Superfluidity and sound propagation in disordered Bose gases

TL;DR

This paper investigates how speckle disorder affects sound propagation in a 2D Bose-Einstein condensate, revealing disorder-induced reductions in superfluid fraction and sound speed, with results applicable to cold-atom experiments.

Contribution

It provides a theoretical and numerical analysis of disorder effects on superfluid sound propagation, including a perturbation theory for weak disorder and validation of hydrodynamic models.

Findings

Disorder reduces superfluid fraction and sound speed.

Weak disorder effects are accurately described by quadratic perturbation theory.

Hydrodynamic approach remains valid over a broad parameter range.

Abstract

Superfluidity describes the ability of quantum matter to flow without friction. Due to its fundamental role in many transport phenomena, it is crucial to understand the robustness of superfluid properties to external perturbations. Here, we theoretically study the effects of speckle disorder on the propagation of sound waves in a two-dimensional Bose-Einstein condensate at zero temperature. We numerically solve the Gross-Pitaevskii equation in the presence of disorder and employ a superfluid hydrodynamic approach to elucidate the role of the compressibility and superfluid fraction on the propagation of sound. A key result is that disorder reduces the superfluid fraction and hence the speed of sound; it also introduces damping and mode coupling. In the limit of weak disorder, the predictions for the speed of sound and its damping rate are well reproduced by a quadratic perturbation theory. The hydrodynamic description is valid over a wide range of parameters, while discrepancies become evident if the disorder becomes too strong, the effect being more significant for disorder applied in only one spatial direction. Our predictions are well within the reach of state-of-the-art cold-atom experiments and carry over to more general disorder potentials.