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arXiv:1104.4727 · Physical Review A

Thermalization of atom-molecule Bose gases in a double-well potential

篤 本橋

Published Dec 22, 2011• 6 citations
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Abstract

We study the nonequiliribium dynamics of atom-molecule Bose gases in a double-well potential. In this system, the internal atom-molecule tunneling has significant influence on the dynamics. We investigate the regularity of dynamics by studying the level statistics of the quantum system. We find that chaotic energy eigenstates arise from the competition between the interwell and the atom-molecule internal tunnelings. Furthermore, we show that the physical quantities relax to the microcanonical averages in the full-quantum dynamics when the system is chaotic. This thermalization is caused by the verification of the eigenstate thermalization hypothesis (ETH). We show numerically that the onset of ETH occurs simultaneously with that of chaos. In addition, we show that the energy eigenstates become exponentially localized states simultaneously with the onset of chaos.

DOI
10.1103/physreva.84.063631

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We study the nonequiliribium dynamics of atom-molecule Bose gases in a double-well potential. In this system, the internal atom-molecule tunneling has significant influence on the dynamics. We investigate the regularity of dynamics by studying the level statistics of the quantum system. We find that chaotic energy eigenstates arise from the competition between the interwell and the atom-molecule internal tunnelings. Furthermore, we show that the physical quantities relax to the microcanonical averages in the full-quantum dynamics when the system is chaotic. This thermalization is caused by the verification of the eigenstate thermalization hypothesis (ETH). We show numerically that the onset of ETH occurs simultaneously with that of chaos. In addition, we show that the energy eigenstates become exponentially localized states simultaneously with the onset of chaos.
This paper is an attempt to establish a link between the quantum nonequilibrium dynamics of cold gases and 50 years of progress in low-dimensional quantum chaos. We identify two atomic systems lying in the interface: two interacting atoms in a harmonic multimode waveguide and an interacting two-component Bose–Bose mixture in a double-well potential. In particular, we study the level spacing distribution, the wavefunction statistics, the eigenstate thermalization and the ability to thermalize in a relaxation process as such.
The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.
We numerically investigate the relaxation dynamics in an isolated quantum system of interacting bosons trapped in a double-well potential after an integrability breaking quench. Using the statistics of the spectrum, we identify the postquench Hamiltonian as nonchaotic and close to integrability over a wide range of interaction parameters. We demonstrate that the system exhibits thermalization in the context of the eigenstate thermalization hypothesis (ETH). We also explore the possibility of an initial state to delocalize with respect to the eigenstates of the postquench Hamiltonian even for energies away from the middle of the spectrum. We observe distinct regimes of equilibration process depending on the initial energy. For low energies, the system rapidly relaxes in a single step to a thermal state. As the energy increases towards the middle of the spectrum, the relaxation dynamics exhibits prethermalization and the lifetime of the metastable states grows. Time evolution of the occupation numbers and the von Neumann entropy in the mode-partitioned system underpins the analyses of the relaxation dynamics.
Thermalization in closed quantum systems can be understood either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum-mechanical formalism, such as spectral properties of the eigenstates or entanglement between subsystems, respectively. Here we study instead the onset of thermalization of Bose particles in a two-band double-well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to understand quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state mimics a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.
The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy eigenstates behave in many ways like a statistical ensemble. A more detailed statement of this is named the eigenstate thermalization hypothesis (ETH). The reasons for why it works in so many cases are rooted in the early work of Wigner on random matrix theory and our understanding of quantum chaos. The ETH has now been studied extensively by both analytic and numerical means, and applied to a number of physical situations ranging from black hole physics to condensed matter systems. It has recently become the focus of a number of experiments in highly isolated systems. Current theoretical work also focuses on where the ETH breaks down leading to new interesting phenomena. This review of the ETH takes a somewhat intuitive approach as to why it works and how this informs our understanding of many body quantum states.
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems.These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos.By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space.We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable.As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems.When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators.Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.