Collective many-body bounce in the breathing-mode oscillations of a Tonks-Girardeau gas

TL;DR

This paper predicts and analyzes a collective many-body bounce effect in a Tonks-Girardeau gas's breathing oscillations, observable via momentum distribution narrowing, explained through a finite-temperature hydrodynamic theory.

Contribution

It introduces the concept of a many-body bounce in a TG gas, revealing a new collective phenomenon observable through momentum distribution dynamics and providing a theoretical framework for its understanding.

Findings

The many-body bounce occurs at twice the breathing frequency.

The effect is visible in momentum distribution, not in in-situ density.

A phase diagram maps regimes where the bounce can be observed.

Abstract

We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure of the gas during the isentropic compression, which acts as a potential barrier at the inner turning points of the breathing cycle.