Anderson localization of a Bose-Einstein condensate in a 3D random potential

TL;DR

This paper investigates how Anderson localization affects the expansion of a Bose-Einstein condensate in a three-dimensional random potential, revealing that the long-term behavior depends on a key ratio involving the mobility edge and chemical potential.

Contribution

It introduces a theoretical framework linking the condensate's expansion dynamics to the localization transition parameters using scaling and self-consistent theories.

Findings

The long-time condensate density is governed by a single ratio parameter.

Critical exponents of the localization transition influence the condensate evolution.

The study provides a theoretical understanding of localization effects in BEC dynamics.

Abstract

We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.