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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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2
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Figueroa-Romero P, Modi K, Pollock FA. Equilibration on average in quantum processes with finite temporal resolution. Phys Rev E 2020; 102:032144. [PMID: 33075897 DOI: 10.1103/physreve.102.032144] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 09/15/2020] [Indexed: 11/07/2022]
Abstract
We characterize the conditions under which a multitime quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a system remains closed to a fixed equilibrium for most times, to one which can be operationally assessed at multiple times, we place an upper-bound on a new observable distinguishability measure comparing a multitime process with a finite temporal resolution against a fixed equilibrium one. While the same conditions on single-time equilibration, such as a large occupation of energy levels in the initial state remain necessary, we obtain genuine multitime contributions depending on the temporal resolution of the process and the amount of disturbance of the observer's operations on it.
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Affiliation(s)
| | - Kavan Modi
- School of Physics & Astronomy, Monash University, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics & Astronomy, Monash University, Victoria 3800, Australia
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Kaplan HB, Guo L, Tan WL, De A, Marquardt F, Pagano G, Monroe C. Many-Body Dephasing in a Trapped-Ion Quantum Simulator. PHYSICAL REVIEW LETTERS 2020; 125:120605. [PMID: 33016720 DOI: 10.1103/physrevlett.125.120605] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 08/20/2020] [Indexed: 06/11/2023]
Abstract
How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.
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Affiliation(s)
- Harvey B Kaplan
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Lingzhen Guo
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
| | - Wen Lin Tan
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Arinjoy De
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Florian Marquardt
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
- Physics Department, University of Erlangen-Nuremberg, Staudtstrasse 5, 91058 Erlangen, Germany
| | - Guido Pagano
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, Texas 77005, USA
| | - Christopher Monroe
- Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
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4
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Kim H, Park Y, Kim K, Sim HS, Ahn J. Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators. PHYSICAL REVIEW LETTERS 2018; 120:180502. [PMID: 29775353 DOI: 10.1103/physrevlett.120.180502] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Indexed: 06/08/2023]
Abstract
Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.
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Affiliation(s)
- Hyosub Kim
- Department of Physics, KAIST, Daejeon 34141, Korea
| | - YeJe Park
- Department of Physics, KAIST, Daejeon 34141, Korea
| | - Kyungtae Kim
- Department of Physics, KAIST, Daejeon 34141, Korea
| | - H-S Sim
- Department of Physics, KAIST, Daejeon 34141, Korea
| | - Jaewook Ahn
- Department of Physics, KAIST, Daejeon 34141, Korea
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5
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Universality in volume-law entanglement of scrambled pure quantum states. Nat Commun 2018; 9:1635. [PMID: 29691372 PMCID: PMC5915398 DOI: 10.1038/s41467-018-03883-9] [Citation(s) in RCA: 50] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2018] [Accepted: 03/14/2018] [Indexed: 11/17/2022] Open
Abstract
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases. The entanglement in a quantum system between a small region and the surrounding environment contains details about the whole state. Nakagawa et al. find a formula for the entanglement entropy of a class of thermal-like states and show that it can be applied more broadly to identify equilibrating states.
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6
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Torres-Herrera EJ, Santos LF. Dynamical manifestations of quantum chaos: correlation hole and bulge. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0434. [PMID: 29084885 PMCID: PMC5665786 DOI: 10.1098/rsta.2016.0434] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/22/2017] [Indexed: 06/07/2023]
Abstract
A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- E J Torres-Herrera
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla 72570, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York, NY 10016, USA
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Hess PW, Becker P, Kaplan HB, Kyprianidis A, Lee AC, Neyenhuis B, Pagano G, Richerme P, Senko C, Smith J, Tan WL, Zhang J, Monroe C. Non-thermalization in trapped atomic ion spin chains. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2017.0107. [PMID: 29084886 PMCID: PMC5665787 DOI: 10.1098/rsta.2017.0107] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/27/2017] [Indexed: 05/27/2023]
Abstract
Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- P W Hess
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - P Becker
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - H B Kaplan
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - A Kyprianidis
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - A C Lee
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - B Neyenhuis
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - G Pagano
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - P Richerme
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - C Senko
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - J Smith
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - W L Tan
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - J Zhang
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
| | - C Monroe
- Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, USA
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