Spatial nonlocal pair correlations in a repulsive 1D Bose gas

TL;DR

This paper analytically derives the spatial nonlocal pair correlation function for a 1D Bose gas at finite temperature, revealing how various length scales and interactions influence correlations, with implications for experimental measurement.

Contribution

It provides a comprehensive analytical framework for understanding nonlocal correlations in a 1D Bose gas across different interaction regimes.

Findings

Correlation lengths are determined by four key scales.

Interactions can cause pair correlations to peak at finite separation.

The results apply across weakly and strongly interacting regimes.

Abstract

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.