Quenched Solitons And Shock Waves In Bose-einstein Condensates

The Bose-Einstein condensate(BEC)formed by ultracold atomic gases provides an ideal platform for studying various quantum phenomena.In this platform,researchers have deeply explored important equilibrium and steady phenomena including superfluidity,vortices,and solitons,and recently started to explore nonequilibrium problems.In classical systems,nonequilibrium problems,for example explosion,usually occur together with shock waves,which is presented when the explosion speed is larger than the local sound speed.While for BEC systems which posess quantum properties,how to produce and understand the shock waves becomes a hot research topic.In this thesis,we systematically discussed the possibility of quantum shock wave and its essential mechanism in a one-dimensional BEC initially containing dark solitons through quenching interactions.Our main results include:(1)When the system is quenched to the limit of non-interaction,we analytically obtained the post-quench dynamics of initially immobile dark solitons,and discovered the existence of shock wave,which is explained through the quantum interference effect.(2)When the system is quenched to finite interaction,we found similar phenomena through numerically solving the Gross-Pitaevskii equation,and analyzed different situations: a.When the system is quenched to a finite weaker interaction,the situation is similar to that in the non-interaction case;b.When the system is quenched to a stronger interaction,the shock waves is accompanied by the splitting of the initial soliton,and the two objects can synchronous change;c.Specifically when the quenched ratio of strength is a integer square,the shock wave is disappeared,and the soliton is split perfectly.We further explored the properties of the shock wave including its amplitude and speed,and obtained the full scenarios as the quenched interaction varies.This work provides theoretical guidance for the realization and measurement in experiments.