- Coherent Transport of Matter Waves in Disordered Optical Potentials (2007)
- The development of modern techniques for the cooling and the manipulation of atoms in recent years, and the possibility to create Bose-Einstein condensates and degenerate Fermi gases and to load them into regular optical lattices or disordered optical potentials, has evoked new interest for the disorder-induced localization of ultra-cold atoms. This work studies the transport properties of matter waves in disordered optical potentials, which are also known as speckle potentials. The effect of correlated disorder on localization is first studied numerically in the framework of the Anderson model. The relevant transport parameters in the configuration average over many different realizations of the speckle potential are then determined analytically, using self-consistent diagrammatic perturbation techniques. This allows to make predictions for a possible experimental observation of coherent transport phenomena for cold atoms in speckle potentials. Of particular importance are the spatial correlations of the speckle fluctuations, which are responsible for the anisotropic character of the single scattering processes in the effective medium. Coherent multiple scattering leads to quantum interference effects, which entail a renormalization of the diffusion constant as compared to the classical description. This so-called weak localization of matter waves is studied as the underlying mechanism for the disorder-driven transition to the Anderson-localization regime, explicitly taking into account the correlations of the speckle fluctuations.