1.Department of Aerospace Science and Technology, University of Space Engineering, Beijing 101400, China 2.State Key Laboratory for Laser Propulsion and Its Applications, University of Space Engineering, Beijing 101400, China 3.Beijing Institute of Aerospace Control Instruments, Beijing 100094, China
Fund Project:Project supported by the Program for National Defense Science and Technology Innovation Special Zone of China, the National Natural Science Foundation of China (Grant Nos. 11772001, 61805283), and the Youth Top-Notch Talent Support Program of Beijing, China (Grant No. 2017000026833ZK23)
Received Date:11 May 2020
Accepted Date:14 July 2020
Available Online:02 December 2020
Published Online:05 December 2020
Abstract:The gyroscope established on quantization vortices formed from exciton-polariton Bose-Einstein condensate has important potential applications in the field of quantum guidance. Thus, we assume a concept of quantum gyroscope based on Sagnac effect of the superposition states of quantum vortices existing in exciton-polariton condensates. To study the gyroscopic effect of superimposed vortices, which is the core issue of the project, it is essential to study the dynamic characteristics in the case of system rotating. Therefore, in this paper, the stability and dynamics of positive-negative vortex superposed states of two-dimensional exciton-polariton condensate in the disordered potential are studied under the rotation of the semiconductor microcavity, thereby laying a foundation for studying the gyroscopic effect of the superposed state of exciton-polariton condensates in the semiconductor microcavity. On the basis of reconstructing the mono-component Gross-Pitaevskii equation under the rotational situation, a numerical model with Coriolis items is constructed by the Runge-Kutta method and the finite difference time domain method, which is capable of depicting the rotation of the system. Moreover, the real-time evolution process of positive-negative vortex superposed states with different topological charges and the relationship between the number of steady-state local particles and the angular speed of the rotation of semiconductor microcavity are investigated by the real-time evolution method when the semiconductor microcavity is rotated. In the meantime, the relationship between the rotation speed in the excitation of vortex superposed states and the rotation speed of the semiconductor microcavity is also studied in the presence of the influence of the rotation speed of the semiconductor microcavity on the phase stability of vortex superposed states. According to the study, the rotation speed of the semiconductor microcavity has a significant influence on the evolution process and dynamic characteristics of vortex superposed states of exciton-polariton condensates. The rotation of the exciton-polariton system will accelerate the evolution of superimposed vortices, and overly rapid rotary rate will signalize the fluctuation of the local particle number thus the system unstability occurs. Moreover, along with the system rotation, the exciton-polariton superimposed vortices begin to rotate when the evolution approaches to saturation. It is noticeable that the angular acceleration of superimposed vortices is positively associated with the system rotary rate. Further, the topological charge has a significant influence on the rotation rate of exciation region of superposition state of vortices that it rotates more slowly when the topological charge increases but lower evolution stability simultaneously. These findings possess important guiding significance for establishing the quantum gyroscope in the future. Keywords:quantum vortex gyroscope/ exciton polariton/ superposition state of vortices/ rotational dynamics
最后, 本文研究了体系旋转角速率对不同拓扑荷数的涡旋叠加态的影响. 利用寻找干涉极大区域的中心位置的方法, 可以找出始末时刻“花瓣解”极大值的位置, 从而测算出体系在经历了一段时间的旋转后, 激子极化激元涡旋叠加态旋转的角度. 图6(a)反映了当体系旋转角速率$\varOmega \in( 2.{\rm{0}} \times {{10}^{ - 7}}, 1.{\rm{0}} \times {{10}^{ - 6}} )$时, 在$ t=80\hbar /{\rm{meV}}$时刻, 拓扑荷数分别为$l = \pm 4$和$l = \pm 12$的涡旋叠加态相对于初态转过的角度. 如前文所得出的结论, 体系转速越高, 到达稳态时涡旋叠加态相较于初态转过的角度就越大. 当$l = \pm 4$时, 涡旋叠加态最终转动了14.1°, 而$l = \pm 12$时涡旋叠加态最终转动了8.3°. 显然, 拓扑荷数越大, 其涡旋叠加态的位置受体系转动影响越小. 图6(b)给出了不同拓扑荷数情况下, 体系旋转角速率对演化过程产生的影响, 其Y轴表示体系到达稳态所需的时间. 可见, 一定体系转速情况下, 涡旋叠加态拓扑荷数与其容易受激发的程度成反比, 因此可以推测, 当拓扑荷数较大时涡旋叠加态更易因体系的旋转而过度激发, 从而失稳. 相反地, 拓扑荷数越小, 涡旋叠加态在旋转状态下的稳定性越好. 这种稳定性来源于相位分布的稳定性, 也即是涡旋的稳定性. 当拓扑荷数足够大时, 涡旋相对更容易被破坏并分裂, 这就表现为体系容易被激发达到饱和状态. 图 6 转动角速率对不同拓扑荷数激子极化激元涡旋叠加态的影响 (a)体系旋转角速率$\varOmega \in (2.{\rm{0}} \times {{10}^{ - 7}}, 1.{\rm{0}} \times {{10}^{ - 6}})$, t = 80?/meV时刻, 拓扑荷数分别为$l = \pm 4$和$l = \pm 12$的涡旋叠加态相对于初态转过的角度; (b)不同拓扑荷数情况下, 体系旋转角速率对演化过程产生的影响 Figure6. Effects of the angular velocities on the superposition state of exciton polariton vortexes with different topological charge number: (a) Angle of rotation of superposition state vortexes to the initial state at the moment of t = 80?/meV with different topological charge of $l = \pm 4$ and $l = \pm 12$ in the angular rate range of $\varOmega \in (2.{\rm{0}} \times {{10}^{ - 7}}, 1.{\rm{0}} \times {{10}^{ - 6}} )$; (b) effect of the system angular rate on the evolution process with different topological charges.