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

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.