Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials

摘要

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 σ_R. For speckle potentials the Fourier transform of the correlation function vanishes for momenta k > 2/σ_R so that the Lyapunov exponent vanishes in the Born approximation for k > 1/σ_R. Then, for the initial healing length of the condensate ξ_(in) > σ_R the localization is exponential, and for ξ_(in) < σ_R it changes to algebraic.