Confinement of bright matter-wave solitons on top of a pedestal-shaped potential

Abstract

Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons and breathers with the main emphasis on the possibility to trap them on top of a pedestal-shaped potential. In numerical simulations with particular parameter settings, we observed that moving solitons return from the borders of the potential and remain trapped for a sufficiently long time. The shuttle motion of the soliton is accompanied by shedding some amount of matter at each reflection from the borders of the trap, thus reducing its norm. The time-shift observed in a step-like decay of the moving soliton's norm in the two-soliton configuration is linked to the trajectory jump phenomenon. In the framework of the proposed model, several fundamental properties of solitons have been illustrated, such as a discontinuous jump of trajectories of colliding solitons, splitting of the breather, and the absence of matter exchange between interacting solitons. The obtained results can be of interest for the design of new soliton experiments with Bose-Einstein condensates.