1
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Karamlou AH, Rosen IT, Muschinske SE, Barrett CN, Di Paolo A, Ding L, Harrington PM, Hays M, Das R, Kim DK, Niedzielski BM, Schuldt M, Serniak K, Schwartz ME, Yoder JL, Gustavsson S, Yanay Y, Grover JA, Oliver WD. Probing entanglement in a 2D hard-core Bose-Hubbard lattice. Nature 2024; 629:561-566. [PMID: 38658761 PMCID: PMC11096108 DOI: 10.1038/s41586-024-07325-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 03/15/2024] [Indexed: 04/26/2024]
Abstract
Entanglement and its propagation are central to understanding many physical properties of quantum systems1-3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour4-7. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems8-14. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose-Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.
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Affiliation(s)
- Amir H Karamlou
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Google Quantum AI, Santa Barbara, CA, USA.
| | - Ilan T Rosen
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Sarah E Muschinske
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Cora N Barrett
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Physics, Wellesley College, Wellesley, MA, USA
| | - Agustin Di Paolo
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Leon Ding
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Patrick M Harrington
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Max Hays
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | | | | | | | | | - Kyle Serniak
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- MIT Lincoln Laboratory, Lexington, MA, USA
| | | | | | - Simon Gustavsson
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yariv Yanay
- Laboratory for Physical Sciences, College Park, MD, USA
| | - Jeffrey A Grover
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - William D Oliver
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- MIT Lincoln Laboratory, Lexington, MA, USA.
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2
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Wang B, Aidelsburger M, Dalibard J, Eckardt A, Goldman N. Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:163402. [PMID: 38701474 DOI: 10.1103/physrevlett.132.163402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/05/2024]
Abstract
Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.
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Affiliation(s)
- Botao Wang
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Monika Aidelsburger
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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3
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Qin Y, Li L. Occupation-Dependent Particle Separation in One-Dimensional Non-Hermitian Lattices. PHYSICAL REVIEW LETTERS 2024; 132:096501. [PMID: 38489628 DOI: 10.1103/physrevlett.132.096501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 11/28/2023] [Accepted: 02/02/2024] [Indexed: 03/17/2024]
Abstract
We unveil an exotic phenomenon arising from the intricate interplay between non-Hermiticity and many-body physics, namely, an occupation-dependent particle separation for hardcore bosons in a one-dimensional lattice driven by unidirectional non-Hermitian pumping. Taking hardcore bosons as an example, we find that a pair of particles occupying the same unit cell exhibit an opposite non-Hermitian pumping direction to that of unpaired ones occupying different unit cells. By turning on an intracell interaction, many-body eigenstates split in their real energies, forming separable clusters in the complex energy plane with either left-, right-, or bipolar-types of non-Hermitian skin effect (NHSE). The dependency of skin accumulating directions on particle occupation is further justified with local sublattice correlation and entanglement entropy of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests as uni- or bidirectional pumping for many-body initial states, allowing for spatially separating paired and unpaired particles. Our results unveil the possibility of designing and exploring novel non-Hermitian phases originated from particle nonconservation in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial configurations.
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Affiliation(s)
- Yi Qin
- Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, and School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China
| | - Linhu Li
- Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, and School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China
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4
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Lim LK, Lou C, Tian C. Mesoscopic fluctuations in entanglement dynamics. Nat Commun 2024; 15:1775. [PMID: 38413673 PMCID: PMC10899636 DOI: 10.1038/s41467-024-46078-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 02/12/2024] [Indexed: 02/29/2024] Open
Abstract
Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable-either interacting or noninteracting-lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.
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Affiliation(s)
- Lih-King Lim
- School of Physics, Zhejiang University, 310027, Hangzhou, Zhejiang, China
| | - Cunzhong Lou
- School of Physics, Zhejiang University, 310027, Hangzhou, Zhejiang, China
| | - Chushun Tian
- CAS Key Laboratory of Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China.
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5
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Di Carli A, Parsonage C, La Rooij A, Koehn L, Ulm C, Duncan CW, Daley AJ, Haller E, Kuhr S. Commensurate and incommensurate 1D interacting quantum systems. Nat Commun 2024; 15:474. [PMID: 38212298 PMCID: PMC10784295 DOI: 10.1038/s41467-023-44610-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 12/19/2023] [Indexed: 01/13/2024] Open
Abstract
Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments.
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Affiliation(s)
- Andrea Di Carli
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Christopher Parsonage
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Arthur La Rooij
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Lennart Koehn
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Clemens Ulm
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Callum W Duncan
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Andrew J Daley
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Elmar Haller
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Stefan Kuhr
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom.
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6
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Mitra A, Srivastava SCL. Sunburst quantum Ising model under interaction quench: Entanglement and role of initial state coherence. Phys Rev E 2023; 108:054114. [PMID: 38115417 DOI: 10.1103/physreve.108.054114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 10/13/2023] [Indexed: 12/21/2023]
Abstract
We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered XXZ model with disorder strength putting it in the many-body localized phase.
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Affiliation(s)
- Akash Mitra
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India and Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India
| | - Shashi C L Srivastava
- Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India and Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India
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7
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Northe C. Entanglement Resolution with Respect to Conformal Symmetry. PHYSICAL REVIEW LETTERS 2023; 131:151601. [PMID: 37897788 DOI: 10.1103/physrevlett.131.151601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 09/12/2023] [Accepted: 09/18/2023] [Indexed: 10/30/2023]
Abstract
Entanglement is resolved in conformal field theory (CFT) with respect to conformal families to all orders in the UV cutoff. To leading order, symmetry-resolved entanglement is connected to the quantum dimension of a conformal family, while to all orders it depends on null vectors. Criteria for equipartition between sectors are provided in both cases. This analysis exhausts all unitary conformal families. Furthermore, topological entanglement entropy is shown to symmetry-resolve the Affleck-Ludwig boundary entropy. Configuration and fluctuation entropy are analyzed on grounds of conformal symmetry.
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Affiliation(s)
- Christian Northe
- Department of Physics, Ben-Gurion University of the Negev, David Ben Gurion Boulevard 1, Be'er Sheva 84105, Israel
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8
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Bertini B, Calabrese P, Collura M, Klobas K, Rylands C. Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality. PHYSICAL REVIEW LETTERS 2023; 131:140401. [PMID: 37862655 DOI: 10.1103/physrevlett.131.140401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Accepted: 08/28/2023] [Indexed: 10/22/2023]
Abstract
Owing to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution-or its Fourier transform known as full counting statistics (FCS)-contains much more information than say the mean value of the measured observable, and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables-the charged moments-that characterize how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry. Here we consider the evolution of the FCS and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. For large scales these quantities take a simple large-deviation form, showing two different regimes as functions of time: while for times much larger than the size of the region they approach a stationary value set by the local equilibrium state, for times shorter than region size they show a nontrivial dependence on time. We show that, whenever the initial state is also U(1) symmetric, the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality. Namely, it coincides with the stationary value in the system where the roles of time and space are exchanged. We use this observation to find some general properties of FCS and charged moments out of equilibrium, and to derive an exact expression for these quantities in interacting integrable models. We test this expression against exact results in the Rule 54 quantum cellular automaton and exact numerics in the XXZ spin-1/2 chain.
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Affiliation(s)
- Bruno Bertini
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Pasquale Calabrese
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Mario Collura
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Katja Klobas
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Colin Rylands
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
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9
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Hummel Q, Richter K, Schlagheck P. Genuine Many-Body Quantum Scars along Unstable Modes in Bose-Hubbard Systems. PHYSICAL REVIEW LETTERS 2023; 130:250402. [PMID: 37418734 DOI: 10.1103/physrevlett.130.250402] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 05/30/2023] [Indexed: 07/09/2023]
Abstract
The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.
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Affiliation(s)
- Quirin Hummel
- CESAM research unit, University of Liege, B-4000 Liège, Belgium
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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10
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Bauer NP, Budich JC, Trauzettel B, Calzona A. Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading. PHYSICAL REVIEW LETTERS 2023; 130:190401. [PMID: 37243652 DOI: 10.1103/physrevlett.130.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 04/11/2023] [Indexed: 05/29/2023]
Abstract
We propose a novel spatially inhomogeneous setup for revealing quench-induced fractionalized excitations in entanglement dynamics. In this quench-probe setting, the region undergoing a quantum quench is tunnel coupled to a static region, the probe. Subsequently, the time-dependent entanglement signatures of a tunable subset of excitations propagating to the probe are monitored by energy selectivity. We exemplify the power of this generic approach by identifying a unique dynamical signature associated with the presence of an isolated Majorana zero mode in the postquench Hamiltonian. In this case excitations emitted from the topological part of the system give rise to a fractionalized jump of log(2)/2 in the entanglement entropy of the probe. This dynamical effect is highly sensitive to the localized nature of the Majorana zero mode, but does not require the preparation of a topological initial state.
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Affiliation(s)
- Nicolas P Bauer
- Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
| | - Jan Carl Budich
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
- Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
| | - Björn Trauzettel
- Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
| | - Alessio Calzona
- Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
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11
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Sauerwein N, Orsi F, Uhrich P, Bandyopadhyay S, Mattiotti F, Cantat-Moltrecht T, Pupillo G, Hauke P, Brantut JP. Engineering random spin models with atoms in a high-finesse cavity. NATURE PHYSICS 2023; 19:1128-1134. [PMID: 37575364 PMCID: PMC10415180 DOI: 10.1038/s41567-023-02033-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 03/23/2023] [Indexed: 08/15/2023]
Abstract
All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics over holographic duality in high-energy physics to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realizations in nature. Here we realize an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark-state manifold cross over to a random distribution of weakly mixed light-matter, 'grey', states. In the Lipkin-Meshkov-Glick model, the ferromagnetic finite-sized ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localized eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present substantial steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.
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Affiliation(s)
- Nick Sauerwein
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Francesca Orsi
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Philipp Uhrich
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Soumik Bandyopadhyay
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Francesco Mattiotti
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Tigrane Cantat-Moltrecht
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Guido Pupillo
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Philipp Hauke
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Jean-Philippe Brantut
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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12
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Ares F, Murciano S, Calabrese P. Entanglement asymmetry as a probe of symmetry breaking. Nat Commun 2023; 14:2036. [PMID: 37041181 PMCID: PMC10090046 DOI: 10.1038/s41467-023-37747-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 03/24/2023] [Indexed: 04/13/2023] Open
Abstract
Symmetry and symmetry breaking are two pillars of modern quantum physics. Still, quantifying how much a symmetry is broken is an issue that has received little attention. In extended quantum systems, this problem is intrinsically bound to the subsystem of interest. Hence, in this work, we borrow methods from the theory of entanglement in many-body quantum systems to introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a prototypical illustration, we study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global U(1) symmetry is restored dynamically. We adapt the quasiparticle picture for entanglement evolution to the analytic determination of the entanglement asymmetry. We find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored, a sort of quantum Mpemba effect, a phenomenon that we show to occur in a large variety of systems.
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Affiliation(s)
| | - Sara Murciano
- SISSA and INFN, via Bonomea 265, 34136, Trieste, Italy
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Pasquale Calabrese
- SISSA and INFN, via Bonomea 265, 34136, Trieste, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy
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13
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Liu T, Liu S, Li H, Li H, Huang K, Xiang Z, Song X, Xu K, Zheng D, Fan H. Observation of entanglement transition of pseudo-random mixed states. Nat Commun 2023; 14:1971. [PMID: 37031244 PMCID: PMC10082798 DOI: 10.1038/s41467-023-37511-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 03/17/2023] [Indexed: 04/10/2023] Open
Abstract
Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.
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Affiliation(s)
- Tong Liu
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
| | - Shang Liu
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Kaixuan Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
| | - Zhongcheng Xiang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- Hefei National Laboratory, Hefei, 230088, China
- CAS Center of Excellence for Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China
| | - Xiaohui Song
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- Hefei National Laboratory, Hefei, 230088, China
- CAS Center of Excellence for Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China
| | - Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- Hefei National Laboratory, Hefei, 230088, China.
- CAS Center of Excellence for Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China.
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- Hefei National Laboratory, Hefei, 230088, China.
- CAS Center of Excellence for Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China.
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- Hefei National Laboratory, Hefei, 230088, China.
- CAS Center of Excellence for Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China.
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14
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Han C, Meir Y, Sela E. Realistic Protocol to Measure Entanglement at Finite Temperatures. PHYSICAL REVIEW LETTERS 2023; 130:136201. [PMID: 37067316 DOI: 10.1103/physrevlett.130.136201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 03/14/2023] [Indexed: 06/19/2023]
Abstract
It is desirable to relate entanglement of many-body systems to measurable observables. In systems with a conserved charge, it was recently shown that the number entanglement entropy (NEE)-i.e., the entropy change due to an unselective subsystem charge measurement-is an entanglement monotone. Here we derive finite-temperature equilibrium relations between Rényi moments of the NEE, and multipoint charge correlations. These relations are exemplified in quantum dot systems where the desired charge correlations can be measured via a nearby quantum point contact. In quantum dots recently realizing the multichannel Kondo effect we show that the NEE has a nontrivial universal temperature dependence which is now accessible using the proposed methods.
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Affiliation(s)
- Cheolhee Han
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yigal Meir
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, 84105 Israel
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
| | - Eran Sela
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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15
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Brunner E, Pausch L, Carnio EG, Dufour G, Rodríguez A, Buchleitner A. Many-Body Interference at the Onset of Chaos. PHYSICAL REVIEW LETTERS 2023; 130:080401. [PMID: 36898099 DOI: 10.1103/physrevlett.130.080401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 01/16/2023] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
We unveil the signature of many-body interference across dynamical regimes of the Bose-Hubbard model. Increasing the particles' indistinguishability enhances the temporal fluctuations of few-body observables, with a dramatic amplification at the onset of quantum chaos. By resolving the exchange symmetries of partially distinguishable particles, we explain this amplification as the fingerprint of the initial state's coherences in the eigenbasis.
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Affiliation(s)
- Eric Brunner
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Lukas Pausch
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Edoardo G Carnio
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Gabriel Dufour
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Alberto Rodríguez
- Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain
- Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, E-37008 Salamanca, Spain
| | - Andreas Buchleitner
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
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16
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Down-conversion of a single photon as a probe of many-body localization. Nature 2023; 613:650-655. [PMID: 36697866 DOI: 10.1038/s41586-022-05615-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Accepted: 12/01/2022] [Indexed: 01/26/2023]
Abstract
Decay of a particle into more particles is a ubiquitous phenomenon to interacting quantum systems, taking place in colliders, nuclear reactors or solids. In a nonlinear medium, even a single photon would decay by down-converting (splitting) into lower-frequency photons with the same total energy1, at a rate given by Fermi's golden rule. However, the energy-conservation condition cannot be matched precisely if the medium is finite and only supports quantized modes. In this case, the fate of the photon becomes the long-standing question of many-body localization, originally formulated as a gedanken experiment for the lifetime of a single Fermi-liquid quasiparticle confined to a quantum dot2. Here we implement such an experiment using a superconducting multimode cavity, the nonlinearity of which was tailored to strongly violate the photon-number conservation. The resulting interaction attempts to convert a single photon excitation into a shower of low-energy photons but fails owing to the many-body localization mechanism, which manifests as a striking spectral fine structure of multiparticle resonances at the standing-wave-mode frequencies of the cavity. Each resonance was identified as a many-body state of radiation composed of photons from a broad frequency range and not obeying Fermi's golden rule theory. Our result introduces a new platform to explore the fundamentals of many-body localization without having to control many atoms or qubits3-9.
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17
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Vardi A. Chaos and bipartite entanglement between Bose-Josephson junctions. Phys Rev E 2022; 106:064210. [PMID: 36671102 DOI: 10.1103/physreve.106.064210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 12/02/2022] [Indexed: 12/24/2022]
Abstract
The entanglement between two weakly coupled bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system, containing symmetry-related regular islands separated by chaos. The symmetry-resolved entanglement spectrum and bipartite entanglement entropy of the system's energy eigenstates are calculated and compared to their expected structure for random states that exhibit complete or partial ergodicity. The entanglement spectra of chaos-supported eigenstates match the microcanonical structure of a Generalized Gibbs Ensemble due to the existence of an adiabatic invariant that restricts ergodization on the energy shell. The symmetry-resolved entanglement entropy of these quasistochastic states consists of a mean-field maximum entanglement term and a fluctuation correction due to the finite size of the constituent subsystems. The total bipartite entanglement entropy of the eigenstates correlates with their chaoticity. Island-supported eigenstates are macroscopic Schrödinger cat states for particles and excitations with substantially lower entanglement.
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Affiliation(s)
- Amichay Vardi
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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18
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Wang XK, Zhou ZY, Li MD, Zheng YG, Zhang WY, Su GX, He MG, Yuan ZS. Low-noise and high-power second harmonic generation of 532 nm laser for trapping ultracold atoms. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:123002. [PMID: 36586898 DOI: 10.1063/5.0117561] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 11/13/2022] [Indexed: 06/17/2023]
Abstract
Optical lattices for coherently manipulating ultracold atoms demand high-power, low-noise, narrow-line-width, and continuous-wave lasers. Here, we report the implementation of a 30 W 532 nm low-noise laser by second harmonic generation from a 1064 nm fiber laser, which is capable to generate optical lattices for a quantum gas microscope of Rb87 atoms. The overall conversion efficiency is 59% at an input power of 51 W with a lithium triborate crystal coupled to a ring cavity. The relative intensity noise of the output laser is suppressed to -120 dBc/Hz in the range of 10 Hz-100 kHz with a high dynamic range of over 50 dB, which is suitable for long-term trapping and coherent manipulation of the quantum gases.
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Affiliation(s)
- Xuan-Kai Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhao-Yu Zhou
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Meng-Da Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yong-Guang Zheng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Wei-Yong Zhang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guo-Xian Su
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ming-Gen He
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhen-Sheng Yuan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
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19
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Wellnitz D, Preisser G, Alba V, Dubail J, Schachenmayer J. Rise and Fall, and Slow Rise Again, of Operator Entanglement under Dephasing. PHYSICAL REVIEW LETTERS 2022; 129:170401. [PMID: 36332243 DOI: 10.1103/physrevlett.129.170401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
The operator space entanglement entropy, or simply "operator entanglement" (OE), is an indicator of the complexity of quantum operators and of their approximability by matrix product operators (MPOs). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial "rise and fall," the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a U(1) conservation law. We argue that in an XXZ spin model and a Bose-Hubbard model the OE grows universally as 1/4log_{2}t at long times and as 1/2log_{2}t for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.
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Affiliation(s)
- D Wellnitz
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
| | - G Preisser
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
| | - V Alba
- Dipartimento di Fisica, Università di Pisa, and INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
| | - J Dubail
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- Université de Lorraine, CNRS, LPCT, F-54000 Nancy, France
| | - J Schachenmayer
- ISIS (UMR 7006) and CESQ, CNRS and Université de Strasbourg, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
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20
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Maskara N, Deshpande A, Ehrenberg A, Tran MC, Fefferman B, Gorshkov AV. Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians. PHYSICAL REVIEW LETTERS 2022; 129:150604. [PMID: 36269971 DOI: 10.1103/physrevlett.129.150604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2019] [Revised: 05/18/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard "phases" and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.
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Affiliation(s)
- Nishad Maskara
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Abhinav Deshpande
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Adam Ehrenberg
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Minh C Tran
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Bill Fefferman
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
- Department of Computer Science, University of Chicago, Chicago, Illinois 60637, USA
| | - Alexey V Gorshkov
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
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21
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Luo Y, Zeng C, Huang T, Ai BQ. Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness. Phys Rev E 2022; 106:034208. [PMID: 36266857 DOI: 10.1103/physreve.106.034208] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Stochastic resetting causes kinetic phase transitions, whereas its underlying physical mechanism remains to be elucidated. We here investigate the anomalous transport of a particle moving in a chaotic system with a stochastic resetting and a rough potential and focus on how the stochastic resetting, roughness, and nonequilibrium noise affect the transports of the particle. We uncover the physical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system: The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics. From the view of the energy landscape, the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state. This resetting can lead to a kinetic phase transition between no transport and a finite net transport or between negative mobility and positive mobility. The roughness and noise also lead to the transition. Based on the mechanism, the transport of the particle can be tuned by these parameters. For example, the combination of the stochastic resetting, roughness, and noise can enhance the transport and tune negative mobility, the enhanced stability of the system, and the resonant-like activity. We analyze these results through variances (e.g., mean-squared velocity, etc.) and correlation functions (i.e., velocity autocorrelation function, position-velocity correlation function, etc.). Our results can be extensively applied in the biology, physics, and chemistry, even social system.
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Affiliation(s)
- Yuhui Luo
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
- School of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
| | - Chunhua Zeng
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Tao Huang
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China
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22
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23
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Šuntajs J, Vidmar L. Ergodicity Breaking Transition in Zero Dimensions. PHYSICAL REVIEW LETTERS 2022; 129:060602. [PMID: 36018665 DOI: 10.1103/physrevlett.129.060602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here, we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon tuning the coupling between an ergodic quantum dot and distant particles with spin-1/2. The model is effectively zero dimensional; however, a variant of the model was proposed by De Roeck and Huveneers to describe the avalanche mechanism of ergodicity breaking transition in one-dimensional disordered spin chains. We show that exact numerical results based on the spectral form factor calculation accurately agree with theoretical predictions, and hence unambiguously confirm existence of the ergodicity breaking transition in this model. We benchmark specific properties that represent hallmarks of the ergodicity breaking transition in finite systems.
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Affiliation(s)
- Jan Šuntajs
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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24
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Murciano S, Vitale V, Dalmonte M, Calabrese P. Negativity Hamiltonian: An Operator Characterization of Mixed-State Entanglement. PHYSICAL REVIEW LETTERS 2022; 128:140502. [PMID: 35476496 DOI: 10.1103/physrevlett.128.140502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 03/10/2022] [Indexed: 06/14/2023]
Abstract
In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non-Hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free-fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasilocal functional form, that is captured by simple functional relations.
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Affiliation(s)
- Sara Murciano
- SISSA, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Vittorio Vitale
- SISSA, via Bonomea 265, 34136 Trieste, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Marcello Dalmonte
- SISSA, via Bonomea 265, 34136 Trieste, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Pasquale Calabrese
- SISSA, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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25
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Jansen ND, Loucks M, Gilbert S, Fleming-Dittenber C, Egbert J, Hunt KLC. Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states. Phys Chem Chem Phys 2022; 24:7666-7681. [PMID: 35297927 DOI: 10.1039/d1cp05255a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Using IBM's publicly accessible quantum computers, we have analyzed the entropies of Schrödinger's cat states, which have the form Ψ = (1/2)1/2 [|0 0 0⋯0〉 + |1 1 1⋯1〉]. We have obtained the average Shannon entropy SSo of the distribution over measurement outcomes from 75 runs of 8192 shots, for each of the numbers of entangled qubits, on each of the quantum computers tested. For the distribution over N fault-free measurements on pure cat states, SSo would approach one as N → ∞, independent of the number of qubits; but we have found that SSo varies nearly linearly with the number of qubits n. The slope of SSoversus the number of qubits differs among computers with the same quantum volumes. We have developed a two-parameter model that reproduces the near-linear dependence of the entropy on the number of qubits, based on the probabilities of observing the output 0 when a qubit is set to |0〉 and 1 when it is set to |1〉. The slope increases as the error rate increases. The slope provides a sensitive measure of the accuracy of a quantum computer, so it serves as a quickly determinable index of performance. We have used tomographic methods with error mitigation as described in the qiskit documentation to find the density matrix ρ and evaluate the von Neumann entropies of the cat states. From the reduced density matrices for individual qubits, we have calculated the entanglement entropies. The reduced density matrices represent mixed states with approximately 50/50 probabilities for states |0〉 and |1〉. The entanglement entropies are very close to one.
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Affiliation(s)
- Nathan D Jansen
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
| | - Matthew Loucks
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
| | - Scott Gilbert
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
| | | | - Julia Egbert
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
| | - Katharine L C Hunt
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
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26
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Tunable Geometries in Sparse Clifford Circuits. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040666] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.
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27
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Bhatt RP, Kilinc J, Höcker L, Jendrzejewski F. Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud. Sci Rep 2022; 12:2422. [PMID: 35165302 PMCID: PMC8844084 DOI: 10.1038/s41598-022-05778-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 01/14/2022] [Indexed: 11/15/2022] Open
Abstract
Single particle resolution is a requirement for numerous experimental protocols that emulate the dynamics of small systems in a bath. Here, we accurately resolve through atom counting the stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud. This capability enables us to rule out the effect of inter-species interaction on sodium atom number dynamics, at very low atomic densities present in these experiments. We study the noise sources for sodium and potassium in a common framework. Thereby, we assign the detection limits to 4.3 atoms for potassium and 0.2 atoms (corresponding to 96% fidelity) for sodium. This opens possibilities for future experiments with a few atoms immersed in a quantum degenerate gas.
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Kunkel P, Prüfer M, Lannig S, Strohmaier R, Gärttner M, Strobel H, Oberthaler MK. Detecting Entanglement Structure in Continuous Many-Body Quantum Systems. PHYSICAL REVIEW LETTERS 2022; 128:020402. [PMID: 35089742 DOI: 10.1103/physrevlett.128.020402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 12/06/2021] [Indexed: 06/14/2023]
Abstract
A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.
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Affiliation(s)
- Philipp Kunkel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Maximilian Prüfer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Stefan Lannig
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Robin Strohmaier
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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29
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One-Dimensional Disordered Bosonic Systems. ATOMS 2021. [DOI: 10.3390/atoms9040112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
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30
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Xu J. Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:085402. [PMID: 34794135 DOI: 10.1088/1361-648x/ac3b25] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 11/18/2021] [Indexed: 06/13/2023]
Abstract
We study the non-adiabatic dynamics of a typical symmetry-protected topological (SPT) phase-the Haldane insulator (HI) phase with broken bond-centered inversion. By continuously breaking the middle chain, we find the gap closes at a critical point in the deep HI regime with a change of particle number partition of the left or right system. The adiabatic evolution fails at this critical point and we show how to predict the dynamics of the entanglement entropy near this point using a two-level model. These results show that one can find a critical regime where the entanglement measurement is relatively robust against perturbation that breaks the protecting symmetries in the HI. This is in contrast to the common belief that the SPT phases are fragile without the protecting symmetries.
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Affiliation(s)
- Junjun Xu
- Institute of Theoretical Physics, University of Science and Technology Beijing, Beijing 100083, People's Republic of China
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31
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Observation of Stark many-body localization without disorder. Nature 2021; 599:393-398. [PMID: 34789908 PMCID: PMC9747247 DOI: 10.1038/s41586-021-03988-0] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 09/01/2021] [Indexed: 02/08/2023]
Abstract
Thermalization is a ubiquitous process of statistical physics, in which a physical system reaches an equilibrium state that is defined by a few global properties such as temperature. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails1. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state2,3. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a spatially increasing field-but no disorder-can also exhibit MBL4, resulting in 'Stark MBL'5. Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Furthermore, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and non-thermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.
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32
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Kokail C, Sundar B, Zache TV, Elben A, Vermersch B, Dalmonte M, van Bijnen R, Zoller P. Quantum Variational Learning of the Entanglement Hamiltonian. PHYSICAL REVIEW LETTERS 2021; 127:170501. [PMID: 34739272 DOI: 10.1103/physrevlett.127.170501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 08/20/2021] [Accepted: 09/01/2021] [Indexed: 06/13/2023]
Abstract
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
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Affiliation(s)
- Christian Kokail
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Bhuvanesh Sundar
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Torsten V Zache
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Andreas Elben
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Benoît Vermersch
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
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33
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Bohrdt A, Kim S, Lukin A, Rispoli M, Schittko R, Knap M, Greiner M, Léonard J. Analyzing Nonequilibrium Quantum States through Snapshots with Artificial Neural Networks. PHYSICAL REVIEW LETTERS 2021; 127:150504. [PMID: 34678012 DOI: 10.1103/physrevlett.127.150504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Revised: 08/11/2021] [Accepted: 09/07/2021] [Indexed: 06/13/2023]
Abstract
Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and, in particular, the thermalization behavior of an interacting quantum system that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.
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Affiliation(s)
- A Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S Kim
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - A Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Rispoli
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - R Schittko
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - J Léonard
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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34
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Zhao H, Smith A, Mintert F, Knolle J. Orthogonal Quantum Many-Body Scars. PHYSICAL REVIEW LETTERS 2021; 127:150601. [PMID: 34678002 DOI: 10.1103/physrevlett.127.150601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 09/16/2021] [Indexed: 06/13/2023]
Abstract
Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.
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Affiliation(s)
- Hongzheng Zhao
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Adam Smith
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Florian Mintert
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Johannes Knolle
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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35
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Nguyen T, Andrejevic N, Po HC, Song Q, Tsurimaki Y, Drucker NC, Alatas A, Alp EE, Leu BM, Cunsolo A, Cai YQ, Wu L, Garlow JA, Zhu Y, Lu H, Gossard AC, Puretzky AA, Geohegan DB, Huang S, Li M. Signature of Many-Body Localization of Phonons in Strongly Disordered Superlattices. NANO LETTERS 2021; 21:7419-7425. [PMID: 34314183 DOI: 10.1021/acs.nanolett.1c01905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Many-body localization (MBL) has attracted significant attention because of its immunity to thermalization, role in logarithmic entanglement entropy growth, and opportunities to reach exotic quantum orders. However, experimental realization of MBL in solid-state systems has remained challenging. Here, we report evidence of a possible phonon MBL phase in disordered GaAs/AlAs superlattices. Through grazing-incidence inelastic X-ray scattering, we observe a strong deviation of the phonon population from equilibrium in samples doped with ErAs nanodots at low temperature, signaling a departure from thermalization. This behavior occurs within finite phonon energy and wavevector windows, suggesting a localization-thermalization crossover. We support our observation by proposing a theoretical model for the effective phonon Hamiltonian in disordered superlattices, and showing that it can be mapped exactly to a disordered 1D Bose-Hubbard model with a known MBL phase. Our work provides momentum-resolved experimental evidence of phonon localization, extending the scope of MBL to disordered solid-state systems.
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Affiliation(s)
- Thanh Nguyen
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Nina Andrejevic
- Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Hoi Chun Po
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Qichen Song
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Yoichiro Tsurimaki
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Nathan C Drucker
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Ahmet Alatas
- Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Esen E Alp
- Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Bogdan M Leu
- Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Department of Physics, Miami University, Oxford, Ohio 45056, United States
| | - Alessandro Cunsolo
- Department of Physics, University of Wisconsin at Madison, Madison, Wisconsin 53706, United States
| | - Yong Q Cai
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Lijun Wu
- Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Joseph A Garlow
- Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Yimei Zhu
- Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Hong Lu
- College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
| | - Arthur C Gossard
- Materials Department, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Alexander A Puretzky
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - David B Geohegan
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Shengxi Huang
- Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Mingda Li
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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36
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Niknam M, Santos LF, Cory DG. Experimental Detection of the Correlation Rényi Entropy in the Central Spin Model. PHYSICAL REVIEW LETTERS 2021; 127:080401. [PMID: 34477434 DOI: 10.1103/physrevlett.127.080401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Revised: 03/15/2021] [Accepted: 07/15/2021] [Indexed: 06/13/2023]
Abstract
We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with 15 other spins. Because of the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multispin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multispin correlations and use them to compute the evolution of what we call correlation Rényi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation Rényi entropy depend on the system size.
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Affiliation(s)
- Mohamad Niknam
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L3G1
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L3G1
- Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095-1059, USA
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York City, New York, 10016, USA
| | - David G Cory
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L3G1
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L3G1
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37
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Walsh C, Charlebois M, Sémon P, Sordi G, Tremblay AMS. Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator. Proc Natl Acad Sci U S A 2021; 118:e2104114118. [PMID: 34161286 PMCID: PMC8237656 DOI: 10.1073/pnas.2104114118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A key open issue in condensed-matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information-theory tools on the two-dimensional (2D) Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels and shows a broad peak versus doping, as a result of competing quantum and classical effects.
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Affiliation(s)
- Caitlin Walsh
- Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom
| | - Maxime Charlebois
- Département de Chimie, Biochimie et Physique, Institut de Recherche sur l'Hydrogène, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada
| | - Patrick Sémon
- Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973-5000
| | - Giovanni Sordi
- Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom;
| | - André-Marie S Tremblay
- Département de Physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Institut Quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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38
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Hart O, Gopalakrishnan S, Castelnovo C. Logarithmic Entanglement Growth from Disorder-Free Localization in the Two-Leg Compass Ladder. PHYSICAL REVIEW LETTERS 2021; 126:227202. [PMID: 34152181 DOI: 10.1103/physrevlett.126.227202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 03/11/2021] [Indexed: 06/13/2023]
Abstract
We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions decay with an exponent that varies continuously with temperature and model parameters. These quasi-1D models offer an experimentally realizable setting in which natural dynamical probes show signatures of disorder-free many-body localization.
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Affiliation(s)
- Oliver Hart
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Sarang Gopalakrishnan
- Physics Program and Initiative for the Theoretical Sciences, Graduate Center, CUNY, New York, New York 10016, USA
- Physics and Astronomy, College of Staten Island, Staten Island, New York 10314, USA
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Claudio Castelnovo
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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39
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Bergh B, Gärttner M. Experimentally Accessible Bounds on Distillable Entanglement from Entropic Uncertainty Relations. PHYSICAL REVIEW LETTERS 2021; 126:190503. [PMID: 34047593 DOI: 10.1103/physrevlett.126.190503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 04/01/2021] [Indexed: 06/12/2023]
Abstract
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level may shed light on these puzzles. However, measuring, or even bounding, entanglement experimentally has proven to be an outstanding challenge, especially when the prepared quantum states are mixed. We use entropic uncertainty relations for bipartite systems to derive measurable lower bounds on distillable entanglement. We showcase these bounds by applying them to physical models realizable in cold-atom experiments. The derived entanglement bounds rely on measurements in only two different bases and are generically applicable to any quantum simulation platform.
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Affiliation(s)
- Bjarne Bergh
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
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40
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Li MD, Lin W, Luo A, Zhang WY, Sun H, Xiao B, Zheng YG, Yuan ZS, Pan JW. High-powered optical superlattice with robust phase stability for quantum gas microscopy. OPTICS EXPRESS 2021; 29:13876-13886. [PMID: 33985115 DOI: 10.1364/oe.423776] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 04/12/2021] [Indexed: 06/12/2023]
Abstract
Optical superlattice has a wide range of applications in the study of ultracold atom physics. Especially, it can be used to trap and manipulate thousands of atom pairs in parallel which constitutes a promising system for quantum simulation and quantum computation. In the present work, we report on a high-power optical superlattice formed by a 532-nm and 1064-nm dual-wavelength interferometer with a short lattice spacing of 630 nm. The short-term fluctuation (in 10 seconds) of the relative phase between the short lattice and the long lattice is measured to be 0.003π, which satisfies the needs for performing two-qubit gates among neighboring lattice sites. We further implement this superlattice in a 87Rb experiment with a quantum gas microscope of single-site resolution, where the high-power 532-nm laser is necessary for pinning atoms in the short lattice during imaging, providing a unique platform for engineering quantum states.
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41
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Klobas K, Bertini B, Piroli L. Exact Thermalization Dynamics in the "Rule 54" Quantum Cellular Automaton. PHYSICAL REVIEW LETTERS 2021; 126:160602. [PMID: 33961472 DOI: 10.1103/physrevlett.126.160602] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 03/03/2021] [Indexed: 06/12/2023]
Abstract
We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.
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Affiliation(s)
- Katja Klobas
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Bruno Bertini
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Lorenzo Piroli
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
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42
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Gong Z, Piroli L, Cirac JI. Topological Lower Bound on Quantum Chaos by Entanglement Growth. PHYSICAL REVIEW LETTERS 2021; 126:160601. [PMID: 33961458 DOI: 10.1103/physrevlett.126.160601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the evolution operator. Here we show that, for one-dimensional quantum cellular automata (QCA), there exists a lower bound on quantum chaos quantified by such entanglement entropy. This lower bound is equal to twice the index of the QCA, which is a topological invariant that measures the chirality of information flow, and holds for all the Rényi entropies, with its strongest Rényi-∞ version being tight. The rigorous bound rules out the possibility of any sublinear entanglement growth behavior, showing in particular that many-body localization is forbidden for unitary evolutions displaying nonzero index. Since the Rényi entropy is measurable, our findings have direct experimental relevance. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians.
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Affiliation(s)
- Zongping Gong
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
| | - Lorenzo Piroli
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
| | - J Ignacio Cirac
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
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Krause U, Pellegrin T, Brouwer PW, Abanin DA, Filippone M. Nucleation of Ergodicity by a Single Mobile Impurity in Supercooled Insulators. PHYSICAL REVIEW LETTERS 2021; 126:030603. [PMID: 33543943 DOI: 10.1103/physrevlett.126.030603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 12/18/2020] [Indexed: 05/16/2023]
Abstract
We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder.
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Affiliation(s)
- Ulrich Krause
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Théo Pellegrin
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
| | - Piet W Brouwer
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Dmitry A Abanin
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
- Department of Theoretical Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
| | - Michele Filippone
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
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Bohrdt A, Wang Y, Koepsell J, Kánasz-Nagy M, Demler E, Grusdt F. Dominant Fifth-Order Correlations in Doped Quantum Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 126:026401. [PMID: 33512175 DOI: 10.1103/physrevlett.126.026401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t-J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T_{c} superconductivity.
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Affiliation(s)
- A Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Y Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - J Koepsell
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - M Kánasz-Nagy
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - E Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstrasse 37, München D-80333, Germany
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Rademaker L, Abanin DA. Slow Nonthermalizing Dynamics in a Quantum Spin Glass. PHYSICAL REVIEW LETTERS 2020; 125:260405. [PMID: 33449733 DOI: 10.1103/physrevlett.125.260405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.
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Affiliation(s)
- Louk Rademaker
- Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Dmitry A Abanin
- Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
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Paul S, Bäcker A. Linear and logarithmic entanglement production in an interacting chaotic system. Phys Rev E 2020; 102:050102. [PMID: 33327075 DOI: 10.1103/physreve.102.050102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 10/28/2020] [Indexed: 11/07/2022]
Abstract
We investigate entanglement growth for a pair of coupled kicked rotors. For weak coupling, the growth of the entanglement entropy is found to be initially linear followed by a logarithmic growth. We calculate analytically the time after which the entanglement entropy changes its profile, and a good agreement with the numerical result is found. We further show that the different regimes of entanglement growth are associated with different rates of energy growth displayed by a rotor. At a large time, energy grows diffusively, which is preceded by an intermediate dynamical localization. The time span of intermediate dynamical localization decreases with increasing coupling strength. We argue that the observed diffusive energy growth is the result of one rotor acting as an environment to the other, which destroys the coherence. We show that the decay of the coherence is initially exponential followed by a power law.
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Affiliation(s)
- Sanku Paul
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.,Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
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Šuntajs J, Bonča J, Prosen T, Vidmar L. Quantum chaos challenges many-body localization. Phys Rev E 2020; 102:062144. [PMID: 33466008 DOI: 10.1103/physreve.102.062144] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 12/02/2020] [Indexed: 06/12/2023]
Abstract
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator g=log_{10}(t_{H}/t_{Th}), which is defined through the ratio of two characteristic many-body time scales, the Thouless time t_{Th} and the Heisenberg time t_{H}, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, t_{Th}≈t_{H}, and g becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of g across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.
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Affiliation(s)
- Jan Šuntajs
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Janez Bonča
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Pari NAÁ, García DJ, Cornaglia PS. Quasiparticle Mass Enhancement as a Measure of Entanglement in the Kondo Problem. PHYSICAL REVIEW LETTERS 2020; 125:217601. [PMID: 33274973 DOI: 10.1103/physrevlett.125.217601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 08/25/2020] [Accepted: 10/20/2020] [Indexed: 06/12/2023]
Abstract
We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z in the Kondo regime. This indicates that the interaction induced mass enhancement, which is generally used to quantify correlations in quantum many body systems, could be used as a measure of entanglement in the Kondo problem.
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Affiliation(s)
- Nayra A Álvarez Pari
- Centro Atómico Bariloche and Instituto Balseiro, CNEA, 8400 Bariloche, Argentina
| | - D J García
- Centro Atómico Bariloche and Instituto Balseiro, CNEA, 8400 Bariloche, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), 8400 Bariloche, Argentina
| | - Pablo S Cornaglia
- Centro Atómico Bariloche and Instituto Balseiro, CNEA, 8400 Bariloche, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), 8400 Bariloche, Argentina
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White DH, Haase TA, Brown DJ, Hoogerland MD, Najafabadi MS, Helm JL, Gies C, Schumayer D, Hutchinson DAW. Observation of two-dimensional Anderson localisation of ultracold atoms. Nat Commun 2020; 11:4942. [PMID: 33009375 PMCID: PMC7532155 DOI: 10.1038/s41467-020-18652-w] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2019] [Accepted: 09/01/2020] [Indexed: 11/29/2022] Open
Abstract
Anderson localisation -the inhibition of wave propagation in disordered media- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.
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Affiliation(s)
- Donald H White
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Waseda Research Institute for Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan
| | - Thomas A Haase
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
| | - Dylan J Brown
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Light-Matter Interactions for Quantum Technologies Unit, Okinawa Institute of Science and Technology, Tancha, Onna, Okinawa, Japan
| | - Maarten D Hoogerland
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand.
| | - Mojdeh S Najafabadi
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - John L Helm
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Christopher Gies
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
| | - Daniel Schumayer
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - David A W Hutchinson
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand.
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.
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Lenarčič Z, Alberton O, Rosch A, Altman E. Critical Behavior near the Many-Body Localization Transition in Driven Open Systems. PHYSICAL REVIEW LETTERS 2020; 125:116601. [PMID: 32976013 DOI: 10.1103/physrevlett.125.116601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is nonthermal or when the system is also weakly driven, local conserved quantities acquire a highly nonthermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the nonthermal baths plays a similar role as a finite temperature in a T=0 quantum phase transition. By tuning this parameter, we can detect key features of the many-body localization (MBL) transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here, we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.
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Affiliation(s)
- Zala Lenarčič
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ori Alberton
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
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