二维激子极化激元凝聚中涡旋叠加态稳态及动力学特性研究
Stability and dynamics study of vortex superposed states in two-dimensional exciton-polariton condensates

利用分步Crank-Nicolson方案的虚时和实时有限差分方法求解耗散系统的Gross-Pitaevskii(GP)方程, 研究了二维激子极化激元凝聚(exciton-polariton condensates)体系中正反涡旋叠加态的稳态结构并直观地验证这种稳态结构在半导体微腔旋转下的稳定性和动力学特性. 通过虚时和实时演化相结合的方法求解出几种角动量情况下所对应的稳定涡旋叠加态. 然后利用实时演化方法研究在半导体微腔旋转的情况下, 正反涡旋叠加态的稳定性及其旋转角速率和半导体微腔旋转角速率之间的定量关系. 最后研究了单涡旋态在半导体微腔旋转时形成涡旋阵列的动力学过程, 并给出了泵浦光宽度和增益项对涡旋阵列结构的影响. 研究表明, 系统的泵浦, 损耗和增益对稳定性和动力学特性有重要影响.
The Gross-Pitaevskii (GP ) equation of the dissipative system is solved by using the algorithm involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. The steady-state structure of the vortex and antivortex superposed state in a two-dimensional exciton-polariton condensates is studied , and the stability and dynamic characteristics of the steady state structure under the semiconductor micro-cavity rotation are intuitively verified . The stable vortex superposition states corresponding to several angular momentum conditions are solved by combining real- and imaginary-time propagation. Then the quantitative relationship of the rotational angular velocity between vortex and antivortex superposed state and the semiconductor microcavity is studied by using the real-time propagation method, and the rotational stability of the inverse vortex superposition state is investigated. Finally , the dynamic process of the vortex array formed by the rotation of a single vortex in a semiconductor micro cavity is studied , and the influence of the width of pumping light and gain on the structure of the vortex array is given . The results show that the pump , loss and gain of the system have important influence on the stability and dynamic characteristics .