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Anderson localization of a weakly interacting one-dimensional Bose gas ; ; Schlagheck, Peter et al in Physical Review. A (2009), 80(3), 033615 We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow we ... [more ▼] We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow we identified [T. Paul, P. Schlagheck, P. Leboeuf, and N. Pavloff, Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale L* for the disordered region, above which most of the realizations of the random potential lead to time-dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed. [less ▲] Detailed reference viewed: 27 (4 ULg)Superfluidity versus Anderson localization in a dilute Bose gas ; Schlagheck, Peter ; et al in Physical Review Letters (2007), 98(21), We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of ... [more ▼] We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic and dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples. [less ▲] Detailed reference viewed: 16 (2 ULg)Nonlinear transport of Bose-Einstein condensates through waveguides with disorder ; ; et al in Physical Review. A (2005), 72(6), We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations ... [more ▼] We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allows for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small L) a stationary flow is observed. In this regime, the transmission decreases exponentially with increasing L. For strong interaction (or large L), the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission. [less ▲] Detailed reference viewed: 37 (0 ULg) |
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