Is a Trapped One-Dimensional Bose Gas a Luttinger Liquid?

TL;DR

This paper investigates the low-energy behavior of a trapped one-dimensional Bose gas, demonstrating it can be modeled as a Luttinger liquid under certain conditions, with a transition to Bose-Einstein condensation at lower temperatures.

Contribution

It shows that a trapped 1D Bose gas can be described as a Luttinger liquid and identifies the temperature-dependent transition to Bose-Einstein condensation.

Findings

Correlation functions decay algebraically in the Luttinger liquid regime

Bose-Einstein condensation is suppressed at higher temperatures

A finite size gap at low temperatures restores Bose-Einstein condensation

Abstract

The low-energy fluctuations of a trapped, interacting quasi one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically preventing Bose-Einstein condensation. At significantly lower temperatures a finite size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.