Full counting statistics of the interference contrast from independent Bose-Einstein condensates

TL;DR

This paper establishes a direct link between interference contrast in Bose-Einstein condensates and the condensate fraction, providing analytical full counting statistics that reveal universal behaviors and phase transition signatures.

Contribution

It introduces a method to obtain the full counting statistics of condensed atom numbers from interference contrast measurements in Bose gases, including analytical results for 2D systems.

Findings

Contrast distribution is non-Gaussian and unimodal.

Variance of contrast relates to superfluid density.

Visibility distribution reflects universal order parameter near criticality.

Abstract

We show that the visibility in interference experiments with Bose-Einstein condensates is directly related to the condensate fraction. The probability distribution of the contrast over many runs of an interference experiment thus gives the full counting statistics of the condensed atom number. For two-dimensional Bose gases, we discuss the universal behavior of the probability distribution in the superfluid regime and provide analytical expressions for the distributions for both homogeneous and harmonically trapped samples. They are non-Gaussian and unimodal with a variance that is directly related to the superfluid density. In general, the visibility is a self-averaging observable only in the presence of long range phase coherence. Close to the transition temperature, the visibility distribution reflects the universal order parameter distribution in the vicinity of the critical point.