Matter-wave localization in a random potential

TL;DR

This paper investigates the localization behavior of Bose-Einstein condensates in disordered potentials using numerical and variational methods, revealing exponential tails and oscillatory dynamics characteristic of Anderson localization.

Contribution

It provides a combined numerical and variational analysis of BEC localization in disordered potentials, including the effects of weak interactions and dynamic expansion behavior.

Findings

Localized BECs exhibit exponential tails similar to Anderson localization.

The BEC becomes trapped in localized states after initial expansion.

Localized BECs show breathing oscillations around a mean shape.

Abstract

By numerical and variational solution of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the case of a single BEC fragment, the variational analysis produced good results. For a weakly disordered potential, the localized BECs are found to have an exponential tail as in weak Anderson localization. We also investigated the expansion of a noninteracting BEC in these potential. We find that the BEC will be locked in an appropriate localized state after an initial expansion and will execute breathing oscillation around a mean shape when a BEC at equilibrium in a harmonic trap is suddenly released into a disorder potential.