Quantum reflection of a Bose-Einstein condensate from a rapidly varying potential: the role of dark soliton

Abstract

We study the dynamic behavior of a Bose-Einstein condensate (BEC) containing a dark soliton separately reflected from potential drops and potential barriers. It is shown that for a rapidly varying potential and in a certain regime of incident velocity, the quantum reflection probability displays the cosine of the deflection angle between the incident soliton and the reflected soliton, i.e., $R(\theta )\sim \cos 2\theta$. For a potential drop, $R(\theta )$ is susceptible to the widths of potential drop up to the length of the dark soliton and the difference of the reflection rates between the orientation angle of the soliton $\theta =0$ and $\theta =\pi /2$, $\delta R_s$, displays oscillating exponential decay with increasing potential widths. However, for a barrier potential, $R(\theta )$ is insensitive for the potential width less than the decay length of the matter wave and $\delta R_s$ presents an exponential trend. This discrepancy of the reflectances in two systems is arisen from the different behaviors of matter waves in the region of potential variation.

7 pages of RevTex4-1, 5 figures

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