One-body correlations and momentum distributions of trapped one-dimensional Bose gases at finite temperature

TL;DR

This paper presents a versatile analytical and numerical approach for calculating one-body correlations and momentum distributions in trapped one-dimensional Bose gases at finite temperature and interaction strengths, bridging theoretical and experimental insights.

Contribution

It introduces a combined asymptotic and short-distance expansion method for accurate correlation calculations across interaction regimes in 1D Bose gases.

Findings

Method accurately predicts correlations at various interaction strengths.

Results agree with exact numerical calculations.

Predictions match recent experimental data.

Abstract

We introduce a general approximate method for calculating the one-body correlations and the momentum distributions of one-dimensional Bose gases at finite interaction strengths and temperatures trapped in smooth confining potentials. Our method combines asymptotic techniques for the long-distance behavior of the gas (similar to Luttinger liquid theory) with known short-distance expansions. We derive analytical results for the limiting cases of strong and weak interactions, and provide a general procedure for calculating one-body correlations at any interaction strength. A step-by-step explanation of the numerical method used to compute Green's functions (needed as input to our theory) is included. We benchmark our method against exact numerical calculations and compare its predictions to recent experimental results.