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See detailAnderson localization of a weakly interacting one-dimensional Bose gas
Paul, T.; Albert, M.; Schlagheck, Peter ULg 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 ▲]

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See detailSuperfluidity versus Anderson localization in a dilute Bose gas
Paul, T.; Schlagheck, Peter ULg; Leboeuf, P. 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 ▲]

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See detailNonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
Paul, T.; Hartung, M.; Richter, K. et al

in Physical Review. A (2007), 76(6),

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to ... [more ▼]

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasibound states of the quantum dot. [less ▲]

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See detailComplex-scaling approach to the decay of Bose-Einstein condensates
Schlagheck, Peter ULg; Paul, T.

in Physical Review. A (2006), 73(2),

The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show ... [more ▼]

The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement. [less ▲]

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See detailNonlinear transport of Bose-Einstein condensates through waveguides with disorder
Paul, T.; Leboeuf, P.; Pavloff, N. 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 ▲]

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See detailNonlinear resonant transport of Bose-Einstein condensates
Paul, T.; Richter, K.; Schlagheck, Peter ULg

in Physical Review Letters (2005), 94(2),

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a ... [more ▼]

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales. [less ▲]

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