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., $R(θ) \sim \cos 2θ$. For a potential drop, $R(θ)$ 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 $θ=0$ and $θ=π/2$, $δR_s$, displays oscillating exponential decay with increasing potential widths. However, for a barrier potential, $R(θ)$ is insensitive for the potential width less than the decay length of the matter wave and $δR_s$ 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.