Dynamics Of Spatially Localized Spin-orbit Coupled Bose-einstein Condensation

In 1995,the experimental team from JILA successfully realized the Bose-Einstein condensate by using the thin atomic gas⁸⁷Rb for the first time.Since then,with the rapid development of experimental technology,ultracold atomic gas Bose Einstein condensa-tion has become an important experimental platform for quantum simulation and quan-tum control in recent years because of its highly adjustable parameters and high manip-ulation.Among them,the simulation of the spin-orbit coupling effect in ultracold atoms solves the shortcoming of the difficulty in controlling the spin-orbit coupling in solid materials,and provides the possibility of detecting more novel physical phenomena.In this paper,the ground state properties and quench dynamic properties of the lo-cal spin-orbit coupled Bose-Einstein condensation system induced by spatially localized Raman coupling are discussed.First,this article briefly introduces the thermodynamic properties of Bose-Einstein condensation,and the experimental method to realize the dilute atom gas Bose-Einstein condensation,etc.Second,this article introduces the basic properties of spin-orbit coupling,as well as the theoretical and experimental methods for achieving the spin-orbit coupling ef-fect in Bose-Einstein condensation.Therefore,the physical properties of the disper-sion spectrum of the single-particle spin-orbit coupled Bose-Einstein condensate and the ground state properties of the system under the action of mean-field many-body inter-action are further introduced,and related simulations are carried out through numerical calculations.Furthermore,the ground state properties of the localized spin-orbit cou-pled Bose-Einstein condensate system are studied.The ground state phase is the same as that in the spatially uniform spin-orbit coupled system.There are three ground state:fringe phase,plane wave phase,and zero momentum phase.But what is interesting is that all the particles will spontaneously localize in the region with spin-orbit coupling effect without any external potential well.We explained the cause of this phenomenon and proposed that local Raman coupling can be used as an experimental technique for manipulating atoms.Third,we introduce the origin of Zitterbewegung in the Dirac equation and the simulation method of Zitterbewegung in the ultracold atom system.And by quenching,the Zitterbewegung phenomenon was induced in the spatially localized spin-orbit coupled Bose-Einstein condensate system,and related research was carried out.