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 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.PACS numbers: 03.75. Dg, 03.75.Kk, 42.65.Pc The rapid progress in the fabrication and manipulation of ultracold Bose-Einstein condensates has lead to a number of fascinating experiments probing complex condensed matter phenomena in perfectly controllable environments, such as the creation of vortex lattices [1] and the quantum phase transition from a superfluid to a Mott insulator state in optical lattices [2]. With the development of "atom chips" [3][4][5], new perspectives are opened also towards mesoscopic physics. The possibility to generate atomic waveguides of arbitrary complexity above microfabricated surfaces does not only permit highly accurate matter-wave interference experiments [6], but would also allow to study the interplay between interaction and transport with an unprecedented degree of control of the involved parameters. The connection to electronic mesoscopic physics was appreciated by Thywissen et al. [7] who proposed a generalization of Landauer's theory of conductance [8] to the transport of noninteracting atoms through point contacts. Related theoretical studies were focused on the adiabatic propagation of a Bose-Einstein condensate in presence of obstacles [9][10][11][12], the dynamics of soliton-like structures in waveguides (e.g. [13]), and the influence of optical lattices on transport (e.g. [14]), to mention just a few examples.Particularly interesting in this context is the propagation of a Bose-Einstein condensate through a double barrier potential, which can be seen as a Fabry-Perot interferometer for matter waves. In the context of atom chips, such a bosonic quantum dot could be realized by suitable geometries of microfabricated wires. An alternative implementation based on optical lattices was suggested by Carusotto and La Rocca [15,16] who pointed out that the interaction-induced nonlinearity in the meanfield dynamics would lead to a bistability behaviour of the transmitted flux in the vicinity of resonances. This phenomenon is well known from nonlinear optics [17] and arises also in electronic transport through quantum wells (e.g. [18][19][20]) due to the Coulomb interaction in the well.In this Letter, we investigate to which extent resonant transport through such a double barrier potential can be achieved for an interacting condensate in a realistic propagation p...

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 L͒ a stationary flow is observed. In this regime, the transmission decreases exponentially with increasing L. For strong interaction ͑or large L͒, the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission.

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.