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

TL;DR

This paper investigates the full statistical distribution of the superfluid fraction in a one-dimensional disordered Bose gas, revealing how extreme disorder configurations can cause condensate fragmentation and zero superfluidity, with both numerical and analytical insights.

Contribution

It provides the first detailed numerical and analytical analysis of the superfluid fraction distribution, including extreme-value statistics, in disordered 1D Bose gases.

Findings

Bimodal distribution of superfluid fraction due to disorder

Analytical scaling law for zero-superfluid probability

Relevance for current ultracold atom experiments

Abstract

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-1D mean-field regime of ultracold atoms in laser speckle potentials. Using extreme-value statistics, an analytical scaling of the zero-superfluid probability as 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.