Two-body momentum correlations in a weakly interacting one-dimensional Bose gas

TL;DR

This paper investigates how two-body momentum correlations in a weakly interacting one-dimensional Bose gas change from strong positive correlations in a true condensate to reduced and anticorrelated behaviors in a phase-fluctuating quasicondensate, using analytical and numerical methods.

Contribution

It provides an analytic expression for momentum correlations in a quasicondensate and explores the crossover to the ideal Bose gas regime through numerical simulations.

Findings

Opposite-momentum correlations are reduced and broadened in a quasicondensate.

Anticorrelations emerge at small momenta in the quasicondensate regime.

Anticorrelations disappear in the ideal Bose-gas limit.

Abstract

We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit.