Finite temperature correlations and density profiles of an inhomogeneous interacting 1D Bose gas

TL;DR

This paper provides exact finite-temperature density profiles and correlations for an inhomogeneous 1D Bose gas in a trap, enabling experimental tests of different interaction regimes from weak to strong coupling.

Contribution

It introduces a method combining exact uniform solutions with local density approximation to analyze inhomogeneous 1D Bose gases at finite temperature.

Findings

Density profiles match experimental conditions for slowly varying traps.

The local pair correlation at the trap center approximates bulk properties.

Results enable testing the transition from Gross-Pitaevskii to Tonks-Girardeau regimes.

Abstract

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential which is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak coupling Gross-Pitaevskii regime to the strong coupling, 'fermionic' Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.