Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials

TL;DR

This paper demonstrates that expanding 1D Bose-Einstein condensates can exhibit Anderson localization in weak random potentials, with the nature of localization depending on the initial healing length relative to the potential's correlation length.

Contribution

It reveals how the interplay between initial condensate properties and the correlation length of the disorder affects localization behavior in 1D Bose-Einstein condensates.

Findings

Localization is exponential when healing length exceeds correlation length.

Localization becomes algebraic when healing length is less than correlation length.

The Fourier transform of speckle potential correlations vanishes for high momenta.

Abstract

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length \sigma_R. For speckle potentials the Fourier transform of the correlation function vanishes for momenta k > 2/\sigma_R so that the Lyapunov exponent vanishes in the Born approximation for k > 1/\sigma_R. Then, for the initial healing length of the condensate \xi > \sigma_R the localization is exponential, and for \xi < \sigma_R it changes to algebraic.