Publications Hannes PICHLER

2023

Article

• M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. Lukin, S.-T. Wang, Hannes Pichler Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum 4 010316 (2023-02-14), http://dx.doi.org/10.1103/PRXQuantum.4.010316 doi:10.1103/PRXQuantum.4.010316 (ID: 720883) Toggle Abstract
  Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on the so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from the original computation problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

Preprint

• D. González-Cuadra, D. Bluvstein, M. Kalinowski, C. R. Kaubrügger, N. Maskara, P. Naldesi, T. Zache, A. Kaufman, M. Lukin, H. Pichler, B. Vermersch, J. Ye, P. Zoller Fermionic quantum processing with programmable neutral atom arrays, (2023-03-13), arXiv:2303.06985 arXiv:2303.06985 (ID: 721066) Toggle Abstract
  Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding non-local fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement non-local tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation, as well as to simulate lattice gauge theory dynamics.

2022

Articles

• Giacomo Giudice, F. M. Surace, Hannes Pichler, G. Giudici Trimer states with Z3 topological order in Rydberg atom arrays, Phys. Rev. B 106 195155 (2022-11-28), http://dx.doi.org/10.1103/PhysRevB.106.195155 doi:10.1103/PhysRevB.106.195155 (ID: 720842) Toggle Abstract
  Trimers are defined as two adjacent edges on a graph. We study the quantum states obtained as equal-weight superpositions of all trimer coverings of a lattice, with the constraint of having a trimer on each vertex: the so-called trimer resonating-valence-bond (tRVB) states. Exploiting their tensor network representation, we show that these states can host Z3 topological order or can be gapless liquids with U(1)×U(1) local symmetry. We prove that this continuous symmetry emerges whenever the lattice can be tripartite such that each trimer covers all the three sublattices. In the gapped case, we demonstrate the stability of topological order against dilution of maximal trimer coverings, which is relevant for realistic models where the density of trimers can fluctuate. Furthermore, we clarify the connection between gapped tRVB states and Z3 lattice gauge theories by smoothly connecting the former to the Z3 toric code, and discuss the non-local excitations on top of tRVB states. Finally, we analyze via exact diagonalization the zero-temperature phase diagram of a diluted trimer model on the square lattice and demonstrate that the ground state exhibits topological properties in a narrow region in parameter space. We show that a similar model can be implemented in Rydberg atom arrays exploiting the blockade effect. We investigate dynamical preparation schemes in this setup and provide a viable route for probing experimentally Z3 quantum spin liquids.
• K Slagle, Yue Liu, David Aasen, Hannes Pichler, R. S. Mong, Xie Chen, Manuel Endres, Jason Alicea Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays, Phys. Rev. B 106 115122 (2022-09-14), http://dx.doi.org/10.1103/PhysRevB.106.115122 doi:10.1103/PhysRevB.106.115122 (ID: 720829) Toggle Abstract
  Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a new strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model, albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state 'Kitaev materials' and, more generally, spotlights a new angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.
• G. Giudici, M. Lukin, H. Pichler Dynamical preparation of quantum spin liquids in Rydberg atom arrays, Phys. Rev. Lett. 129 90401 (2022-08-26), http://dx.doi.org/10.1103/PhysRevLett.129.090401 doi:10.1103/PhysRevLett.129.090401 (ID: 720742) Toggle Abstract
  We theoretically analyze recent experiments [G. Semeghini et al., Science 374, 1242 (2021)] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasi-adiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase -- the resonating valence bond (RVB) state of hard dimers -- in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network (TN) states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the non-equilibrium state, establishing the emergence of topological order.
• T. Vovk, Hannes Pichler Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes, Phys. Rev. Lett. 128 243601 (2022-06-13), http://dx.doi.org/10.1103/PhysRevLett.128.243601 doi:10.1103/PhysRevLett.128.243601 (ID: 720844) Toggle Abstract
  We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum stochastic propagator, which minimizes the expected entanglement in the many-body quantum state, thus minimizing the computational cost of the matrix product state representation of each trajectory. We illustrate this approach on the example of a one-dimensional open Brownian circuit. We show that this model displays an entanglement phase transition between area and volume law when changing between different propagators and that our method autonomously finds an efficiently representable area law unraveling.
• S. Ebadi, Alexander Keesling, Madelyn Cain, Tout T. Wang, H. Levine, D. Bluvstein, Giulia Semeghini, Ahmed Omran, Junqiu Liu, R. Samajdar, Xiu-Zhe Luo, B. Latz, J. Gao, B. Dayan, Edward Fahri, S. Sachdev, Nathan Gemelke, Lop Zhou, Soonwon Choi, Hannes Pi Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays, Science 376 1215 (2022-05-05), http://dx.doi.org/10.1126/science.abo6587 doi:10.1126/science.abo6587 (ID: 720815) Toggle Abstract
  Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
• D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuletic, M. Lukin A quantum processor based on coherent transport of entangled atom arrays, Nature 604 456 (2022-04-20), http://dx.doi.org/10.1038/s41586-022-04592-6 doi:10.1038/s41586-022-04592-6 (ID: 720723) Toggle Abstract
  The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is central for building scalable quantum information systems. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here, we demonstrate a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, in between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state. Furthermore, we shuttle entangled ancilla arrays to realize a surface code with 19 qubits and a toric code state on a torus with 24 qubits. Finally, we use this architecture to realize a hybrid analog-digital evolution and employ it for measuring entanglement entropy in quantum simulations, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars. Realizing a long-standing goal, these results pave the way toward scalable quantum processing and enable new applications ranging from simulation to metrology.
• B. Windt, H. Pichler Squeezing Quantum Many-Body Scars, Phys. Rev. Lett. 128 90606 (2022-03-04), http://dx.doi.org/10.1103/PhysRevLett.128.090606 doi:10.1103/PhysRevLett.128.090606 (ID: 720724) Toggle Abstract
  We develop an analytical approach for the description of quantum many-body scars in PXP models. We show that the scarred dynamics in the PXP model on a complete bipartite graph can be interpreted as a one-dimensional chiral scattering problem, and solve this problem analytically. The insights from this analysis allow us to predict that dynamical signatures of scars in PXP models can be enhanced by spin squeezing the initial states. We show numerically that this stabilization mechanism applies not only to the complete bipartite graph but also to one- and two-dimensional lattices, which are relevant for Rydberg atom array experiments. Moreover, our findings provide a physical motivation for Hamiltonian deformations reminiscent of those known to produce perfect scars.

Preprints

• C. Fromonteil, D. Bluvstein, Hannes Pichler Protocols for Rydberg entangling gates featuring robustness against quasi-static errors, (2022-10-17), arXiv:2210.08824 arXiv:2210.08824 (ID: 720959) Toggle Abstract
  We introduce a novel family of protocols for entangling gates for neutral atom qubits based on the Rydberg blockade mechanism. These protocols realize controlled-phase gates through a series of global laser pulses that are on resonance with the Rydberg excitation frequency. We analyze these protocols with respect to their robustness against calibration errors of the Rabi frequency or shot-to-shot laser intensity fluctuations, and show that they display robustness in various fidelity measures. In addition, we discuss adaptations of these protocols in order to make them robust to atomic-motion-induced Doppler shifts as well.
• Iris Cong, N. Maskara, M. C. Tran, Hannes Pichler, G. Semeghini, S. F. Yelin, Soonwon Choi, M. Lukin Enhancing Detection of Topological Order by Local Error Correctio, (2022-09-26), arXiv:2209.12428 arXiv:2209.12428 (ID: 720882) Toggle Abstract
  The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new approach for quantifying topological states -- locally error-corrected decoration (LED) -- by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Extensions to the characterization of other exotic states of matter are discussed.
• Vinicius S. Ferreira, G. Kim, Andreas Butler, Hannes Pichler, O. Painter Deterministic Generation of Multidimensional Photonic Cluster States with a Single Quantum Emitter, (2022-06-21), arXiv:2206.10076 arXiv:2206.10076 (ID: 720849) Toggle Abstract
  Multidimensional photonic graph states, such as cluster states, have prospective applications in quantum metrology, secure quantum communication, and measurement-based quantum computation. However, to date, generation of multidimensional cluster states of photonic qubits has relied on probabilistic methods that limit the scalability of typical generation schemes in optical systems. Here we present an experimental implementation in the microwave domain of a resource-efficient scheme for the deterministic generation of 2D photonic cluster states. By utilizing a coupled resonator array as a slow-light waveguide, a single flux-tunable transmon qubit as a quantum emitter, and a second auxiliary transmon as a switchable mirror, we achieve rapid, shaped emission of entangled photon wavepackets, and selective time-delayed feedback of photon wavepackets to the emitter qubit. We leverage these capabilities to generate a 2D cluster state of four photons with 70\% fidelity, as verified by tomographic reconstruction of the quantum state. We discuss how our scheme could be straightforwardly extended to the generation of even larger cluster states, of even higher dimension, thereby expanding the scope and practical utility of such states for quantum information processing tasks.

2021

Articles

• K. Slagle, D. Aasen, H. Pichler, R. S. Mong, P. Fendley, X. Chen, M. Endres, J. Alicea Microscopic characterization of Ising conformal field theory in Rydberg chains, Phys. Rev. B 104 235109 (2021-12-06), http://dx.doi.org/10.1103/PhysRevB.104.235109 doi:10.1103/PhysRevB.104.235109 (ID: 720682)
• G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletic, M. Lukin Probing Topological Spin Liquids on a Programmable Quantum Simulator, Science 374 1247 (2021-12-02), http://dx.doi.org/10.1126/science.abi8794 doi:10.1126/science.abi8794 (ID: 720644)
• D. S. Wild, D. Sels, H. Pichler, C. Zanoci, M. Lukin Quantum Sampling Algorithms for Near-Term Devices, Phys. Rev. Lett. 127 100504 (2021-09-02), http://dx.doi.org/10.1103/PhysRevLett.127.100504 doi:10.1103/PhysRevLett.127.100504 (ID: 720685) Toggle Abstract
  Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples, including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices, as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.
• D. S. Wild, D. Sels, H. Pichler, C. Zanoci, M. Lukin Quantum sampling algorithms, phase transitions, and computational complexity, Phys. Rev. A 104 32602 (2021-09-02), http://dx.doi.org/10.1103/PhysRevA.104.032602 doi:10.1103/PhysRevA.104.032602 (ID: 720684) Toggle Abstract
  Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can be solved in principle on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.
• S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletic, M. Lukin Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (2021-07-07), http://dx.doi.org/10.1038/s41586-021-03582-4 doi:10.1038/s41586-021-03582-4 (ID: 720710)
• R. Samajdar, W. Ho, H. Pichler, M. Lukin, S. Sachdev Quantum phases of Rydberg atoms on a kagome lattice, Proc. Natl. Acad. U.S.A. 118 e2015785118 (2021-01-26), http://dx.doi.org/10.1073/pnas.2015785118 doi:10.1073/pnas.2015785118 (ID: 720622) Toggle Abstract
  Programmable quantum simulators based on Rydberg atom arrays have recently emerged as versatile platforms for exploring exotic many-body phases and quantum dynamics of strongly correlated systems. In this work, we theoretically investigate the quantum phases that can be realized by arranging such Rydberg atoms on a kagome lattice. Along with an extensive analysis of the states which break lattice symmetries due to classical correlations, we identify an intriguing regime that constitutes a promising candidate for hosting a phase with long-range quantum entanglement and topological order. Our results provide a route to experimentally realizing and probing highly entangled quantum matter.

Preprints

• C. Miles, R. Samajdar, S. Ebadi, T. T. Wang, H. Pichler, S. Sachdev, M. Lukin, M. Greiner, K. Q. Weinberger, E. Kim Machine learning discovery of new phases in programmable quantum simulator snapshots, (2021-12-20), arXiv:2112.10789 arXiv:2112.10789 (ID: 720731) Toggle Abstract
  Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply Hybrid-CCNN to analyze new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and characterize each phase by training fully interpretable CCNNs and extracting the relevant correlations for each phase. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify two previously undetected phases, the rhombic and boundary-ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.
• J. Choi, A. L. Shaw, I. S. Madjarov, X. Xie, J. P. Covey, J. S. Cotler, D. K. Mark, H. Y. Huang, A. Kale, H. Pichler, F. G. Brandão, S. Choi, M. Endres Emergent Randomness and Benchmarking from Many-Body Quantum Chaos, (2021-03-05), arXiv:2103.03535 arXiv:2103.03535 (ID: 720643)

2020

Article

• A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. Lukin, P. Zoller Emerging 2D Gauge theories in Rydberg configurable arrays, Phys. Rev. X 10 (2020-06-16), http://dx.doi.org/10.1103/PhysRevX.10.021057 doi:10.1103/PhysRevX.10.021057 (ID: 720355) Toggle Abstract
  Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian --a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically, and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.

2019

Article

• A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletic, M. Lukin Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature 568 211 (2019-04-01), http://dx.doi.org/10.1038/s41586-019-1070-1 doi:10.1038/s41586-019-1070-1 (ID: 720062) Toggle Abstract
  Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.

2017

Articles

• J. Perczel, J. Borregaard, D. Chang, H. Pichler, S. F. Yelin, P. Zoller, M. Lukin Photonic band structure of two-dimensional atomic lattices, Phys. Rev. A 96 63801 (2017-12-04), http://dx.doi.org/10.1103/PhysRevA.96.063801 doi:10.1103/PhysRevA.96.063801 (ID: 719916) Toggle Abstract
  Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation, and long-lived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including long-range interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such long-range interactions for arbitrary two-dimensional atomic lattices. As applications of our method, we investigate the topological properties of atomic lattices both in free space and near plasmonic surfaces.
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• H. Pichler, S. Choi, P. Zoller, M. Lukin Universal photonic quantum computation via time-delayed feedback, PNAS 114 (2017-10-17), http://dx.doi.org/10.1073/pnas.1711003114 doi:10.1073/pnas.1711003114 (ID: 720008) Toggle Abstract
  We propose and analyze a deterministic protocol to generate two-dimensional photonic cluster states using a single quantum emitter via time-delayed quantum feedback. As a physical implementation, we consider a single atom or atom-like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits, while the mirror allows the implementation of feedback. We identify the class of many-body quantum states that can be produced using this approach and characterize them in terms of 2D tensor network states.
• H. Pichler, S. Choi, P. Zoller, M. Lukin Photonic tensor networks produced by a single quantum emitter, PNAS 114 11362 (2017-10-10), http://dx.doi.org/10.1073/pnas.1711003114 doi:10.1073/pnas.1711003114 (ID: 719751) Toggle Abstract
  We propose and analyze a protocol to generate two dimensional tensor network states using a single quantum system that sequentially interacts with a 1D string of qubits. This is accomplished by using parts of the string itself as a quantum queue memory. As a physical implementation, we consider a single atom or atom like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits while the mirror allows the implementation of the queue memory. We identify the class of many-body quantum states that can be produced using this approach. These include universal resources for measurement based quantum computation and states associated with topologically ordered phases. We discuss an explicit protocol to deterministically create a 2D cluster state in a quantum nanophotonic experiment, that allows for a realization of a quantum computer using a single atom coupled to light.
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• A. Glätzle, K. Ender, D. S. Wild, S. Choi, H. Pichler, M. Lukin, P. Zoller Quantum Spin Lenses in Atomic Arrays, Phys. Rev. X 7 31049 (2017-09-20), http://dx.doi.org/10.1103/PhysRevX.7.031049 doi:10.1103/PhysRevX.7.031049 (ID: 719790) Toggle Abstract
  We propose and discuss `quantum spin lenses', where quantum states of delocalized spin excitations in an atomic medium are `focused' in space in a coherent quantum process down to (essentially) single atoms. These can be employed to create controlled interactions in a quantum light-matter interface, where photonic qubits stored in an atomic ensemble are mapped to a quantum register represented by single atoms. We propose Hamiltonians for quantum spin lenses as inhomogeneous spin models on lattices, which can be realized with Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive spin-spin interactions lead to focusing dynamics conditional to the number of spin excitations. This allows the mapping of quantum superpositions of delocalized spin excitations to superpositions of spatial spin patterns, which can be addressed by light fields and manipulated. Finally, we propose multifocal quantum spin lenses as a way to generate and distribute entanglement between distant atoms in an atomic lattice array.
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• P. Guimond, M. Pletyukhov, H. Pichler, P. Zoller Delayed Coherent Quantum Feedback from a Scattering Theory and a Matrix Product State Perspective, Quantum Sci. Technol. 2 44012 (2017-09-08), http://dx.doi.org/10.1088/2058-9565/aa7f03 doi:10.1088/2058-9565/aa7f03 (ID: 719814) Toggle Abstract
  We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter's dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.
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• J. Perczel, J. Borregaard, D. Chang, H. Pichler, S. F. Yelin, P. Zoller, M. Lukin Topological Quantum Optics in Two-Dimensional Atomic Arrays, Phys. Rev. Lett. 119 23603 (2017-07-14), http://dx.doi.org/10.1103/PhysRevLett.119.023603 doi:10.1103/PhysRevLett.119.023603 (ID: 719767) Toggle Abstract
  We demonstrate that two-dimensional atomic arrays with subwavelength spacing can be used to create topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with non-trivial Chern numbers. Such a system displays topologically protected bound states and unidirectional emission by individual atoms into long-lived edge states. Possible experimental realizations and applications are discussed.
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• B. Vermersch, P. Guimond, H. Pichler, P. Zoller Quantum State Transfer via Noisy Photonic and Phononic Waveguides, Phys. Rev. Lett. 118 133601 (2017-03-27), http://dx.doi.org/10.1103/PhysRevLett.118.133601 doi:10.1103/PhysRevLett.118.133601 (ID: 719696) Toggle Abstract
  We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g. thermal noise) injected into the waveguide. We extend the model and protocol to a cavity QED setup, where atomic ensembles, or single atoms representing quantum memory, are coupled to a cavity mode. We present a detailed study of sensitivity to imperfections, and develop a quantum error correction protocol to account for random losses (or additions) of photons in the waveguide. Our numerical analysis is enabled by Matrix Product State techniques to simulate the complete quantum circuit, which we generalize to include thermal input fields. Our discussion applies both to photonic and phononic quantum networks.
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• P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, P. Zoller Chiral Quantum Optics, Nature 541 473 (2017-01-26), http://dx.doi.org/10.1038/nature21037 doi:10.1038/nature21037 (ID: 719634)

2016

Articles

• M. Łącki, M. Baranov, H. Pichler, P. Zoller Nano-Scale `Dark State' Optical Potentials for Cold Atoms, Phys. Rev. Lett. 117 233001 (2016-11-30), http://dx.doi.org/10.1103/PhysRevLett.117.233001 doi:10.1103/PhysRevLett.117.233001 (ID: 719619) Toggle Abstract
  We discuss generation of subwavelength optical barriers on the scale of tens of nanometers, as conservative optical potentials for cold atoms. These arise from non-adiabatic corrections to Born-Oppenheimer potentials from dressed `dark states' in atomic Λ -configurations. We illustrate the concepts with a double layer potential for atoms obtained from inserting an optical subwavelength barrier into a well generated by an off-resonant optical lattice, and discuss bound states of pairs of atoms interacting via magnetic dipolar interactions. The subwavelength optical barriers represent an optical `Kronig-Penney' potential. We present a detailed study of the bandstructure in optical `Kronig-Penney' potentials, including decoherence from spontaneous emission and atom loss to open `bright' channels.
• P. Guimond, H. Pichler, A. Rauschenbeutel, P. Zoller Chiral quantum optics with V-level atoms and coherent quantum feedback, Phys. Rev. A 94 33829 (2016-09-16), http://dx.doi.org/10.1103/PhysRevA.94.033829 doi:10.1103/PhysRevA.94.033829 (ID: 719590) Toggle Abstract
  We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, and this direction is opposite for the two transitions. The waveguide is terminated by a mirror which coherently feeds the photon stream emitted by one transition back to the atom. First, we are interested in the dynamics of the atom in the Markovian limit where the time-delay in the feedback is negligible. Specifically, we study the conditions under which the atom evolves towards a pure "dark" stationary state, where the photons emitted by both transitions interfere destructively thanks to the coherent feedback, and the overall emission vanishes. This is a single-atom analogue of the quantum dimer, where a pair of laser-driven two-level atoms is coupled to a unidirectional waveguide and dissipates towards a pure entangled dark state. Our setup should be feasible with current state-of-the-art experiments. Second, we extend our study to non-Markovian regimes and investigate the effect of the feedback retardation on the steady-state.
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• T. Ramos, B. Vermersch, P. Hauke, H. Pichler, P. Zoller Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons, Phys. Rev. A 93 62104 (2016-06-02), http://dx.doi.org/10.1103/PhysRevA.93.062104 doi:10.1103/PhysRevA.93.062104 (ID: 719497) Toggle Abstract
  We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to the familiar photonic networks consisting of driven two-level atoms exchanging photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D XX-spin chains representing a spin waveguide. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.
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• H. Pichler, G. Zhu, A. Seif, P. Zoller, M. Hafezi A Measurement Protocol for the Entanglement Spectrum of Cold Atoms, Phys. Rev. X 6 41033 (2016-05-17), http://dx.doi.org/10.1103/PhysRevX.6.041033 doi:10.1103/PhysRevX.6.041033 (ID: 719569) Toggle Abstract
  Entanglement plays a major role in characterizing many-body quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum many-body systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to this date, due to the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian, and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.
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• H. Pichler, P. Zoller Photonic Quantum Circuits with Time Delays, Phys. Rev. Lett. 116 93601 (2016-03-03), http://dx.doi.org/10.1103/PhysRevLett.116.093601 doi:10.1103/PhysRevLett.116.093601 (ID: 719362) Toggle Abstract
  We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where the time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where a quantum signal is fed back on a system with a time delay. We develop a matrix product state approach to solve the quantum stochastic Schrödinger equation with time delays, which accounts in an efficient way for the entanglement of nodes with the stream of emitted photons in the waveguide, and thus the non-Markovian character of the dynamics. We illustrate this approach with two paradigmatic quantum optical examples: two coherently driven distant atoms coupled to a photonic waveguide with a time delay, and a driven atom coupled to its own output field with a time delay as an instance of a quantum feedback problem.
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• M. Łącki, H. Pichler, A. Sterdyniak, A. Lyras, V. Lembessis, O. Al-Dossary, J. Budich, P. Zoller Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices, Phys. Rev. A 93 13604 (2016-01-07), http://dx.doi.org/10.1103/PhysRevA.93.013604 doi:10.1103/PhysRevA.93.013604 (ID: 719282) Toggle Abstract
  We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by counter-propagating Laguerre-Gauss beams, i.e. light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.
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2015

Article

• H. Pichler, T. Ramos, A. J. Daley, P. Zoller Quantum Optics of Chiral Spin Networks, Phys. Rev. A 91 042116 (2015-04-14), http://dx.doi.org/10.1103/PhysRevA.91.042116 doi:10.1103/PhysRevA.91.042116 (ID: 719040) Toggle Abstract
  We study the driven-dissipative dynamics of a network of spin-1/2 systems coupled to one or more chiral 1D bosonic waveguides within the framework of a Markovian master equation. We determine how the interplay between a coherent drive and collective decay processes can lead to the formation of pure multipartite entangled steady states. The key ingredient for the emergence of these many-body dark states is an asymmetric coupling of the spins to left and right propagating guided modes. Such systems are motived by experimental possibilities with internal states of atoms coupled to optical fibers, or motional states of trapped atoms coupled to a spin-orbit coupled Bose-Einstein condensate. We discuss the characterization of the emerging multipartite entanglement in this system in terms of the Fisher information.
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2014

Article

• T. Ramos, H. Pichler, A. J. Daley, P. Zoller Quantum Spin-Dimers from Chiral Dissipation in Cold Atom Chains, Phys. Rev. Lett. 113 237203 (2014-12-03), http://dx.doi.org/10.1103/PhysRevLett.113.237203 doi:10.1103/PhysRevLett.113.237203 (ID: 718977) Toggle Abstract
  We consider the non-equilibrium dynamics of a driven dissipative spin chain with chiral coupling to a 1D bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasi-condensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left and right moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.
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Dissertation

• H. Pichler Atomic Quantum Simulators: Detecting Entanglement and Designing Open Many-Body Dynamics, (2014-11-07), (ID: 719070)

2013

Articles

• L. Bonnes, H. Pichler, A. Läuchli Entropy perspective on the thermal crossover in a fermionic Hubbard chainr in a fermionic Hubbard chain, Phys. Rev. B 88 155103 (2013-10-02), http://dx.doi.org/10.1103/PhysRevB.88.155103 doi:10.1103/PhysRevB.88.155103 (ID: 718498) Toggle Abstract
  We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$ oscillations that are a hallmark of its Luttinger liquid nature. The interplay between the (extensive) thermal entropy and the ground state features is studied and we analyze the temperature induced decay of the amplitude of the oscillations as well as the scaling of the purity. Furthermore, we show how the spin and charge velocities can be extracted from the temperature dependence of the Renyi entropy, bridging our findings to recent experimental proposals on how to implement the measurement of Renyi entropies in cold atom system. Studying the Renyi mutual information, we also demonstrate how constraints such as particle number conservation can induce persistent correlations visible in the mutual information even at high temperature.
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• H. Pichler, L. Bonnes, A. J. Daley, A. Läuchli, P. Zoller Thermal versus entanglement entropy: a measurement protocol for fermionic atoms with a quantum gas microscope, New J. Phys. 15 063003 (2013-06-06), http://dx.doi.org/10.1088/1367-2630/15/6/063003 doi:10.1088/1367-2630/15/6/063003 (ID: 718531) Toggle Abstract
  We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi–Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.
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• H. Pichler, J. Schachenmayer, A. J. Daley, P. Zoller Heating dynamics of bosonic atoms in a noisy optical lattice, Phys. Rev. A 87 033606 (2013-03-05), http://dx.doi.org/10.1103/PhysRevA.87.033606 doi:10.1103/PhysRevA.87.033606 (ID: 718344) Toggle Abstract
  We analyze the heating of interacting bosonic atoms in an optical lattice due to intensity fluctuations of the lasers forming the lattice. We focus in particular on fluctuations at low frequencies below the band gap frequency, such that the dynamics is restricted to the lowest band. We derive stochastic equations of motion, and analyze the effects on different many-body states, characterizing heating processes in both strongly and weakly interacting regimes. In the limit where the noise spectrum is flat at low frequencies, we can derive an effective Master equation describing the dynamics. We compute heating rates and changes to characteristic correlation functions both in the perturbation theory limit, and using a full time-dependent calculation of the stochastic many-body dynamics in 1D based on time-dependent density-matrix-renormalization-group methods.
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2012

Articles

• H. Pichler, J. Schachenmayer, J. Simon, P. Zoller, A. J. Daley Noise- and disorder-resilient optical lattices, Phys. Rev. A 86 051605 (2012-11-16), http://dx.doi.org/10.1103/PhysRevA.86.051605 doi:10.1103/PhysRevA.86.051605 (ID: 718093) Toggle Abstract
  We show how a dressed lattice scheme can provide control over certain types of noise for atomic quantum gases in the lowest band of an optical lattice, removing the effects of global lattice amplitude noise to first order for particular choices of the dressing field parameters. We investigate the nonequilibrium many-body dynamics of bosons and fermions induced by noise away from this parameter regime, and show how the same technique can reduce spatial disorder in projected lattice potentials.
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• A. J. Daley, H. Pichler, J. Schachenmayer, P. Zoller Measuring entanglement growth in quench dynamics of bosons in an optical lattice, Phys. Rev. Lett. 109 020505 (2012-07-12), http://dx.doi.org/10.1103/PhysRevLett.109.020505 doi:10.1103/PhysRevLett.109.020505 (ID: 718070) Toggle Abstract
  We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Renyi entropies can be extracted using tunnel-coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a Superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfections in the measurements.
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2010

Article

• H. Pichler, A. J. Daley, P. Zoller Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission, Phys. Rev. A 82 063605 (2010-12-06), http://dx.doi.org/10.1103/PhysRevA.82.063605 doi:10.1103/PhysRevA.82.063605 (ID: 717301) Toggle Abstract
  We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the time scale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based on both perturbation-theory calculations and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for one-dimensional systems by combining time-dependent density-matrix-renormalization-group methods with quantum trajectory techniques.
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