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arXiv:1112.0013 · Science

Relaxation and Prethermalization in an Isolated Quantum System

Michael Gring, Maximilian Kuhnert, Tim Langen, Takuya Kitagawa, Bernhard Rauer, Matthias Schreitl, I. E. Mazets, David A. Smith, Eugene Demler, Jörg Schmiedmayer

Published Sep 6, 2012• 1,046 citations
arXivHTMLPDF

Abstract

Prethermalization When a physical system is subjected to a rapid change of conditions (for example, a gas of atoms is allowed to occupy a volume twice the size of the original container), it quickly achieves a new temperature (thermalizes) through collisions. However, in some quantum systems many conserved variables inhibit thermalization; understanding the phases the systems go through in the slowing process is of great interest to cosmologists and physicists. Gring et al. (p. 1318 , published online 31 August) separate an ultracold one-dimensional gas of bosonic atoms into two nearly identical halves, and follow how local differences in phase between the halves evolve in time by examining their interference. Initially, the local phases are almost identical, but a rapid decoherence ensues, followed by a very slow further decay. The authors analyze the relative state reached after the initial fast decay and find that it can be described by an equilibrium function with an effective temperature several times less than the initial temperature. Because this cannot be the final state of the system, the authors term the initial process prethermalization.

DOI
10.1126/science.1224953

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Prethermalization When a physical system is subjected to a rapid change of conditions (for example, a gas of atoms is allowed to occupy a volume twice the size of the original container), it quickly achieves a new temperature (thermalizes) through collisions. However, in some quantum systems many conserved variables inhibit thermalization; understanding the phases the systems go through in the slowing process is of great interest to cosmologists and physicists. Gring et al. (p. 1318 , published online 31 August) separate an ultracold one-dimensional gas of bosonic atoms into two nearly identical halves, and follow how local differences in phase between the halves evolve in time by examining their interference. Initially, the local phases are almost identical, but a rapid decoherence ensues, followed by a very slow further decay. The authors analyze the relative state reached after the initial fast decay and find that it can be described by an equilibrium function with an effective temperature several times less than the initial temperature. Because this cannot be the final state of the system, the authors term the initial process prethermalization.
Abstract. We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization. We study the dynamics of a rapidly and coherently split one-dimensional Bose gas. An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves towards a quasi-steady state. This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state. We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model, and show that the system dephases to a prethermalized state rather than undergoing thermalization towards a final thermal equilibrium state.
We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization.We study the dynamics of a rapidly and coherently split one-dimensional Bose gas.An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves toward a quasi-steady state.This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state.We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model, and show that the system dephases to a prethermalized state rather than undergoing thermalization toward a final thermal equilibrium state.
This paper explores the phenomenon of universal prethermalization in out-of-equilibrium interacting Bose-Fermi degenerate systems. Prethermalization, a transient non-equilibrium state characterized by a quasi-stationary distribution that is thermal with respect to a restricted set of effective conserved quantities, has emerged as a fundamental concept in the understanding of isolated quantum many-body systems far from equilibrium. We specifically focus on the unique interplay between bosonic and fermionic degrees of freedom, which introduces novel pathways for relaxation and distinct characteristics of prethermal plateaus. The universality of prethermal dynamics, implying independence from microscopic details and initial conditions within certain regimes, is investigated in the context of interspecies interactions, density imbalances, and dimensionality. We review the theoretical frameworks, including mean-field descriptions, effective Hamiltonians, and kinetic equations, alongside experimental observations in ultracold atomic gases that provide a fertile ground for studying such non-equilibrium phenomena. The emergence of universal scaling laws and the role of conservation laws in defining the prethermal state are discussed, paving the way for a deeper understanding of thermalization processes and the persistence of non-equilibrium states in complex quantum matter.
Abstract The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.
Abstract We review the recent progress in the understanding of the relaxation of isolated near-integrable quantum many-body systems. Focusing on prethermalization and universal dynamics following a quench, we describe the experiments with ultracold atomic gases that illustrate these phenomena and summarize the essential theoretical concepts employed to interpret them. Our discussion highlights the key topics that link the different approaches to this interdisciplinary field, including the generalized Gibbs ensemble, non-thermal fixed points, critical slowing and universal scaling. Finally, we point to new experimental challenges demonstrating these fundamental features of many-body quantum systems out of equilibrium.
Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.