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Communications in Theoretical Physics

Analytic Study of a Bose–Einstein Condensate in Waveguide with an Obstacle Potential

Jianwen Song, Hai Wen-Hua, Zhong Hong-Hua, Xiaobing Luo

Published Jul 1, 2008• 6 citations
Publisher

Abstract

We investigate the exact solutions of one-dimensional (1D) time-independent Gross–Pitaevskii equation (GPE), which governs a Bose–Einstein condensate (BEC) in the magnetic waveguide with a square-Sech potential. Both the bound state and transmission state are found and the corresponding spatial configurations and transport properties of BEC are analyzed. It is shown that the well-known absolute transmission of the linear system can occur in the considered nonlinear system.

DOI
10.1088/0253-6102/50/1/19

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We investigate the exact solutions of one-dimensional (1D) time-independent Gross–Pitaevskii equation (GPE), which governs a Bose–Einstein condensate (BEC) in the magnetic waveguide with a square-Sech potential. Both the bound state and transmission state are found and the corresponding spatial configurations and transport properties of BEC are analyzed. It is shown that the well-known absolute transmission of the linear system can occur in the considered nonlinear system.
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 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.
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