Solitary Wave Dynamics In Bose-Einstein Condensates Of Open System

In 1995,the Bose-Einstein condensates of rubidium atomic gas were successfully realized experimentally,the related research on its theory and experiment has always been a hot issue in modern physics.Bose-Einstein condensation is a macroscopic quantum phenomenon,all particles of the condensate are in the same quantum state,with the same phase,and their dynamic properties can be described by a macroscopic wave function.Bose-Einstein condensates have been widely used,such as cold atom clocks,cold atom interferometers,optical tweezers,and so on.At the same time,it is possible to develop a new generation of electronic circuits and quantum computers.At present,soliton,superfluid,vortex and other nonlinear phenomena in Bose-Einstein condensates of open systems are still hot issues.Exciton polaritons are bosons with half-light and half-matter properties,which are produced by strong coupling between photons in microcavity and excitons in quantum wells.Since the effective mass of the exciton polaritons is much smaller than that of the cold atoms,it is possible to realize Bose-Einstein condensates at room temperature.In 2006,Bose-Einstein condensation of exciton polaritons was successfully realized,and then nonlinear phenomena such as solitons,superfluids and vortices were observed.The research on exciton polariton superfluids has become one of the most important topics.The main research contents of this paper are as follows:In the third chapter,the effect of three-body interactions on the existence and stability of solitons of Bose-Einstein condensates in PT-symmetric potential is considered.The expressions of chemical potential,width and phase of the condensate are obtained analytically by variational method.It is found that the chemical potential,width and density distribution of condensates can be significantly affected by the three-body interactions.Through the dynamic evolution of solitons,we find that there is a critical intensity χc of three-body interactions,when the three-body interactions intensity lies in the parameter interval χc>χ0>0,a stable bright soliton will appear.Combined with Vakhitov-Kolokolov(VK)stability analysis,it is further proved that the soliton is stable.In the fourth chapter,the dynamics and stability of solitons in resonantly driven exciton polariton superfluid are studied.We get a set of ordinary differential equations to describe the dynamics of solitons in a exciton polariton superfluid,by employing a perturbed variational method,and obtain a unidirectional walking soliton in the exciton polariton superfluid.The analysis shows that the pump intensity F and the decay rate γ can significantly affect the existence and stability of solitons.Through the dynamic evolution of solitons,we can find that there is a critical value of the decay rate for a set of fixed initial conditions.When the decay rate is less than the critical value,the soliton can exist stably and occur a unidirectional motion,when the decay rate is greater than the critical value,the soliton cannot exist stably.Next,we analyze the stability of solitons through the P(V)stability criterion.When the decay rate is less than the critical value,the slopes of the P(V)curves are positive,the soliton can exist stably.And when the decay rate is greater than the critical value,the P(V)curves have branches with negative slopes,the soliton cannot exist stably.Finally,we analyze the influence of the pump intensity on the stability of solitons.When the pump intensity is less than the critical value,the soliton can exist stably and occur a unidirectional motion,when the pump intensity is greater than the critical value,the soliton cannot exist stably.