Physical replicas and the Bose glass in cold atomic gases

We study cold atomic gases in a disorder potential and analyse the correlations between different systems subjected to the same disorder landscape. Such independent copies with the same disorder landscape are known as replicas. While, in general, these are not accessible experimentally in condensed matter systems, they can be realized using standard tools for controlling cold atomic gases in an optical lattice. Of special interest is the overlap function which represents a natural order parameter for disordered systems and is a correlation function between the atoms of two independent replicas with the same disorder. We demonstrate an efficient measurement scheme for the determination of this disorder-induced correlation function. As an application, we focus on the disordered Bose -Hubbard model and determine the overlap function within the perturbation theory and a numerical analysis. We find that the measurement of the overlap function allows for the identification of the Bose-glass phase in certain parameter regimes.