Analytical study of resonant transport of Bose-Einstein condensates

K. Rapedius, D. Witthaut, and H. J. Korsch
Phys. Rev. A 73, 033608 – Published 13 March 2006

Abstract

We study the stationary nonlinear Schrödinger 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.

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  • Received 19 December 2005

DOI:https://doi.org/10.1103/PhysRevA.73.033608

©2006 American Physical Society

Authors & Affiliations

K. Rapedius, D. Witthaut, and H. J. Korsch*

  • Technische Universität Kaiserslautern, FB Physik, D-67653 Kaiserslautern, Germany

  • *Electronic address: korsch@physik.uni-kl.de

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Issue

Vol. 73, Iss. 3 — March 2006

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