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arXiv:0707.1830 · Physical Review A

Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

Tobias Paul, Michael Hartung, Klaus Richter, Peter Schlagheck

Published Dec 5, 2007• 59 citations
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Abstract

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.

DOI
10.1103/physreva.76.063605

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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.
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The recent experimental advances in manipulating ultra-cold atoms make it feasible to study coherent transport of Bose-Einstein condensates (BEC) through various mesoscopic structures. In this work the quasi-stationary propagation of BEC matter waves through two dimensional cavities is investigated using numerical simulations within the mean-field approach of the Gross-Pitaevskii equation. The focus is on the interplay between interference effects and the interaction term in the non-linear wave equation. One sees that the transport properties show a complicated behaviour with multi-stability, hysteresis and dynamical instabilities for non-vanishing interaction. Furthermore, the prominent weak localization effect, which is a robust interference effect emerging after taking a configuration average, is reduced and partially inverted for non-vanishing interaction.
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one-dimensional finite square-well potential. By neglecting the mean-field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound states are obtained analytically. The transmitted flux shows a bistable behavior. Novel crossing scenarios of eigenstates similar to beak-to-beak structures are observed for a repulsive mean-field interaction. It is proven that resonances transform to bound states due to an attractive nonlinearity and vice versa for a repulsive nonlinearity, and the critical nonlinearity for the transformation is calculated analytically. The bound-state wave functions of the system satisfy an oscillation theorem as in the case of linear quantum mechanics. Furthermore, the implications of the eigenstates on the dymamics of the system are discussed.