Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice

TL;DR

This paper studies the static and dynamic behaviors of a Tonks-Girardeau gas in a one-dimensional optical lattice, exploring the pinning transition and non-adiabatic dynamics across different lattice depths, bridging continuum and lattice models.

Contribution

It provides a comprehensive analysis of both static and dynamic properties of the Tonks-Girardeau gas in a continuum setting, including non-adiabatic effects of lattice motion.

Findings

Pinning transition occurs at infinitesimal lattice depths for commensurate densities.

The study characterizes the non-adiabatic response to sudden lattice motion.

Provides a continuum model complementing discrete lattice studies.

Abstract

We investigate the properties of a Tonks-Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.