Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases

TL;DR

This paper explores the strongly correlated regime of a 1D Bose gas with attractive interactions, revealing a stable gas-like state more correlated than a Tonks-Girardeau gas, and analyzing its properties and stability limits.

Contribution

It introduces a variational approach to describe the strongly attractive regime, extending understanding beyond the Tonks-Girardeau limit in quasi-1D Bose gases.

Findings

The gas-like state remains stable at small densities.

The system exhibits stronger correlations than a Tonks-Girardeau gas.

The critical density for instability is estimated.

Abstract

We consider a homogeneous 1D Bose gas with contact interactions and large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using a variational {\it ansatz} for the many-body wavefunction, we show that for small densities the gas-like state is stable and the corresponding equation of state is well described by a gas of hard rods. By calculating the compressibility of the system, we provide an estimate of the critical density at which the gas-like state becomes unstable against cluster formation. Within the hard-rod model we calculate the one-body density matrix and the static structure factor of the gas. The results show that in this regime the system is more strongly correlated than a Tonks-Girardeau gas. The frequency of the lowest breathing mode for harmonically trapped systems is also discussed as a function of the interaction strength.