Bose-Einstein-condensed systems in random potentials

TL;DR

This paper investigates how Bose-Einstein condensates behave in random potentials, revealing a first-order phase transition and the destabilizing effect of disorder on ideal condensates, while interacting systems can remain stable.

Contribution

It develops a self-consistent stochastic mean-field theory for Bose-Einstein condensates in disordered potentials, including finite temperature and interaction effects.

Findings

Pure Bose glass phase does not occur.

Disorder induces a first-order phase transition with simultaneous loss of condensate and superfluid fractions.

Weak disorder destroys ideal condensates, but interacting systems can be stable under finite disorder.

Abstract

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state. But the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.