Full distribution of the superfluid fraction and extreme value statistics in a one-dimensional disordered Bose gas

The full statistical distribution of the superfluid fraction characterizing one-dimensional Bose gases in random potentials is discussed. Rare configurations with extreme fluctuations of the disorder potential can fragment the condensate and reduce the superfluid fraction to zero. The resulting bimodal probability distribution for the superfluid fraction is calculated numerically in the quasi-one-dimensional mean-field regime of ultracold atoms in laser speckle potentials. Using extreme value statistics, an analytical scaling of the zero-superfluid probability as a function of disorder strength, disorder correlation length, and system size is presented. It is argued that similar results can be expected for point-like impurities and that these findings are in reach for present-day experiments.