Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases

TL;DR

This paper derives exact expressions for the short-distance correlations in the Lieb-Liniger model and reveals a universal 1/p^4 tail in the momentum distribution, useful for identifying strong correlation regimes in 1D atomic gases.

Contribution

It provides the first exact short-distance expansion of the one-body correlation function and characterizes the universal high-momentum tail across interaction strengths.

Findings

Exact short-distance correlation expressions derived

Universal 1/p^4 tail in momentum distribution established

Method to experimentally observe strong correlation regimes proposed

Abstract

We derive exact closed form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics of the momentum distribution of both free and harmonically trapped atoms and show that it obeys a universal 1/p^4 law for_all_ values of the interaction strength. We discuss the ways to observe the predicted momentum distributions experimentally, regarding them as a sensitive identifier for the Tonks-Girardeau regime of strong correlations.