Exact coherent states of a harmonically confined Tonks-Girardeau gas

TL;DR

This paper provides an exact analysis of the dynamics of a harmonically confined Tonks-Girardeau gas, revealing phenomena like dynamical fermionization and undamped breathing oscillations during trap variations.

Contribution

It introduces an exact method using a scaling transformation to analyze the nonequilibrium dynamics of the Tonks-Girardeau gas under arbitrary trap frequency changes.

Findings

Momentum distribution approaches that of an ideal Fermi gas during expansion

Undamped breathing oscillations with alternating bosonic and fermionic character

Absence of damping is unique to the Tonks regime

Abstract

Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a ``dynamical fermionization'' occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime.