Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons

TL;DR

This paper investigates how many-body entropies and correlations evolve during interaction quenches in ultracold bosons, revealing the emergence of statistical relaxation and thermalization in finite quantum systems.

Contribution

It demonstrates the first use of an optimized, time-dependent many-body basis to study thermalization and entropy production in finite quantum systems of ultracold bosons.

Findings

Entropy approaches Gaussian orthogonal ensemble predictions at strong interactions

Statistical relaxation occurs despite the basis being optimized and time-dependent

Correlation and coherence loss are directly linked to entropy production

Abstract

We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of $N=10$ interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schr\"odinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information entropy approaches the value predicted for the Gaussian orthogonal ensemble of random matrices and implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a non-trivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the build-up of correlations and loss of coherence in the system. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. Our results are the first ones obtained for thermalization of finite quantum systems using an optimized time-dependent and genuinely many-body basis set.