Eur. Phys. J. B 68, 353-364 (2009)
https://doi.org/10.1140/epjb/e2008-00463-7

Quantum diffusion of matter waves in 2D speckle potentials

¹ Institut Non Linéaire de Nice, UMR 6618, Université de Nice Sophia, CNRS; 1361 route des Lucioles, 06560 Valbonne, France
² Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
³ IPAL, CNRS, I2R; 1 Fusionopolis Way, 138632 Singapore, Singapore
⁴ Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
⁵ Laboratoire Kastler-Brossel, Université Pierre et Marie Curie-Paris 6, ENS, CNRS; 4 Place Jussieu, 75005 Paris, France

Corresponding author: ^a cord.mueller@uni-bayreuth.de

Received: 23 July 2008
Revised: 28 October 2008
Published online: 24 December 2008

Abstract

This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment.