【作者】 李明；

【导师】 漆伟；

【作者基本信息】 陕西科技大学 ， 物理学， 2022， 硕士

【摘要】 1995年人们在实验上成功实现了铷原子气体的玻色-爱因斯坦凝聚,关于其理论和实验的相关研究一直是现代物理学中的热点问题。玻色-爱因斯坦凝聚是一种宏观的量子现象,凝聚体中所有的粒子都处于同一量子态,具有相同的相位,可以用一个宏观波函数描述其动力学性质。玻色-爱因斯坦凝聚已经得到了广泛的应用,例如冷原子钟、冷原子干涉仪、光学镊子等,同时为开发新一代电子电路和量子计算机提供了可能。目前开放系统玻色-爱因斯坦凝聚中的孤子、超流、涡旋等非线性现象依然是研究的热点问题。激子极化激元是微腔中的光子和量子阱中的激子发生强耦合产生的具有半光半物质性质的玻色子。由于激子极化激元的有效质量远远小于冷原子,使得其有希望在室温实现玻色-爱因斯坦凝聚。2006年人们成功实现了激子极化激元的玻色-爱因斯坦凝聚,并随后在其中观测到了孤子、超流、涡旋等非线性现象。对于激子极化激元超流体的相关研究已经成为目前重要的课题之一。本论文主要研究内容如下:第三章,研究了三体相互作用对PT对称势中玻色-爱因斯坦凝聚体中孤子的存在性和稳定性的影响。采用变分法解析得到了凝聚体的化学势、宽度和相位的表达式。发现三体相互作用可以显著的影响凝聚体的化学势、宽度和密度分布。通过孤子的动力学演化,我们发现存在一个临界三体相互作用强度χc,当三体相互作用的强度位于参数区间χc>χ0>0时,将会出现一个稳定的亮孤子。结合Vakhitov-Kolokolov(VK)稳定性分析,进一步佐证了该孤子是稳定存在的。第四章,研究了共振驱动激子极化激元超流体中孤子的动力学和稳定性。采用微扰变分法推导出描述激子极化激元超流体中孤子动力学行为的常微分方程组,并在激子极化激元超流体中得到一个单向行走孤子。分析显示泵浦强度F和衰减率γ可以显著影响孤子的存在性和稳定性。通过孤子的动力学演化,我们可以得到对于一组固定的初始条件存在一个衰减率的临界值,当衰减率的值小于临界值时孤子可以稳定存在并单向运动,当衰减率大于临界值时孤子不能稳定存在。接下来我们通过P(V)稳定性判据分析孤子的稳定性,当衰减率小于临界值时P(V)曲线的斜率是正的,孤子能够稳定存在,而当衰减率大于临界值时P(V)曲线出现负斜率的分支,孤子不能稳定存在。最后我们分析了泵浦强度对于孤子稳定性的影响,当泵浦强度小于临界值时,孤子可以稳定存在并单向运动,当泵浦强度大于临界值时孤子不能稳定存在。更多还原

【Abstract】 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.更多还原