Collective dynamics and expansion of a Bose-Einstein condensate in a random potential

TL;DR

This paper studies how a Bose-Einstein condensate behaves in a random optical potential, examining collective oscillations and expansion, and providing insights relevant to recent experimental observations.

Contribution

It offers a combined theoretical and numerical analysis of disorder effects on BEC dynamics, including collective modes and expansion, with implications for localization phenomena.

Findings

Weak disorder causes uncorrelated frequency shifts in collective modes.

Numerical solutions confirm sum rules predictions for mode shifts.

Disorder influences expansion and potential localization in optical guides.

Abstract

We investigate the dynamics of a Bose-Einstein condensate in the presence of a random potential created by optical speckles. We first consider the effect of a weak disorder on the dipole and quadrupole collective oscillations, finding uncorrelated frequency shifts of the two modes with respect to the pure harmonic case. This behaviour, predicted by a sum rules approach, is confirmed by the numerical solution of the Gross-Pitaevskii equation. Then we analyze the role of disorder on the one-dimensional expansion in an optical guide, discussing possible localization effects. Our theoretical analysis provides a useful insight into the recent experiments performed at LENS [J. Lye et al., Phys. Rev. Lett. 95, 070401 (2005); C. Fort et al., cond-mat/0507144].