Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials

Laurent Sanchez-Palencia (1) , David Clément (1) , Pierre Lugan (1) , Philippe Bouyer (1) , Georgy V. Shlyapnikov (2, 3) , Alain Aspect (1)

1 laboratoire Charles Fabry de l'Institut d'Optique / Optique atomique
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 Van der Waals-Zeeman Institute

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length \sigma_R. For speckle potentials the Fourier transform of the correlation function vanishes for momenta k > 2/\sigma_R so that the Lyapunov exponent vanishes in the Born approximation for k > 1/\sigma_R. Then, for the initial healing length of the condensate \xi > \sigma_R the localization is exponential, and for \xi < \sigma_R it changes to algebraic.

Mots clés: Bose-Einstein condensate; ultracold; cold; matterwave; Anderson; localization; disorder; random; mobility edge

Domaines: Autre [cond-mat.other]

Laurent Sanchez-Palencia, David Clément, Pierre Lugan, Philippe Bouyer, Georgy V. Shlyapnikov, et al.. Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials. Physical Review Letters, 2007, 98, pp.210401. ⟨10.1103/PhysRevLett.98.210401⟩. ⟨hal-00122278v4⟩