Smoothing effect and delocalization of interacting Bose-Einstein condensates in random potentials

TL;DR

This paper develops a theoretical framework to understand how weak, possibly random potentials affect the shape and localization of Bose-Einstein condensates, revealing conditions for delocalization and smoothing effects.

Contribution

It introduces a perturbation approach applicable to arbitrary potential variations, elucidating the interplay between healing length and disorder correlation length on condensate localization.

Findings

Delocalized Thomas-Fermi profile when healing length is smaller than disorder correlation length.

Potential smoothing occurs when correlation length is smaller than healing length.

Condensate can remain delocalized despite small disorder correlation lengths.

Abstract

We theoretically investigate the physics of interacting Bose-Einstein condensates at equilibrium in a weak (possibly random) potential. We develop a perturbation approach to derive the condensate wavefunction for an amplitude of the potential smaller than the chemical potential of the condensate and for an arbitrary spatial variation scale of the potential. Applying this theory to disordered potentials, we find in particular that, if the healing length is smaller than the correlation length of the disorder, the condensate assumes a delocalized Thomas-Fermi profile. In the opposite situation where the correlation length is smaller than the healing length, we show that the random potential can be significantly smoothed and, in the meanfield regime, the condensate wavefunction can remain delocalized, even for very small correlation lengths of the disorder.