Relaxation, chaos, and thermalization in a three-mode model of a BEC

TL;DR

This paper investigates how quantum chaos and fragmentation lead to the decay of oscillations and thermalization in a three-mode Bose-Einstein condensate model after a quench, highlighting the transition from mean-field to many-body dynamics.

Contribution

It introduces a three-mode quantum model to describe the dynamics of a BEC post-quench, linking chaos, fragmentation, and thermalization phenomena.

Findings

Decay of oscillations correlates with condensate fragmentation.

Chaos enhances eigenstate complexity, facilitating thermalization.

Quantum signatures of chaos depend on interaction strength and atom number.

Abstract

We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose-Einstein condensed state, well described by Thomas-Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.