The European Physical Journal B

, Volume 68, Issue 3, pp 353–364 | Cite as

Quantum diffusion of matter waves in 2D speckle potentials

  • C. Miniatura
  • R. C. Kuhn
  • D. Delande
  • C. A. MüllerEmail author


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.


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 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • C. Miniatura
    • 1
    • 4
    • 5
  • R. C. Kuhn
    • 2
    • 4
  • D. Delande
    • 3
  • C. A. Müller
    • 2
    Email author
  1. 1.Institut Non Linéaire de Nice, UMR 6618Université de Nice Sophia, CNRSValbonneFrance
  2. 2.Physikalisches Institut, Universität BayreuthBayreuthGermany
  3. 3.Laboratoire Kastler-Brossel, Université Pierre et Marie Curie-Paris 6, ENS, CNRS; 4 Place JussieuParisFrance
  4. 4.Centre for Quantum Technologies, National University of SingaporeSingaporeSingapore
  5. 5.IPAL, CNRSSingaporeSingapore

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