Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas

TL;DR

This paper investigates the non-equilibrium dynamics of a harmonically trapped one-dimensional Bose gas undergoing a quench from zero to infinite interaction, revealing periodic breathing, sudden expansion, and refocusing phenomena.

Contribution

It uncovers unique dynamical behaviors due to different thermodynamic limits in trapped systems and demonstrates the applicability of a generalized Gibbs ensemble for describing long-term averages.

Findings

Dynamics are perfectly periodic with a breathing time related to trap strength.

Short-time expansion causes extreme dilution and density tails.

Time-averaged density matches generalized Gibbs ensemble predictions.

Abstract

We study the non-equilibrium dynamics of a one-dimensional Bose gas trapped by a harmonic potential for a quench from zero to infinite interaction. The different thermodynamic limits required for the equilibrium pre- and post-quench Hamiltonians are the origin of a few unexpected phenomena that have no counterparts in the translational invariant setting. We find that the dynamics is perfectly periodic with breathing time related to the strength of the trapping potential. For very short times, we observe a sudden expansion leading to an extreme dilution of the gas and to the emergence of slowly decaying tails in the density profile. The haste of the expansion induces a undertow effect with a pronounced local minimum of the density at the center of the trap. At half period there is a refocusing phenomenon characterized by a sharp central peak of the density, juxtaposed to algebraically decaying tails. We finally show that the time-averaged density is correctly captured by a generalized Gibbs ensemble built with the conserved mode occupations.