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
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.
PACS: 03.75.Kk – Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow / 42.25.Dd – Wave propagation in random media / 72.15.Rn – Localization effects
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008