Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids

The existence of quantum noise is the most direct evidence for the probabilistic nature of quantum mechanics. In strongly interacting systems we expect quantum noise to reveal non-local correlations of the underlying many-body states. Here, we show that quantum noise in interference experiments with cold atoms can be used to investigate the unusual character of one-dimensional interacting systems. We analyse interference experiments for a pair of independent bosonic one-dimensional condensates and explicitly calculate the distribution function of fringe amplitudes using methods of conformal field theory. Moreover, we point out interesting relations between interference experiments with cold atoms, the problem of a quantum impurity in a one-dimensional Luttinger liquid and a variety of statistical models ranging from stochastic growth models to two-dimensional quantum gravity. Such connections can be exploited to design a quantum simulator of unusual two-dimensional models described by non-unitary conformal field theories with negative central charges.