Quantum Monte Carlo study of quasi-one-dimensional Bose gases

TL;DR

This study uses Monte Carlo methods to analyze quasi-one-dimensional Bose gases, confirming their behavior aligns with 1d models, identifying regimes like Tonks-Girardeau and unitary, and pinpointing stability limits.

Contribution

It provides a detailed Monte Carlo analysis of quasi-1d Bose gases, extending previous results and clarifying their regimes and stability conditions.

Findings

Quasi-1d Bose gases are well described by 1d contact interaction models.

The gas reaches the Tonks-Girardeau regime at a critical 3d scattering length.

The gas enters a universal unitary regime as |a_3d| approaches infinity.

Abstract

We study the behavior of quasi-one-dimensional (quasi-1d) Bose gases by Monte Carlo techniques, i.e., by the variational Monte Carlo, the diffusion Monte Carlo, and the fixed-node diffusion Monte Carlo technique. Our calculations confirm and extend our results of an earlier study [Astrakharchik et al., cond-mat/0308585]. We find that a quasi-1d Bose gas i) is well described by a 1d model Hamiltonian with contact interactions and renormalized coupling constant; ii) reaches the Tonks-Girardeau regime for a critical value of the 3d scattering length a_3d; iii) enters a unitary regime for |a_3d| -> infinity, where the properties of the gas are independent of a_3d and are similar to those of a 1d gas of hard-rods; and iv) becomes unstable against cluster formation for a critical value of the 1d gas parameter. The accuracy and implications of our results are discussed in detail.