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

TL;DR

This paper investigates the full quantum distribution of interference fringe amplitudes in one-dimensional Bose liquids, revealing insights into non-local correlations and linking cold atom experiments to complex statistical models.

Contribution

It provides an explicit calculation of the distribution function using conformal field theory and uncovers connections to quantum impurity models and nonunitary conformal field theories.

Findings

Distribution functions encode non-local correlations.

Explicit calculations using conformal field theory.

Connections to statistical models and quantum gravity.

Abstract

We analyze interference experiments for a pair of independent one dimensional condensates of interacting bosonic atoms at zero temperature. We show that the distribution function of fringe amplitudes contains non-trivial information about non-local correlations within individual condensates and can be calculated explicitly using methods of conformal field theory. We point out interesting relations between these distribution functions, the partition function for a quantum impurity in a one-dimensional Luttinger liquid, and transfer matrices of conformal field theories. We demonstrate the connection between interference experiments in cold atoms and a variety of statistical models ranging from stochastic growth models to two dimensional quantum gravity. Such connection can be used to design a quantum simulator of unusual two-dimensional models described by nonunitary conformal field theories with negative central charges.