---
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.'
address: '$^1$Quantum Systems Unit, OIST Graduate University, Onna, Okinawa 904-0495, Japan'
author:
- 'Mathias Mikkelsen$^1$, Thom[á]{}s Fogarty$^1$ and Thomas Busch$^1$'
title: 'Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice'
---

Introduction {#sec:intro}
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The versatility of modern ultracold atomic experiments has in recent years allowed for the realisation of exotic matter wave phases borne from the competition between different physical forces acting on many-body systems [@Sachdev2008; @Sachdev; @Vojta]. The paradigmatic example of this has been the observation of the superfluid-to-Mott-insulator phase transition in ultracold gases confined in three-dimensional optical lattice potentials, which stems from 