Quantum transport of atomic matter waves in anisotropic two-dimensional and three-dimensional disorder

Year: 2013

Authors: Piraud M., Pezzè L., Sanchez-Palencia L.

Autors Affiliation: Laboratoire Charles Fabry, Institut d’Optique, CNRS, Universite Paris Sud, 2 Avenue Augustin Fresnel, F-91127 Palaiseau Cedex, France; QSTAR, INO-CNR and LENS, Largo Enrico Fermi 6, I-50125 Firenze, Italy

Abstract: The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich in counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.


Volume: 15      Pages from: 075007  to: 075007

More Information: We thank B van Tiggelen and P Wolfle for enlightening discussions. This research was supported by the European Research Council (FP7/2007-2013 grant agreement no. 256294), the CoopIntEER CNRS-CNR joint project \’AtoFerTwoD\’ (no. EDC25123), the Ministere de l\’Enseignement Superieur et de la Recherche, and the Institut Francilien de Recherche sur les Atomes Froids (IFRAF). We acknowledge the use of the computing facility cluster GMPCS of the LUMAT federation (FR LUMAT 2764).
KeyWords: disorder physics; Anderson localisation; quantum gases; multiple light-scattering; Bose-Einstein condensate
DOI: 10.1088/1367-2630/15/7/075007

Citations: 29
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