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arXiv:cond-mat/0407488 · Physical Review Letters

Nonlinear Resonant Transport of Bose-Einstein Condensates

Tobias Paul, Klaus Richter, Peter Schlagheck

Published Jan 19, 2005• 115 citations
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Abstract

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.

DOI
10.1103/physrevlett.94.020404

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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.
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.
We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length LLL. 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 LLL) a stationary flow is observed. In this regime, the transmission decreases exponentially with increasing LLL. For strong interaction (or large LLL), the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission.
We numerically study time-dependent quantum transport of an interacting Bose-Einstein condensate based on the Gross-Pitaevskii equation in a two-dimensional correlated disorder potential. The scattering- and transport mean-free-path is numerically calculated and compared with a diagrammatic approach. Furthermore we introduce the phenomenon of coherent backscattering in the context of Bose-Einstein condensates. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. This agrees with results obtained from a diagrammatic theory of weak localization in the presence of nonlinearity. For intermediate interaction strength we observe intrinsic time-dependent dynamic, which leads to a suppression of coherent backscattering.
The stable nonlinear transport of the Bose–Einstein condensates through a double barrier potential in a waveguide is studied. By using the direct perturbation method we have obtained a perturbed solution of Gross–Pitaevskii equation. Theoretical analysis reveals that this perturbed solution is a stable periodic solution, which shows that the transport of Bose–Einstein condensed atoms in this system is a stable nonlinear transport. The corresponding numerical results are in good agreement with the theoretical analytical results.
We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source that models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock--Bogoliubov approximation. We apply this method to study the transport of dilute Bose gases through an atomic quantum dot and through waveguides with disorder. Our numerical simulations reveal that the onset of an explicitly time-dependent flow corresponds to the appearance of strong depletion of the condensate on the microscopic level and leads to a loss of global phase coherence.