Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

We study the behavior of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andregrave model for particles in a quasiperiodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wave packet as well as the interplay between two competing effects of the interaction, namely, self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters even for weak interaction. Conversely, if the diffusion starts from a Gaussian wave packet, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.