motion changes. At both ends, strings are terminated by dislocations with antiparallel 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 doublewell 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 twodimensional nanomaterials.
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C. Kraus, M. Dalmonte, M. Baranov, A. Läuchli, P. Zoller Majorana edge states in two atomic wires coupled by pairhopping,
Phys. Rev. Lett. 111 173004 (20131023),
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 pairhopping interactions in cold atom gases confined in optical lattices, and its possible alternative applications to quantum simulation.
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O. RomeroIsart, C. Navau, A. Sanchez, P. Zoller, J. I. Cirac Superconducting Vortex Lattices for Ultracold Atoms,
Phys. Rev. Lett. 111 145304 (20131004),
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 manybody states. In contrast, here we propose and analyze a nanoengineered vortex array in a thinfilm typeII 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 (20130913),
http://dx.doi.org/10.1103/PhysRevLett.111.110504 doi:10.1103/PhysRevLett.111.110504 (ID: 718537)
Toggle Abstract
We describe a superconductingcircuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a onedimensional U(1) quantumlink 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 condensedmatter and highenergy physics can be visualized with stateoftheart technology in small superconductingcircuit 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 (20130801),
http://dx.doi.org/10.1088/13672630/15/8/085001 doi:10.1088/13672630/15/8/085001 (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 manybody 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 groundstate 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 symmetrybased topological classification of bulk steady states and identify the classes that are achievable by means of quasilocal dissipative processes driving into superfluid paired states. We also explore the fate of the bulkedge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one and twodimensional 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 (20130606),
http://dx.doi.org/10.1088/13672630/15/6/063003 doi:10.1088/13672630/15/6/063003 (ID: 718531)
Toggle Abstract
We show how to measure the ordertwo Renyi entropy of manybody states of spinful fermionic atoms in an optical lattice in equilibrium and nonequilibrium 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 spinresolved 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 opensystem dynamical maps with trapped ions,
Nature Phys. 9 367 (20130519),
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 opensystem, manyparticle context: We experimentally explore the stroboscopic dynamics of a complex manybody spin model by means of a universal quantum simulator using up to five ions. In particular, we generate longrange phase coherence of spin by an iteration of purely dissipative quantum maps. We also demonstrate the characteristics of competition between combined coherent and dissipative nonequilibrium evolution. This opens the door for studying manyparticle nonequilibrium 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 (20130506),
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 laserdriven 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 twomode 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 laserdrives, 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 Phononinduced spinspin interactions in diamond nanostructures: application to spin squeezing,
Phys. Rev. Lett. 110 156402 (20130409),
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 longrange spinspin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogenvacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phononmediated effective spinspin 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 spinensemble magnetometry, as well as phononmediated 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 (20130408),
http://dx.doi.org/10.1073/pnas.1300170110 doi:10.1073/pnas.1300170110 (ID: 718336)
Toggle Abstract
Detecting topological order in coldatom 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 nontrivial topological invariants  have been observed through transport and spectroscopy measurements. Here, we show that opticallatticebased 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 timeevolution 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 NanoDumbbells: NonEquilibrium Phases and SelfAssembly,
Phys. Rev. Lett. 110 143604 (20130405),
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 manybody systems out of solution and highly isolated from the environment. We show that properly tuned optical parameters allow for the study of the nonequilibrium dynamics of composite nanoparticles with nonisotropic optical friction. We find friction induced ordering and nematic transitions with nonequilibrium 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) NonAbelian Lattice Gauge Theories,
Phys. Rev. Lett. 110 125303 (20130321),
http://dx.doi.org/10.1103/PhysRevLett.110.125303 doi:10.1103/PhysRevLett.110.125303 (ID: 718423)
Toggle Abstract
Using ultracold alkalineearth 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 nonzero 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 (20130312),
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 (20130305),
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 manybody 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 timedependent calculation of the stochastic manybody dynamics in 1D based on timedependent densitymatrixrenormalizationgroup methods.
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B. Vogell, K. Stannigel, P. Zoller, K. Hammerer, M. T. Rakher, M. Korppi, A. Jöckel, P. Treutlein CavityEnhanced LongDistance Coupling of an Atomic Ensemble to a Micromechanical Membrane,
Phys. Rev. A 87 023816 (20130214),
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 precooled 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 TwoLevel Defects,
Phys. Rev. Lett. 110 193602 (20130207),
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 twolevel system (TLS) defect states found naturally in integrated optomechanical devices for exploring cavity QEDlike phenomena with localized phonons. The JaynesCummingstype interaction between TLS and mechanics can reach the strong coupling regime for existing nanooptomechanical 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 nonclassical states of the mechanical resonator.
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P. Komar, S. D. Bennett, K. Stannigel, S. Habraken, P. Rabl, P. Zoller, M. Lukin Singlephoton nonlinearities in twomode optomechanics,
Phys. Rev. A 87 013839 (20130128),
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 nearresonantly coupled to a single mechanical mode via a threewave mixing interaction. We calculate one and twotime intensity correlations of the two optical fields and compare them to analogous correlations in atomcavity systems. Nonclassical photon correlations arise when the optomechanical coupling $g$ exceeds the cavity decay rate $\kappa$, and we discuss signatures of one and twophoton resonances as well as quantum interference. We also find a longlived 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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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 (20121226),
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 twodimensional topological nearly flat bands. Our approach utilizes an array of threelevel 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 spinflips. 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 halffilling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultracold 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 (20121207),
http://dx.doi.org/10.1103/PhysRevLett.109.235309 doi:10.1103/PhysRevLett.109.235309 (ID: 718190)
Toggle Abstract
We propose to use subwavelength 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 subwavelength manipulation and strong lightmatter interaction associated with nanoplasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective longrange interactions in coherent and dissipative manybody 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 (20121127),
http://dx.doi.org/10.1088/13672630/14/11/113036 doi:10.1088/13672630/14/11/113036 (ID: 717882)
Toggle Abstract
We introduce a onedimensional 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 zeroenergy edge modes which are Majorana fermions. We propose several universal methods of detecting the Majorana edge states, based on their genuine features: zeroenergy, localized character of the wave functions, and induced nonlocal fermionic correlations.
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H. Pichler, J. Schachenmayer, J. Simon, P. Zoller, A. J. Daley Noise and disorderresilient optical lattices,
Phys. Rev. A 86 051605 (20121116),
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 manybody 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 (20121105),
http://dx.doi.org/10.1088/13672630/14/11/115004 doi:10.1088/13672630/14/11/115004 (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 nonvanishing 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 onchip 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 (20121023),
http://dx.doi.org/10.1103/PhysRevLett.109.175302 doi:10.1103/PhysRevLett.109.175302 (ID: 718094)
Toggle Abstract
Using a FermiBose mixture of ultracold 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 Hubbardtype model which can be quantum simulated. This allows us to investigate string breaking as well as the realtime 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 Drivendissipative dynamics of a strongly interacting Rydberg gas,
Phys. Rev. A 86 043403 (20121002),
http://dx.doi.org/10.1103/PhysRevA.86.043403 doi:10.1103/PhysRevA.86.043403 (ID: 718134)
Toggle Abstract
We study the nonequilibrium manybody 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 dipoledipole 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 longtime 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 DrivenDissipative Atomic Superfluids With Zero Chern Number,
Phys. Rev. Lett. 109 130402 (20120925),
http://dx.doi.org/10.1103/PhysRevLett.109.130402 doi:10.1103/PhysRevLett.109.130402 (ID: 717881)
Toggle Abstract
We investigate dissipationinduced pwave paired states of fermions in two dimensions and show that dissipation can break the bulkedge 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 onedimensional wire where we observe a nonequilibrium 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 (20120914),
http://dx.doi.org/10.1103/PhysRevA.86.033821 doi:10.1103/PhysRevA.86.033821 (ID: 718117)
Toggle Abstract
We study the drivendissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photonnumber conserving nonunitary dynamics, which features a steady state with longrange 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 longrange 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 drivendissipative 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. (20120809),
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, longrange dipolar interactions play a prominent role at the manybody 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 manybody 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 quasi1D 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 (20120712),
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 manybody 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 tunnelcoupling between the copies and measurement of the parity of onsite occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a SuperfluidMott insulator quench in the BoseHubbard model, and also for hardcore 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 (20120706),
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 nanooptomechanical devices, where strong optomechanical coupling on a single photon level is within experimental reach.
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K. Stannigel, P. Rabl, P. Zoller Drivendissipative preparation of entangled states in cascaded quantumoptical networks,
New J. Phys. 14 063014 (20120614),
http://dx.doi.org/10.1088/13672630/14/6/063014 doi:10.1088/13672630/14/6/063014 (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 nontrivial quantum correlations between the individual nodes. For the case of cascaded twolevel systems, we present an explicit preparation scheme that allows for tuning the network into different classes of multipartite 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 longdistance 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 (20120511),
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 Drivendissipative manybody pairing states for cold fermionic atoms in an optical lattice,
New J. Phys. 14 055002 (20120501),
http://dx.doi.org/10.1088/13672630/14/5/055002 doi:10.1088/13672630/14/5/055002 (ID: 717858)
Toggle Abstract
We discuss the preparation of manybody 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 interparticle interactions. We discuss the uniqueness of these states, and demonstrate it with smallscale 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 manybody 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 FermiHubbard Hamiltonian via an adiabatic state preparation process also involving the parent Hamiltonian of the pairing state. We also provide a proofofprinciple 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 (20120402),
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 longterm goal, requiring the full control of a manybody system and, eventually, the implementation of sophisticated errorcorrection protocols to achieve fault tolerance. So, as we still have to wait for a fully fledged universal quantuminformation 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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K. Stannigel, P. Rabl, A. Sorensen, M. Lukin, P. Zoller Optomechanical transducers for quantum information processing,
Phys. Rev. A 84 042341 (20111031),
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 solidstate spin and chargebased systems. We present an effective description of such networks for many qubits and give a derivation of a state transfer protocol for longdistance quantum communication. We also describe how to mediate local onchip 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 (20111014),
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 earthlike atoms, where the decay rate from metastable states can be tuned in experiments. This phenomenon has potential applications towards reservoir engineering and dissipative manybody state preparation in an optical lattice.
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M. Ortner, Y. Zhou, P. Rabl, P. Zoller Quantum information processing in selfassembled crystals of cold polar molecules,
Quant. Inf. Proc. 10 819 (20111013),
http://dx.doi.org/10.1007/s1112801103017 doi:10.1007/s1112801103017 (ID: 717726)
Toggle Abstract
We discuss the implementation of quantum gate operations in a selfassembled dipolar crystal of polar molecules. Here qubits are encoded in longlived spin states of the molecular ground state and stabilized against collisions by repulsive dipoledipole interactions. To overcome the single site addressability problem in this high density crystalline phase, we describe a new approach for implementing controlled single and twoqubit operations based on resonantly enhanced spinspin 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 (20111011),
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 quasiexact 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 finitesize 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 (20111002),
http://dx.doi.org/10.1038/nphys2106 doi:10.1038/nphys2106 (ID: 717686)
Toggle Abstract
Robust edge states and nonAbelian 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 nonlocal decoherence free subspace. The isolation of the edge states is enforced by a dissipative gap in the pwave paired bulk of the wire. We describe dissipative nonAbelian 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 (20110901),
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 fulltime 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 fullscale device is within reach.
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M. Müller, K. Hammerer, Y. Zhou, C. F. Roos, P. Zoller Simulating open quantum systems: from manybody interactions to stabilizer pumping,
New J. Phys. 13 085007 (20110810),
http://dx.doi.org/10.1088/13672630/13/8/085007 doi:10.1088/13672630/13/8/085007 (ID: 717750)
Toggle Abstract
In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an opensystem quantum simulator with trapped ions. Using up to five ions, dynamics were realized by sequences that combined single and multiqubit entangling gate operations with optical pumping. This enabled the implementation of both coherent manybody 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 fourqubit states, the simulation of coherent fourbody spin interactions and the quantum nondemolition measurement of a multiqubit stabilizer operator. In this paper, we present the theoretical framework of this gatebased ('digital') simulation approach for opensystem 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 stateoftheart linear iontrap 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 twodimensional iontrap architectures, which are currently under development.
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A. J. Daley, J. Ye, P. Zoller Statedependent lattices for quantum computing with alkalineearthmetal atoms,
Eur. Phys. J. D 65 217 (20110729),
http://dx.doi.org/10.1140/epjd/e2011200952 doi:10.1140/epjd/e2011200952 (ID: 717608)
Toggle Abstract
Recent experimental progress with AlkalineEarth atoms has opened the door to quantum computing schemes in which qubits are encoded in longlived 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 nuclearspindependent optical lattices, formed by nearresonant 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 ColdAtom Quantum Wires,
Phys. Rev. Lett. 106 220402 (20110602),
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 spinorbit interaction and magnetic field—while a background molecular BEC cloud generates swave pairing for the atoms. The resulting coldatom 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 matterwave revivals with definite atom number in an optical lattice,
Phys. Rev. A 83 043614 (20110418),
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 noninteracting bosons are loaded into the system initially, and we use timedependent 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. SchmidtKaler, 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 (20110415),
http://dx.doi.org/10.1088/13672630/13/7/075014 doi:10.1088/13672630/13/7/075014 (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 opensystem quantum simulator with trapped ions,
Nature 470 491 (20110224),
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 multiqubit gates with optical pumping to implement coherent operations and dissipative processes. We
illustrate our ability to engineer the opensystem dynamics through the dissipative preparation of entangled states,
the simulation of coherent manybody spin interactions, and the quantum nondemolition measurement of multiqubit
observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for opensystem
quantum simulation and computation.
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A. Tomadin, S. Diehl, P. Zoller Nonequilibrium phase diagram of a driven and dissipative manybody system,
Phys. Rev. A 83 013611 (20110118),
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 manybody 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 offdiagonal longrange 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 longrange 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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H. Pichler, A. J. Daley, P. Zoller Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of manybody states due to spontaneous emission,
Phys. Rev. A 82 063605 (20101206),
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 singleparticle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the manybody physics of the state. We characterize the effects on manybody 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 perturbationtheory calculations and a timedependent calculation of the dissipative manybody dynamics. The latter is made possible for onedimensional systems by combining timedependent densitymatrixrenormalizationgroup methods with quantum trajectory techniques.
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K. Stannigel, P. Rabl, A. Sorensen, P. Zoller, M. Lukin Optomechanical Transducers for LongDistance Quantum Communication,
Phys. Rev. Lett. 105 220501 (20101123),
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 qubitlight 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 DissipationInduced dWave Pairing of Fermionic Atoms in an Optical Lattice,
Phys. Rev. Lett. 105 227001 (20101122),
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 twocomponent fermions on a lattice. In particular, we construct a \\\\\\\"parent\\\\\\\" Liouvillian operator so that a BCStype state of a given symmetry, e.g. a dwave state, is reached for arbitrary initial states in the absence of conservative forces. The systembath couplings describe singleparticle, number conserving and quasilocal 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 OneDimensional Quantum Liquids with PowerLaw Interactions: The Luttinger Staircase,
Phys. Rev. Lett. 105 140401 (20100928),
http://dx.doi.org/10.1103/PhysRevLett.105.140401 doi:10.1103/PhysRevLett.105.140401 (ID: 717312)
Toggle Abstract
We study onedimensional fermionic and bosonic gases with repulsive powerlaw interactions 1/xβ, with β>1, in the framework of TomonagaLuttinger 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, powerlaw 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 DipoleBlockaded Gas,
Phys. Rev. Lett. 105 135301 (20100921),
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 dipoleblockade 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) (20100825),
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 standingwave 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 centerofmass 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 ThreeBody Constrained Lattice Bose Gas  Part I: Formal Developments,
Phys. Rev. B 82 064509 (20100813),
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 threebody constrained BoseHubbard model beyond mean field and noninteracting 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 twoparticle 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 diholes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the manybody problem, which can be realized with atoms in optical lattices with strong threebody 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 ThreeBody Constrained Lattice Bose Gas  Part II: Application to the ManyBody Problem,
Phys. Rev. B 82 064510 (20100813),
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 threebody 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 (20100813),
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 quasitwodimensional and quasionedimensional 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 spinpolarized 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 Ionassisted groundstate cooling of a trapped polar molecule,
Phys. Rev. A 83 053413 (20100811),
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 lasercooled ions in a radiofrequency 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 ManyBody Systems,
Phys. Rev. Lett. 105 015702 (20100701),
http://dx.doi.org/10.1103/PhysRevLett.105.015702 doi:10.1103/PhysRevLett.105.015702 (ID: 717159)
Toggle Abstract
We discuss an open drivendissipative manybody 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 Rydbergdressed atoms: quantum and classical dynamics,
Phys. Rev. Lett. 104 223002 (20100601),
http://dx.doi.org/10.1103/PhysRevLett.104.223002 doi:10.1103/PhysRevLett.104.223002 (ID: 716985)
Toggle Abstract
We discuss techniques to generate longrange 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 dipoledipole 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 quantumclassical 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 (20100530),
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 quantumcomputing 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 magneticfield 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 quantumcomputing 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 (20100521),
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 atomicensemblebased 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 longdistance quantum communication.
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A. Kantian, A. J. Daley, P. Zoller An etacondensate of fermionic atom pairs via adiabatic state preparation,
Phys. Rev. Lett. 104 (20100519),
http://dx.doi.org/10.1103/PhysRevLett.104.240406 doi:10.1103/PhysRevLett.104.240406 (ID: 716970)
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We discuss how an $\\eta$condensate, corresponding to an exact excited eigenstate of the FermiHubbard model, can be produced with cold atoms in an optical lattice. Using timedependent 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 manybody 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 (20100420),
http://dx.doi.org/10.1103/PhysRevLett.104.165301 doi:10.1103/PhysRevLett.104.165301 (ID: 716766)
Toggle Abstract
We analyze the BoseHubbard model with threebody 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 ColemanWeinberg 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 (20100315),
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 twolevel 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 nonstationary due to the timedependent boundary conditions and in order to study its spectral distribution we employ the operational definition of the spectrum of nonstationary 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 (20100314),
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) nbody interactions. This includes the simulation of Hamiltonians of exotic spin models involving nparticle 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 nparticle reservoir couplings. The key basic building blocks of our architecture are efficient and highfidelity nqubit 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 highfidelity nparticle 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 Twoorbital SU(N) magnetism with ultracold alkalineearth atoms,
Nature Phys. 6 295 (20100228),
http://dx.doi.org/10.1038/nphys1535 doi:10.1038/nphys1535 (ID: 681277)
Toggle Abstract
Fermionic alkalineearth 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 manybody phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement manybody 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 transitionmetal oxides, heavyfermion materials and spinliquid 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 (20100224),
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 singlecomponent 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 manybody contributions resulting in the mass renormalization, as well as additional contributions to the pairing interaction. We find that the manybody 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. CapogrossoSansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo Quantum Phases of Cold Polar Molecules in 2D Optical Lattices,
Phys. Rev. Lett. 104 125301 (20100223),
http://dx.doi.org/10.1103/PhysRevLett.104.125301 doi:10.1103/PhysRevLett.104.125301 (ID: 686428)
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We study the quantum phases of hardcore bosonic polar molecules on a twodimensional square lattice interacting via repulsive dipoledipole 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 finitesize 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 Singleatom cavity QED and optomicromechanics,
Phys. Rev. A 81 023816 (20100218),
http://dx.doi.org/10.1103/PhysRevA.81.023816 doi:10.1103/PhysRevA.81.023816 (ID: 716968)
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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 micronsized 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 welldeveloped 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 strongcoupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.
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P. Zoller, M. Wallquist, K. Hammerer, P. Rabl, M. Lukin Hybrid quantum devices and quantum engineering,
Physica Scripta 014001 (20091214),
http://dx.doi.org/10.1088/00318949/2009/T137/014001 doi:10.1088/00318949/2009/T137/014001 (ID: 716806)
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We discuss prospects of building hybrid quantum devices involving elements of atomic and molecular physics, quantum optics and solidstate 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 ThreeBody Loss,
Phys. Rev. Lett. 103 240401 (20091209),
http://dx.doi.org/10.1103/PhysRevLett.103.240401 doi:10.1103/PhysRevLett.103.240401 (ID: 707092)
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Large threebody loss rates in a threecomponent 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 BCSpairing phases by suppressing the formation of trions. We study the effect of the constraint on the manybody 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 optomechanics using an optically levitated nanosphere,
Proc. Natl. Acad. U.S.A. 107 1010 (20091110),
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 (20091017),
URL (ID: 708587)
Toggle Abstract
Recently, remarkable advances have been made in coupling a number of highQ modes of nanomechanical systems to highfinesse 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 nanomechanical 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 groundstate cooling and coherent manipulation of a single mesoscopic mechanical system or entanglement generation between spatially separate systems, even in roomtemperature environments. As an example, we show that these goals should be achievable when the mechanical mode consists of the centerofmass 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 (20090918),
http://dx.doi.org/10.1103/PhysRevLett.103.123004 doi:10.1103/PhysRevLett.103.123004 (ID: 686216)
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We propose and analyze a scheme to interface individual neutral atoms with nanoscale solidstate systems. The interface is enabled by optically trapping the atom via the strong nearfield 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 pwave superfluid state in an optical lattice,
Phys. Rev. Lett. 103 070404 (20090814),
http://dx.doi.org/10.1103/PhysRevLett.103.070404 doi:10.1103/PhysRevLett.103.070404 (ID: 707070)
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It is hard to stabilize the pwave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the pwave Feshbach resonance in an optical lattice, and show that it is possible to have a stable pwave 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 onedimensional optical lattice. The results show rich phase transitions between the pwave 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 (20090806),
http://dx.doi.org/10.1103/PhysRevLett.103.063005 doi:10.1103/PhysRevLett.103.063005 (ID: 680115)
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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 highfinesse 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 Cavityassisted squeezing of a mechanical oscillator,
Phys. Rev. A 79 063819 (20090611),
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 optomechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heatbath 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 (20090514),
http://dx.doi.org/10.1088/13672630/11/5/055045 doi:10.1088/13672630/11/5/055045 (ID: 665436)
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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 selfassembled 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 longrange interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonondynamics, 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 (20090428),
http://dx.doi.org/10.1103/PhysRevLett.102.170502 doi:10.1103/PhysRevLett.102.170502 (ID: 628410)
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We demonstrate theoretically a parallelized CNOT 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 longranged 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 manybody 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 (20090424),
http://dx.doi.org/10.1103/PhysRevA.79.043419 doi:10.1103/PhysRevA.79.043419 (ID: 650348)
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We study the excitation dynamics of Rydberg atoms in a onedimensional 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 timeevolution of the mean Rydberg density, densitydensity 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 AlkalineEarth Atoms as FewQubit Quantum Registers,
Phys. Rev. Lett. 102 110503 (20090318),
http://dx.doi.org/10.1103/PhysRevLett.102.110503 doi:10.1103/PhysRevLett.102.110503 (ID: 644448)
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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 alkalineearthmetal 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 fewqubit 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) (20090310),
http://dx.doi.org/10.1103/PhysRevA.79.041602 doi:10.1103/PhysRevA.79.041602 (ID: 620456)
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We study the dynamics of a nonintegrable system comprising interacting cold bosons trapped in an optical lattice in onedimension by means of exact timedependent 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 threebody loss as a dynamical threebody interaction,
Phys. Rev. Lett. 102 040402 (20090130),
http://dx.doi.org/10.1103/PhysRevLett.102.040402 doi:10.1103/PhysRevLett.102.040402 (ID: 627388)
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We discuss how large threebody loss of atoms in an optical lattice can give rise to effective hardcore threebody interactions. For bosons, in addition to the usual atomic superfluid, a dimer superfluid can then be observed for attractive twobody interactions. The nonequilibrium dynamics of preparation and stability of these phases are studied in 1D by combining timedependent 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 Rydbergmediated coherent charge transfer in a Penning trap,
Phys. Rev. A 79 010701(R) (20090114),
http://dx.doi.org/10.1103/PhysRevA.79.010701 doi:10.1103/PhysRevA.79.010701 (ID: 620459)
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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 EinsteinPoldoskyRosen Channels between Nanomechanics and Atomic Ensembles,
Phys. Rev. Lett. 102 020501 (20090112),
http://dx.doi.org/10.1103/PhysRevLett.102.020501 doi:10.1103/PhysRevLett.102.020501 (ID: 637866)
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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, atomicensemble–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. CapogrossoSansone, S. Wessel, H. Büchler, P. Zoller, G. Pupillo Phase diagram of onedimensional hardcore bosons with threebody interactions,
Phys. Rev. B 79 020503 (R) (20090109),
http://dx.doi.org/10.1103/PhysRevB.79.020503 doi:10.1103/PhysRevB.79.020503 (ID: 603828)
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We determine the phase diagram of a onedimensional system of hardcore lattice bosons interacting via repulsive threebody interactions by analytic methods and extensive quantum Monte Carlo simulations. Such threebody 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 chargedensity wave and bond orders
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A. J. Daley, M. M. Boyd, J. Ye, P. Zoller Quantum Computing with AlkalineEarthMetal Atoms,
Phys. Rev. Lett. 101 170504 (20081023),
http://dx.doi.org/10.1103/PhysRevLett.101.170504 doi:10.1103/PhysRevLett.101.170504 (ID: 606889)
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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 (20080910),
http://dx.doi.org/10.1088/13672630/10/9/093009 doi:10.1088/13672630/10/9/093009 (ID: 520204)
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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 dipoledipole energy shifts and strong tunable internalstatedependent forces due to dipolecharge 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 (20080907),
http://dx.doi.org/10.1038/nphys1073 doi:10.1038/nphys1073 (ID: 576233)
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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 systemreservoir coupling. This points out a route towards preparing many body states and nonequilibrium 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 KosterlitzThouless 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 (20080814),
http://dx.doi.org/10.1103/PhysRevLett.101.073201 doi:10.1103/PhysRevLett.101.073201 (ID: 582039)
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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 dipoledipole interaction with a suitable combination of static electric and microwave fields in such a way that the remaining vanderWaalstype potential forms a threedimensional 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 Boseglass in cold atomic gases,
New J. Phys. 10 073032 (20080716),
http://dx.doi.org/10.1088/13672630/10/7/073032 doi:10.1088/13672630/10/7/073032 (ID: 582497)
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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 disorderinduced 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 Boseglass phase in certain parameter regimes.
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W. Yi, A. J. Daley, G. Pupillo, P. Zoller Statedependent, addressable subwavelength lattices with cold atoms,
New J. Phys. 10 073015 (20080708),
http://dx.doi.org/10.1088/13672630/10/7/073015 doi:10.1088/13672630/10/7/073015 (ID: 582500)
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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 alkalineearthlike atoms with nonzero 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 nonadiabatic 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 cavityassisted microwave cooling of polar molecules,
New J. Phys. 10 063005 (20080604),
http://dx.doi.org/10.1088/13672630/10/6/063005 doi:10.1088/13672630/10/6/063005 (ID: 567588)
Toggle Abstract
We analyze cavityassisted 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 tradeoff 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 (20080502),
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 matrixproduct states or projected entangled pair states. In particular, we show that the ground state of the AffleckKennedyLiebTasaki model can be prepared employing a quasilocal 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 (20080420),
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 nonlocal correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally faulttolerant 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 ultracold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access nonlocal 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 Andreevlike reflections with cold atoms,
Phys. Rev. Lett. 100 110404 (20080320),
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 Andreevlike reflections predicted for 1D transport systems could be observed timedependently using cold atoms in a 1D optical lattice. Using timedependent 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 BoseHubbard 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 (20080307),
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 farfield 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 solidstate qubits are discussed.
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G. Pupillo, A. Griessner, A. Micheli, M. Ortner, Wang, DawWei, P. Zoller Cold Atoms and Molecules in SelfAssembled Dipolar Lattices,
Phys. Rev. Lett. 100 050402 (20080205),
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 selfassembled floating mesoscopic lattice structure with quantum
dynamics given by phonons. We show that within an experimentally accessible
parameter regime extended Hubbard models with tunable longrange
phononmediated 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 (20080101),
http://dx.doi.org/10.1038/nphys818 doi:10.1038/nphys818 (ID: 602500)
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A. Kantian, A. J. Daley, P. Törmä, P. Zoller Atomic lattice excitons: from condensates to crystals,
New J. Phys. 9 407 (20071113),
http://dx.doi.org/10.1088/13672630/9/11/407 doi:10.1088/13672630/9/11/407 (ID: 514263)
Toggle Abstract
We discuss atomic lattice excitons (ALEs), bound particlehole 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 meanfield 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 (20071004),
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 dipoledipole 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 (20071003),
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 longrange interactions between polar molecules using external static electric and microwave fields. We consider a setup where molecules are trapped in a twodimensional pancake geometry by a faroffresonance optical trap, which ensures the stability of the dipolar collisions. We detail how to modify the shape and the strength of the longrange 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 (20070919),
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 atomion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The shortrange part of the interaction is described in the framework of quantumdefect theory, by introducing some shortrange parameters, which can be related to the swave scattering length. When the separation between traps is changed we observe trapinduced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasionedimensional geometries, when the scattering exhibit confinementinduced resonances, similar to the ones studied before for shortrange interactions. For quasionedimensional 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 atomion molecules.
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H. Büchler, A. Micheli, P. Zoller Threebody interactions with cold polar molecules,
Nature Phys. 3 731 (20070722),
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 threebody interactions, while the twoparticle 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 manybody interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearestneighbor twobody and threebody interaction. As an illustration, we study the onedimensional BoseHubbard model with dominant threebody interaction and derive its phase diagram.
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G. Brennen, A. Micheli, P. Zoller Designing spin1 lattice models using polar molecules,
New J. Phys. 9 138 (20070518),
http://dx.doi.org/10.1088/13672630/9/5/138 doi:10.1088/13672630/9/5/138 (ID: 430363)
Toggle Abstract
We describe how to design a large class of always on spin1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a rovibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipoledipole 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 (20070208),
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 longrange 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 lowdimensional trapping geometries. As an illustration, we discuss the 2D superfluidcrystal quantum phase transition for polar molecules interacting via an electricfieldinduced dipoledipole 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 (20070105),
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 twodimensional “weakpairing” 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 zeroenergy Majorana mode, which moves to finite energy in the corresponding topologically trivial “strongpairing” state. By braiding vortices in the “weakpairing” 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/10.1088/13672630/9/2/044 doi:10.1088/13672630/9/2/044 (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 subrecoil 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 manybody open quantum system.
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A. Griessner, A. J. Daley, S. Clark, D. Jaksch, P. Zoller Dark state cooling of atoms by superfluid immersion,
Phys. Rev. Lett. 97 220403 (20061204),
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 darkstate laser cooling but replaces electronic states with motional levels and spontaneous emission of photons by emission of phonons into a BoseEinstein 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 allelectrical interface between polar molecules and mesoscopic superconducting resonators,
Nature Phys. 2 636 (20060827),
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 largescale quantum system. Mesoscopic solidstate systems such as Josephson junctions and quantum dots feature robust control techniques using local electrical signals and selfevident 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 singleparticle system—an isolated polar molecule—with mesoscopic solidstate devices in a way that produces robust, coherent, quantumlevel control. Our setup provides a scalable cavityQEDtype quantum computer architecture, where entanglement of distant qubits stored in longlived 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 (20060815),
arXiv:quantph/0511118 arXiv:quantph/0511118 (ID: 313117)
Toggle Abstract
We propose a scheme for controlling interactions between Rydbergexcited neutral atoms in order to perform a fast highfidelity quantum gate. Unlike dipoleblockade mechanisms already found in the literature, we drive resonantly the atoms with a statedependent 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 iontrap 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 (20060721),
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 longlived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a highQ stripline cavity via microwave Raman processes. We show that, for convenient trapsurface 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 dWave Resonating Valence Bond States of Fermionic Atoms in Optical Lattices,
Phys. Rev. Lett. 96 250402 (20060630),
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 dwave 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 timedependent 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 (20060615),
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 (20060500),
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 socalled anyonic statistics. Topologically ordered states can arise in twodimensional latticespin 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 singlevalence 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 twospin 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 errorresilient 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 (20060203),
http://dx.doi.org/10.1103/PhysRevLett.96.043003 doi:10.1103/PhysRevLett.96.043003 (ID: 332288)
Toggle Abstract
Based on a realtime 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.

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 (20051101),
http://dx.doi.org/10.1140/epjd/e2005002511 doi:10.1140/epjd/e2005002511 (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/qipcsr.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 stateoftheart, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC subfields, 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 manybody currents in a single atom transistor,
Phys. Rev. A 72 043618 (20051028),
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 singleatomtransistor 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 spin1/2 impurity is used to switch the transport of atoms in a onedimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a singleatom mirror. We calculate timedependent currents for bosons passing the impurity atom, and find interesting manybody 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 Quantumlimited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency,
Phys. Rev. A 72 043823 (20051027),
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 Lambdasystem based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantumlimited 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 LambDicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the LambDicke 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 (20051000),
URL (ID: 332271)

A. Griessner, A. J. Daley, D. Jaksch, P. Zoller Faulttolerant dissipative preparation of atomic quantum registers with fermions,
Phys. Rev. A 72 032332 (20050928),
http://dx.doi.org/10.1103/PhysRevA.72.032332 doi:10.1103/PhysRevA.72.032332 (ID: 308207)
Toggle Abstract
We propose a faulttolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantuminformation 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 particlehole 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 highfidelity 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 341346 (20050921),
http://dx.doi.org/10.1088/14644266/7/10/020 doi:10.1088/14644266/7/10/020 (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 (20050901),
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 quenchinduced 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 LandauZener 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 (20050831),
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 NonAbelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory,
Phys. Rev. Lett. 95 010403 (20050628),
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 nonAbelian 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 singleparticle 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 nonAbelian interferometry (AharonovBohm effect) and to study manybody dynamics of ultracold matter in external lattice gauge fields.

J. Taylor, W. Dür, P. Zoller, A. Yacoby, C. M. Marcus, M. Lukin SolidState Circuit for Spin Entanglement Generation and Purification,
Phys. Rev. Lett. 94 236803 (20050615),
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 fourparticle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherencefree 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. GarcíaRipoll, P. Zoller, J. I. Cirac Coherent control of trapped ions using offresonant lasers,
Phys. Rev. A 71 062309 (20050609),
http://dx.doi.org/10.1103/PhysRevA.71.062309 doi:10.1103/PhysRevA.71.062309 (ID: 308224)
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In this paper we develop a unified framework to study the coherent control of trapped ions subject to statedependent 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. GarcíaRipoll, P. Zoller, J. I. Cirac Quantum information processing with cold atoms and trapped ions,
J. Phys. B: At. Mol. Opt. Phys. 38 567578 (20050425),
http://dx.doi.org/10.1088/09534075/38/9/008 doi:10.1088/09534075/38/9/008 (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 twoqubit 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 (20050420),
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 spin1/2 (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 singleshot quantum nondemolition 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 BoseEinstein Condensate,
Phys. Rev. Lett. 94 040404 (20050202),
http://dx.doi.org/10.1103/PhysRevLett.94.040404 doi:10.1103/PhysRevLett.94.040404 (ID: 308229)
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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 dotbath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spinboson 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 Faulttolerant architecture for quantum computation using electrically controlled semiconductor spins,
Nature Phys. 1 177183 (20050101),
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 longdistance coupling mechanisms. Our approach is based on a demonstrated encoding of qubits in longlived twoelectron 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 longrange interaction between the qubits by controlled electron transport. This approach yields a scalable architecture with favourable error thresholds for faulttolerant 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:condmat/0503254 arXiv:condmat/0503254 (ID: 302730)
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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 threedimensional U(1) lattice gauge theory.
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D. Jaksch, P. Zoller The cold atom Hubbard toolbox,
Ann. Phys. 315 5279 (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 201208 (2005),
http://dx.doi.org/10.1140/epjd/e2004001725 doi:10.1140/epjd/e2004001725 (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 solidstate 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 ioncharge system due to the charge fluctuations in the solidstate 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.

J. I. Cirac, P. Zoller New Frontiers in Quantum Information With Atoms and Ions,,
Physics Today 3844 (20040300),
URL (ID: 324583)
Toggle Abstract
Both the precision control of trappedion 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 (20040200),
http://dx.doi.org/10.1103/PhysRevLett.92.080401 doi:10.1103/PhysRevLett.92.080401 (ID: 324597)
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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 Singleatom cooling by superfluid immersion: A nondestructive method for qubits,
Phys. Rev. A 69 022306 (20040200),
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. GarcíaRipoll Strong correlation effects and quantum information theory of low dimensional atomic gases,
J. Phys. IV 116 135168 (2004),
http://dx.doi.org/10.1051/jp4:2004116005 doi:10.1051/jp4:2004116005 (ID: 314540)
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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 oneparticle 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 IonNanomechanical Systems,
Phys. Rev. Lett. 93 266403 (2004),
http://dx.doi.org/10.1103/PhysRevLett.93.266403 doi:10.1103/PhysRevLett.93.266403 (ID: 314555)
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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 singleshot quantum nondemolition measurement of the qubit spin.
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W. V. Liu, F. Wilczek, P. Zoller Spindependent 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 spindependent 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 BoseEinstein 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 stateindependent 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 singleatom 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 QuantumOptical and SolidState 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 quantumoptical and solidstate 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. GarcíaRipoll, J. I. Cirac, P. Zoller, C. Kollath, U. Schollwöck, J. von Delft Variational ansatz for the superfluid Mottinsulator transition in optical lattices,
Opt. Express 12 4254 (2004),
arXiv:condmat/0306162 arXiv:condmat/0306162 (ID: 314640)
Toggle Abstract
We develop a variational wave function for the ground state of a onedimensional 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 quasiexact 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 Mottinsulator phase.

I. Martin, A. Shnirman, L. Tian, P. Zoller Groundstate 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 lowerfrequency resonators can be cooled down to microKelvin temperatures. We also consider an alternative setup where dcvoltageinduced 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 Pauliblocking mechanism we show that shining circular polarized light on a singlycharged quantum dot induces spin dependent fluorescence. Employing the quantumjump 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 Qvalue 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 Cavityassisted nondestructive laser cooling of atomic qubits,
J. Phys. B: At. Mol. Opt. Phys. 37 1432 (2004),
http://dx.doi.org/10.1088/09534075/37/7/004 doi:10.1088/09534075/37/7/004 (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. WilsonRae, 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 electronphonon 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.

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 (20030500),
http://dx.doi.org/10.1140/epjd/e2003000202 doi:10.1140/epjd/e2003000202 (ID: 375605)
Toggle Abstract
Carrierphonon interaction in semiconductor quantum dots leads to three classes of phenomena: coherent effects (spectrum reconstruction) due to the nearlydispersionless LO phonons, incoherent effects (transitions) induced by acoustical phonons and dressing phenomena, related to nonadiabatic, subpicosecond excitation. Polaron spectra, relaxation times and dressingrelated decoherence rates are calculated, in accordance with experiment.

E. Pazy, T. Calarco, I. D'Amico, P. Zanardi, F. Rossi, P. Zoller All Optical SpinBased Quantum Information Processing,
J Supercond Nov Magn 16/2 383  385 (20030401),
http://dx.doi.org/10.1023/A:1023646326888 doi:10.1023/A:1023646326888 (ID: 375698)
Toggle Abstract
We propose a spinbased ultrafast 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 DefectSuppressed 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 twobody 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 spincharge separation,
J. Opt. B: Quantum Semiclass. Opt. 5 55 (2003),
http://dx.doi.org/10.1088/14644266/5/2/359 doi:10.1088/14644266/5/2/359 (ID: 336651)
Toggle Abstract
We discuss the properties of quasi1D 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 spincharge 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 faroffresonant 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. Singlequbit quantum logic gates are performed by modulating the Raman couplings, while twoqubit 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. GarcíaRipoll, P. Zoller, J. I. Cirac Speed Optimized TwoQubit 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 twoqubit 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 LambDicke 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 twoqubit proposals.

T. Calarco, A. Datta, P. O. Fedichev, E. Pazy, P. Zoller Spinbased alloptical 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 alloptical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Twoqubit gates are realized by switching on triontrion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read out is performed via a quantumjump 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 QuantumDot 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 alloptical scheme that uses hyperfine interactions to implement laser cooling of quantumdot 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 twoqubit 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 stronginteraction limit, a controlled growing of the disorder drives a dynamical transition from superfluid to Boseglass phase. Similarly, in the weak interaction limit, a dynamical transition from superfluid to Andersonglass phase may be observed. In both regimes, we show that even very lowintensity disorderinducing 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 alloptical spinbased 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 alloptical implementation scheme of a spinbased 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 ultrafast 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 quantumjump technique even in the presence of hole mixing, when the Pauliblocking 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 BoseEinstein 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/10.1088/13672630/5/1/356 doi:10.1088/13672630/5/1/356 (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 nonvanishing 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 setup 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 microtraps. Each atom (ion) supports a twolevel system, on which local unitary operations can be performed through a laser beam. A raw interaction between neighboring twolevel 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 Spinbased optical quantum computation via Pauli blocking in semiconductor quantum dots,
62 181 (2003),
http://dx.doi.org/10.1209/epl/i2003003434 doi:10.1209/epl/i2003003434 (ID: 336663)
Toggle Abstract
We present a solidstate implementation of an alloptical spinbased quantum computer. Our proposal for a quantumcomputing 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 subpicosecond spindependent 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 alloptical spinbased 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)
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We show that, by loading a BoseEinstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mottinsulator 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 SpinCharge 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)
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We investigate the physical properties of quasi1D quantum gases of fermionic atoms confined in harmonic traps. Using the fact that for a homogeneous gas the lowenergy properties are exactly described by a Luttinger model, we analyze the nature and manifestations of spincharge 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 Manyparticle entanglement in twocomponent BoseEinstein condensates,
Phys. Rev. A 67 013607 (2003),
http://dx.doi.org/10.1103/PhysRevA.67.013607 doi:10.1103/PhysRevA.67.013607 (ID: 336666)
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We investigate schemes to dynamically create manyparticle entangled states of a twocomponent BoseEinstein 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.

W. Hofstetter, J. I. Cirac, P. Zoller, E. Demler, M. Lukin HighTemperature Superfluidity of Fermionic Atoms in Optical Lattices,
Phys. Rev. Lett. 89 220407 (20021112),
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 dwave 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 hightemperature superconductivity in cuprates.

B. Paredes, P. Zoller, J. I. Cirac Fermionizing a small gas of ultracold bosons,
Phys. Rev. A 66 033609 (20020920),
http://dx.doi.org/10.1103/PhysRevA.66.033609 doi:10.1103/PhysRevA.66.033609 (ID: 337568)
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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 (20020917),
http://dx.doi.org/10.1103/PhysRevA.66.032309 doi:10.1103/PhysRevA.66.032309 (ID: 337570)
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We propose an allgeometric implementation of quantum computation using neutral atoms in cavity QED. We show how to perform generic single and twoqubit gates, the latter by encoding a twoatom state onto a single, manylevel atom. We compare different strategies to overcome limitations due to cavity imperfections.

L. Duan, J. I. Cirac, P. Zoller Threedimensional theory for interaction between atomic ensembles and freespace light,
Phys. Rev. A 66 023818 (20020827),
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 cavityQED model or a onedimensional 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 threedimensional free space. Here, we propose a perturbative theory to describe the threedimensional effects in interaction between atomic ensembles and freespace 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 modemismatching noise and the optimal modematching conditions. The threedimensional theory confirms the collective enhancement of the signaltonoise ratio which is believed to be one of the main advantages of the ensemblebased quantum information processing schemes, however, it also shows that this enhancement needs to be understood in a more subtle way with an appropriate modematching method.

U. Dorner, P. Zoller Laserdriven atoms in halfcavities,
Phys. Rev. A 66 023816 (20020826),
http://dx.doi.org/10.1103/PhysRevA.66.023816 doi:10.1103/PhysRevA.66.023816 (ID: 337571)
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The behavior of a twolevel atom in a halfcavity, i.e., a cavity with one mirror, is studied within the framework of a onedimensional 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 atommirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delaydifferential equations which contain, for small atommirror 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 (20020729),
http://dx.doi.org/10.1088/14644266/4/4/334 doi:10.1088/14644266/4/4/334 (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 timedependent interactions between trapped twolevel atoms and ions. We describe different possibilities for the kind of interaction to be exploited, including cold controlled collisions, electrostatic forces, and dipoledipole 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 (20020702),
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 BoseEinstein 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 (20020530),
http://dx.doi.org/10.1038/417493a doi:10.1038/417493a (ID: 337575)
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Following the creation of atomic Bose–Einstein condensates in the mid1990s, 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 twocomponent condensate,
Phys. Rev. A 65 033625 (20020301),
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 twocomponent condensate. It is shown that the application of pi/2 pulses allows us to alter the effective interspeciesinteraction 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 manybody entangled states.

L. Duan, J. I. Cirac, P. Zoller Quantum entanglement in spinor BoseEinstein condensates,
Phys. Rev. A 65 033619 (20020227),
http://dx.doi.org/10.1103/PhysRevA.65.033619 doi:10.1103/PhysRevA.65.033619 (ID: 337577)
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We propose a scheme to generate and detect various kinds of quantum entanglement in a spin1 BoseEinstein condensate. It is shown that substantial manyparticle entanglement can be generated directly in the spin1 condensate by free dynamical evolution with a properly prepared initial state. The scheme also provides a simple method to generate threemode entanglement in the secondquantization picture and to detect the continuous variable type of entanglement between two effective modes in the spin1 condensate.

L. Duan, M. Lukin, J. I. Cirac, P. Zoller Longdistance quantum communication with atomic ensembles and linear optics,
Nature 414 413 (20011122),
http://dx.doi.org/10.1038/35106500 doi:10.1038/35106500 (ID: 337580)
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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 singlephoton 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 (20011025),
http://dx.doi.org/10.1002/15213978(200110)49:10/11 doi:10.1002/15213978(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 (20011000),
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 Cooperpaired trapped atoms,
Phys. Rev. A 64 033609 (20010816),
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 Cooperpaired 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 BoseEinstein Condensates,
Phys. Rev. Lett. 87 010402 (20010702),
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 BoseEinstein 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 (20010626),
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 dipoledipole 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 (20010601),
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 allgeometric quantum computation is based on laser manipulation of a set of trapped ions. An allgeometric 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 BoseEinstein Condensates in Optical Resonators,
Phys. Rev. Lett. 86 004733 (20010521),
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 BoseEinstein 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 Ramseytype 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 (20010514),
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 statedependent force. We show how to implement a twoqubit quantum gate between two such particles with a high fidelity.

S. Gardiner, K. M. Gheri, P. Zoller Cavityassisted quasiparticle damping in a BoseEinstein condensate,
Phys. Rev. A 63 051603(R) (20010419),
http://dx.doi.org/10.1103/PhysRevA.63.051603 doi:10.1103/PhysRevA.63.051603 (ID: 337585)
Toggle Abstract
We consider an atomic BoseEinstein 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 BoseEinstein condensates,
Phys. Rev. A 63 023611 (20010117),
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 dilutegas BoseEinstein 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 onedimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an "atom sink," and a tight ringshaped condensate. We also simulate the creation of a stable sonic black hole by solving the GrossPitaevskii 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 stateoftheart or planned technology.

A. Sorensen, L. Duan, J. I. Cirac, P. Zoller Manyparticle entanglement with Bose−Einstein condensates,
Nature 409 63 (20010104),
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 singleparticle 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 BoseEinstein condensate,
Phys. Rev. A 63 023601 (20010104),
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 twomode 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 onsite 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.

L. Duan, J. I. Cirac, P. Zoller, E. Polzik Quantum Communication between Atomic Ensembles Using Coherent Light,
Phys. Rev. Lett. 85 005643 (20001225),
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 BoseEinstein Condensates,
Phys. Rev. Lett. 85 4643 (20001127),
http://dx.doi.org/10.1103/PhysRevLett.85.4643 doi:10.1103/PhysRevLett.85.4643 (ID: 337595)
Toggle Abstract
It is shown that, in dilutegas BoseEinstein 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 wellknown suggested mechanism for blackhole 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 (20001120),
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 crossKerr nonlinearities is analysed.

L. Duan, A. Sorensen, J. I. Cirac, P. Zoller Squeezing and Entanglement of Atomic Beams,
Phys. Rev. Lett. 85 3991 (20001106),
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 BoseEinstein condensate using spinexchanging 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 (20001025),
http://dx.doi.org/10.1002/15213978(200009)48:9/11 doi:10.1002/15213978(200009)48:9/11 (ID: 337593)
Toggle Abstract
We review recent proposals for performing entanglement manipulation via controlled interactions between trapped atoms. Statedependent, timevarying 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 microtraps.

T. Calarco, H. J. Briegel, D. Jaksch, J. I. Cirac, P. Zoller Entangling neutral atoms for quantum information processing,
J. Mod. Opt. 47 2137 (20001015),
URL (ID: 337599)
Toggle Abstract
We review recent proposals for performing entanglement manipulation via cold collisions between neutral atoms. Statedependent, timevarying 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 microtraps.

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 (20000904),
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 twoqubit 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 dipoledipole interaction of atoms excited to lowlying 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 BoseEinstein Condensation in Trapped Dipolar Gases,
Phys. Rev. Lett. 85 1791 (20000828),
http://dx.doi.org/10.1103/PhysRevLett.85.1791 doi:10.1103/PhysRevLett.85.1791 (ID: 337602)
Toggle Abstract
We discuss BoseEinstein condensation in a trapped gas of bosonic particles interacting dominantly via dipoledipole forces. We find that in this case the meanfield 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 continuousvariable quantum states,
Phys. Rev. A 62 32304 (20000814),
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 (20000720),
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 GrossPitaevskii equation used in the context of BoseEinstein condensation. We investigate a specific example of a GrossPitaevskii equation with such a chaotic potential, the onedimensional deltakicked 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 BoseEinstein 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 (20000717),
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 (20000517),
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 singlephoton 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 (20000424),
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 twomode 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 crossKerr interactions.

J. J. GarcíaRipoll, J. I. Cirac, J. R. Anglin, V. M. PerezGarcia, P. Zoller Spin monopoles with BoseEinstein condensates,
Phys. Rev. A 61 053609 (20000417),
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 BoseEinstein condensed sample of atoms in a macroscopic quantum state that resembles a spin monopole. In this state, the atomic internal spins lie in the xy 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 BoseEinstein condensate.

J. I. Cirac, P. Zoller A scalable quantum computer with ions in an array of microtraps,
Nature 404 579 (20000406),
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 twolevel 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 200digit 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 (20000323),
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 (20000320),
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 EinsteinPodolskyRosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any twoparty 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 (20000215),
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 setups: optical lattices and magnetic microtraps. Both offer the possibility of performing certain multiparticle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for faulttolerant 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 (20000204),
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 timedependent traps,
Phys. Rev. A 61 022304 (20000110),
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 twoqubit 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 Nparticles entangled states in both ion traps and highQ 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.

G. Morigi, J. Eschner, J. I. Cirac, P. Zoller Laser Cooling of two trapped ions: Sideband cooling beyond the LambDicke limit,
Phys. Rev. A 59 003793 (19990500),
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 LambDicke regime is shown to work analogously to sideband cooling of a single ion. Outside the LambDicke 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 LambDicke 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 (19990400),
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 (19990400),
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 (19990301),
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. GarciaFernandez, P. Zoller Creation of entangled states of distant atoms by interference,
Phys. Rev. A 59 001025 (19990200),
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 (19990100),
(ID: 352424)

W. Dür, H. J. Briegel, J. I. Cirac, P. Zoller Quantum repeaters based on entanglement purification,
Phys. Rev. A 59 000169 (19990100),
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 twoway 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 LambDicke 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 LambDicke regime is shown to work analogously to sideband cooling of a single ion. Outside the LambDicke 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 LambDicke 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 singlephoton wavepackets using standard CQEDtechniques. 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)

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 (19981226),
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 (19981214),
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 BoseEinstein 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 (19981012),
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 BoseHubbard 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 onephoton wave packets using a singleatom source,
Phys. Rev. A 58 R2627 (19981000),
http://dx.doi.org/10.1103/PhysRevA.58.R2627 doi:10.1103/PhysRevA.58.R2627 (ID: 367766)
Toggle Abstract
We propose a cavityQED scheme for the controlled generation of sequences of entangled singlephoton 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 (19980815),
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 highQ 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 (19980810),
http://dx.doi.org/10.1209/epl/i1998004262 doi:10.1209/epl/i1998004262 (ID: 367757)
Toggle Abstract
Fermi inhibition is a quantumstatistical 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 nontrivial 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 (19980810),
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 twoqubit 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 BoseEinstein condensate at finite temperature including trap loss,
Phys. Rev. A 58 1450 (19980800),
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 BoseEinstein condensate at a finite temperature. The system is divided in a condensate and a noncondensate part. A quantummechanical description based on the numberconserving 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 BoseEinstein condensate, calculate the steady state of the system, and investigate the effect of one, two, and threeparticle 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 γI1 derived in the paper. For the amplitude correlation function, we find ballistic behavior for time differences smaller than γI1, 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 (19980700),
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 Bosecondensed 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 particlenumberconserving 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 BoseEinstein 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 offdiagonal longrange 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 BoseEinstein Condensates,
Phys. Rev. Lett. 80 2972 (19980406),
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 BoseEinstein 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 (19980400),
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 onedimensional 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 LambDicke limit. We present results of a full quantum treatment for a onedimensional model.

J. I. Cirac, M. Lewenstein, K. Moelmer, P. Zoller Quantum superposition states of BoseEinstein condensates,
Phys. Rev. A 57 1208 (19980200),
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 "Schrödingercat" 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 (19980109),
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 squeezedbath interaction: Quantumreservoir engineering with atoms,
57 548 (19980100),
http://dx.doi.org/10.1103/PhysRevA.57.548 doi:10.1103/PhysRevA.57.548 (ID: 367777)
Toggle Abstract
The interaction of an atomic twolevel 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 inphase and outofphase 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 squeezedbathtype interaction for an effective twolevel system. In the simplest example, our twolevel atom is represented by the two ground levels of an atom with an angular momentum J = 1/2 > J = 1/2 transition (a fourlevel 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 squeezedbathtype 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 squeezedbath–atom interactions. The laser parameters allow one to choose properties of the squeezedbath interaction, such as the (effective) photonnumber 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 highQ 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 PhotonWavepackets 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 onephoton wave packet in terms of a generalized master equation is introduced. A corresponding quantum MonteCarlo 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 highQ cavity. We discuss the effects of decoherence and ways to correct for the corresponding errors.

S. van Enk, J. I. Cirac, P. Zoller Purifying TwoBit Quantum Gates and Joint Measurements in Cavity QED,
Phys. Rev. Lett. 79 5178 (19971222),
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 twobit gate.

S. Gardiner, J. I. Cirac, P. Zoller Quantum Chaos in an Ion Trap: The DeltaKicked Harmonic Oscillator,
Phys. Rev. Lett. 79 4790 (19971215),
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 deltakicked 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. PerezGarcia, P. Zoller Stability and collective excitations of a twocomponent BoseEinstein condensed gas: A moment approach,
Phys. Rev. A 56 2978 (19971004),
http://dx.doi.org/10.1103/PhysRevA.56.2978 doi:10.1103/PhysRevA.56.2978 (ID: 367807)
Toggle Abstract
The dynamics of a twocomponent dilute BoseEinstein gas of atoms at zero temperature is described in the meanfield approximation by a twocomponent GrossPitaevskii 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 swave scattering lengths, and obtain the lowenergy excitation frequencies corresponding to the collective motion of the two BoseEinstein condensates.

J. I. Cirac, P. Zoller, H. J. Kimble, H. Mabuchi Quantum state transfer in a quantum network: a quantumoptical implementation,
J. Mod. Opt. 44 1727 (19971001),
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 BoseEinstein Condensation in a Trap,
Phys. Rev. Lett. 79 1793 (19970908),
http://dx.doi.org/10.1103/PhysRevLett.79.1793 doi:10.1103/PhysRevLett.79.1793 (ID: 367808)
Toggle Abstract
The formation process of a BoseEinstein 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 ndot = 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. PerezGarcia, H. Michinel, J. I. Cirac, M. Lewenstein, P. Zoller Dynamics of BoseEinstein condensates: Variational solutions of the GrossPitaevskii equations,
Phys. Rev. A 56 1424 (19970800),
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 timedependent nonlinear Schrödinger equation (GrossPitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the BoseEinstein 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 (19970700),
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 threedimensional squarewell 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 oneparticle 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 (19970602),
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 quantumoptical 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 Groundstate laser cooling beyond the LambDicke limit,
39 13 (19970526),
http://dx.doi.org/10.1209/epl/i1997003063 doi:10.1209/epl/i1997003063 (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 LambDicke 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 BoseEinstein 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 (19970421),
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 timesymmetric 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 (19970400),
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 UehlingUhlenbeck equation, as well as an equation analogous to the GrossPitaevskii 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 (19970300),
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 TwoBit Quantum Gate,
Phys. Rev. Lett. 78 390 (19970113),
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 twoqubit 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 Alloptical gray lattice for atoms,
Phys. Rev. A 55 545 (19970100),
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 lowestenergy 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.

L. You, J. Cooper, P. Zoller Quantumclassical 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: Onedimensional 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 atomplustrap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a onedimensional (1D) freeparticle 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 ``flatbottom´´ trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonicoscillator 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 Quantumstate 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 atomcavity system to ``map´´ atomic groundstate Zeeman coherence onto the cavitymode field. We model photoncounting 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 cavitymode fields to be mapped onto atomic groundstate 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 lowintensity 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 BoseEinstein distributions and multistability of a lasercooled 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 BoseEinstein 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 lasercooling process.

J. I. Cirac, M. Lewenstein, P. Zoller Laser cooling a trapped atom in a cavity: Badcavity 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 onedimensional 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 atomcavity coupling (badcavity 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 LambDicke 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 welldefined 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)

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 (19941228),
(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 (19941121),
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 atomplustrap 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 diodelaser phase noise,
Phys. Lett. A 50 4303–4309 (19941105),
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 phasefluctuating 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 higherorder 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 manyatom systems,
Phys. Rev. A 50 R2799–R2802 (19941004),
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 (19940903),
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 glassvacuum 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 CasimirPolder forces is considered. We conclude with a discussion of the feasibility of the proposed waveguides.
©1994 The American Physical Society

R. Walser, P. Zoller Lasernoiseinduced polarization fluctuations as a spectroscopic tool,
Phys. Rev. A 49 5067–5077 (19940606),
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 phasediffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for twolevel 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 phasediffusing field is calculated. For this fourlevel 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 laserinduced potential wells,
Phys. Rev. A 49 4876–4887 (19940606),
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 faroffresonant standingwave laser. For a twolevel 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 Polarizationgradientassisted subrecoil cooling: Quantum calculations in one dimension,
Phys. Rev. A 49 4826–4836 (19940606),
http://dx.doi.org/10.1103/PhysRevA.49.4826 doi:10.1103/PhysRevA.49.4826 (ID: 375174)
Toggle Abstract
We present a fully quantummechanical 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 velocityselective coherent population trapping (VSCPT) and polarizationgradient cooling. The role of polarizationgradient cooling is to provide (i) for short interaction times ‘‘precooling’’ of the initial momentum distribution and (ii) in the longtime 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 polarizationgradient cooling and VSCPT are in a completely different parameter regime: polarizationgradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarizationgradient 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 (19940509),
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 BoseEinstein or FermiDirac distribution, respectively. Fluorescence from the system reflects quantum statistical properties.
©1994 The American Physical Society

K. Ellinger, J. Cooper, P. Zoller Lightpressure force in Natom systems,
Phys. Rev. A 49 3909–3933 (19940505),
http://dx.doi.org/10.1103/PhysRevA.49.3909 doi:10.1103/PhysRevA.49.3909 (ID: 375180)
Toggle Abstract
An analytical description of longrange collisions between atoms in a laser cooling field is developed. We begin by considering an Natom 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 atomatom 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 twoatom 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 firstorder 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 threedimensional ion trap by adiabatic passage,
Phys. Rev. A 49 R3174–R3177 (19940505),
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 threedimensional harmonic ion trap is proposed. The technique is based on adiabatic passage along dressed energy levels of the strongly coupled iontrap system by varying the laser frequency.
©1994 The American Physical Society

I. Marzoli, J. I. Cirac, R. Blatt, P. Zoller Laser cooling of trapped threelevel ions: Designing twolevel systems for sideband cooling,
Phys. Rev. A 49 2771–2779 (19940404),
http://dx.doi.org/10.1103/PhysRevA.49.2771 doi:10.1103/PhysRevA.49.2771 (ID: 375175)
Toggle Abstract
Laser cooling of threelevel 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 twolevel 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 twolevel 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 (19940302),
(ID: 375184)

L. S. Goldner, C. Gerz, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, P. Zoller Momentum transfer in lasercooled cesium by adiabatic passage in a light field,
Phys. Rev. Lett. 97 997–1000 (19940207),
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 lasercooled 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 (19940202),
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 standingwave light field is described by the JaynesCummings model, which is routinely used for cavityQED 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 (19940101),
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 LambDicke 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 lasercooling treatment with harmonic traps. For laseratom 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 lasercooled 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 BoseEinstein or FermiDirac distributions. The quantumstatistical 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.

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 (19931108),
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 photonnumber states is proposed. By strongly coupling an atom to a cavity field, atomic groundstate 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 (19930903),
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 lasercooled 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 (LambDicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both travelingwave and standingwave 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 travelingwave 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 onedimensional optical molasses,
Phys. Rev. Lett. 71 1335–1338 (19930809),
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 onedimensional 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 (19930802),
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 (LambDicke 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 frequencymodulation spectroscopy,
JOSA B 11 721 (19930606),
URL (ID: 375387)
Toggle Abstract
Phase shifts and intensity dependence in frequencymodulation spectroscopy

R. Taïeb, P. Marte, R. Dumhart, P. Zoller Spectrum of resonance fluorescence and cooling dynamics in quantized onedimensional molasses: Effects of laser configuration,
Phys. Rev. A 47 4986–4993 (19930606),
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 lasercooling dynamics corresponding to quantized atomic motion in onedimensional 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 twolevel atoms in a timedelayed nonMarkovian optical field,
Phys. Rev. A 47 3202–3209 (19930404),
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 timedelayed probe field by a twolevel atomic system [Na 3s1/2(F=2,mF=2)→3p3/2(F=3,mF=3)] saturated by a phasediffusing pump field. The pump and probe, derived from the same artificiallynoisemodulated phasediffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a timedelayed 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 nonMarkovian composite of a pump and timedelayed 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 353359 (19930401),
http://dx.doi.org/10.1016/00304018(93)90502V doi:10.1016/00304018(93)90502V (ID: 375419)
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The interaction of a trapped twolevel 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 (LambDicke limit), and the ioncavitymode coupling is assumed to be larger than or comparable to the spontaneous emission and cavitymode loss rates. With broadband thermal light driving the cavity mode, we show that the cooling rates and final temperatures of the trappedion motion reflect the JaynesCummings energy spectrum of the stronglycoupled ioncavity 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, W2000 Hamburg 36, Germany.

J. I. Cirac, P. Zoller Laser cooling of trapped ions in a squeezed vacuum,
Phys. Rev. A 47 2191–2195 (19930303),
http://dx.doi.org/10.1103/PhysRevA.47.2191 doi:10.1103/PhysRevA.47.2191 (ID: 375417)
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Laser cooling a trapped ion damped by an electromagnetic reservoir in a squeezedvacuum 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 (19930206),
http://dx.doi.org/10.1103/PhysRevLett.70.762 doi:10.1103/PhysRevLett.70.762 (ID: 375422)
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We propose a technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single twolevel 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 onedimensional molasses,
Phys. Rev. A 47 1378–1390 (19930202),
http://dx.doi.org/10.1103/PhysRevA.47.1378 doi:10.1103/PhysRevA.47.1378 (ID: 375414)
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We study theoretically the spectrum of resonance fluoresence from onedimensional molasses consisting of twolevel atoms with Zeeman substructure. The centerofmass 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 wavefunction simulation of the master equation and correlation function employing periodic timedependent 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 (19930201),
http://dx.doi.org/10.1103/PhysRevLett.70.556 doi:10.1103/PhysRevLett.70.556 (ID: 375418)
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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 travelingwave light fields. The squeezed state is produced when the beat frequency between two standingwave 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 atomcavity system via squeezedlight excitation of a ‘‘vacuum’’ Rabi resonance,
Phys. Rev. A 48 758–763 (19930107),
http://dx.doi.org/10.1103/PhysRevA.48.758 doi:10.1103/PhysRevA.48.758 (ID: 375410)
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The system consisting of a twolevel atom coupled strongly to a cavity mode behaves as a twostate system when excited near one of the ‘‘vacuum’’ Rabi resonances. With finitebandwidth squeezed light incident upon the cavity and tuned to one of these resonances, we show that it is possible to realize a twostate 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 twolevel atom in a squeezed vacuum, but requires that only a single cavity mode be subject to squeezing rather than the entire threedimensional vacuum.
©1993 The American Physical Society

Gardiner, Crispin, A. S. Parkins, P. Zoller Wavefunction quantum stochastic differential equations and quantumjump simulation methods,
Phys. Rev. A 46 4363–4381 (19921001),
http://dx.doi.org/10.1103/PhysRevA.46.4363 doi:10.1103/PhysRevA.46.4363 (ID: 375890)
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The quantumstochasticdifferentialequation formulation of driven quantumoptical 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 quantumjump simulations of solutions of the master equation. It is also shown that all conceivable spectral and correlationfunction 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 (19921001),
http://dx.doi.org/10.1103/PhysRevA.46.4382 doi:10.1103/PhysRevA.46.4382 (ID: 375893)
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Wavefunction 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 weakfield absorption spectra of atoms, (ii) decay of a twolevel system in a squeezed vacuum, and (iii) a strongly coupled atomcavity 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 (19920901),
http://dx.doi.org/10.1103/PhysRevA.46.2668 doi:10.1103/PhysRevA.46.2668 (ID: 375895)
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Laser cooling of trapped ions in a standing and runningwave configuration is discussed theoretically. The ions are assumed to be spatially localized on the scale provided by the wavelength of the laser (LambDicke limit). A master equation for the centerofmass distribution of the ion is derived for a multilevel system, and explicit results are presented for two and threelevel systems and harmonic trapping potentials. For the twolevel 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 threelevel system we compare our results with those of Wineland, Dalibard, and CohenTannoudji [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 (19920501),
http://dx.doi.org/10.1103/PhysRevA.45.6522 doi:10.1103/PhysRevA.45.6522 (ID: 375592)
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We describe a theoretical approach to laser cooling with broadband real Gaussian laser fields that is based on adiabatic elimination methods and the FokkerPlanck 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 orderofmagnitude 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 subDopplerwidth 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 lasercooling configuration with broadband laser fields: Instability at zero velocity,
Phys. Rev. A 45 R6161–R6164 (19920501),
http://dx.doi.org/10.1103/PhysRevA.45.R6161 doi:10.1103/PhysRevA.45.R6161 (ID: 375596)
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We investigate theoretically laser cooling with broadband σ+σ lasers acting on J=0→J=1 and J=1→J=2 transitions. For crosscorrelated laser fluctuations an instability in the friction force at zero velocity is predicted for red laser detunings. The dependence of this instability on the crosscorrelation 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 (19920501),
http://dx.doi.org/10.1007/BF00325394 doi:10.1007/BF00325394 (ID: 375719)
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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 atomfield interaction the KapitzaDirac 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 centerofmass wave packets,
Phys. Rev. A 45 5018–5030 (19920401),
http://dx.doi.org/10.1103/PhysRevA.45.5018 doi:10.1103/PhysRevA.45.5018 (ID: 375865)
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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 centerofmass 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 energyabsorption rate from a weak probelaser beam. We also show that a threelevel 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 (19920401),
http://dx.doi.org/10.1103/PhysRevA.45.4879 doi:10.1103/PhysRevA.45.4879 (ID: 375891)
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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 purestate analysis of resonant light scattering, and the SrinivasDavies 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 twolevel systems, and laser cooling of a twolevel atom in an ion trap where the centerofmass motion of the atom is described quantum mechanically.
©1992 The American Physical Society

R. Walser, H. Ritsch, P. Zoller, J. Cooper Lasernoiseinduced population fluctuations in twolevel systems: Complex and real Gaussian driving fields,
Phys. Rev. A 45 468–476 (19920201),
http://dx.doi.org/10.1103/PhysRevA.45.468 doi:10.1103/PhysRevA.45.468 (ID: 375428)
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The nonlinear dynamics of a sample of twolevel 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 onresonance fluctuations for a real Gaussian field compared to a chaotic field of the same bandwidth and intensity. Furthermore, in contrast to phasenoise 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 quantumnoise reduction in multilevellaser systems,
Phys. Rev. A 45 1881–1892 (19920201),
http://dx.doi.org/10.1103/PhysRevA.45.1881 doi:10.1103/PhysRevA.45.1881 (ID: 375590)
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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 outputintensity fluctuations significantly reduced below the shotnoise 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 dynamicpumpnoise 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 fourlevel model of the active atoms, the intensity noise can be reduced 50% below the shotnoise level. Generalizing the model to an mlevel system, we find a quantumnoise reduction by a factor of 1/2m/(m1)(m≥3), leading to perfect outputintensity 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 atomicbeam deflection by a modulated standing light wave,
Mod. Phys. Lett. A 45 R19–R22 (19920101),
http://dx.doi.org/10.1103/PhysRevA.45.R19 doi:10.1103/PhysRevA.45.R19 (ID: 375870)
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The deflection of an atomic beam passing a standingwave 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)
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Quantum noise reduction in Raman lasers