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 ${\xi }_{\mathrm{in}}>{\sigma }_R$ the localization is exponential, and for ${\xi }_{\mathrm{in}}<{\sigma }_R$ it changes to algebraic.

• Received 28 December 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.210401