[Show abstract][Hide abstract] ABSTRACT: We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed with Bose-Einstein condensates of 85Rb, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. In addition to the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally.
[Show abstract][Hide abstract] ABSTRACT: We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose- Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
[Show abstract][Hide abstract] ABSTRACT: An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice, the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive one-dimensional, mean-field numerical model. We fully model the output beam and experimentally important physics such as three-body recombination. We find that at highpump rates, the latter plays a role in suppressing the high-frequency dynamics, which would otherwise limit the stability of the output beam.