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

TL;DR

This paper investigates how dark solitons in a Bose-Einstein condensate reflect from rapidly changing potentials, revealing different behaviors for potential drops and barriers and their dependence on system parameters.

Contribution

It introduces a detailed analysis of quantum reflection of dark solitons from varying potentials, highlighting the influence of potential type and width on reflection probabilities.

Findings

Reflection probability follows a cosine of twice the deflection angle.

Potential drop reflection rates oscillate with potential width and decay exponentially.

Barrier potential reflection is insensitive to width below the decay length, with exponential decay of differences.

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.