Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

We study the dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability, $R_s$. The variation of the reflection probability with respect to the orientation angle, $\theta$, of the dark soliton can be well described by a cosine function $R_s\sim\cos[\lambda(\theta-\pi/2)]$, where $\lambda$ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.