中文摘要：

从光学微腔与双阱中玻色子—费米子混合凝聚体耦合体系的薛定谔方程出发,推导出了粒子数算符以及光子数算符随时间演化的表达式,构造出系统有效的经典哈密顿量,利用数值方法和图示法研究了系统的动力学行为.通过相图发现玻色子和费米子的相互作用以及费米子之间的相互作用能够影响相对粒子数差随时间的变化;光学微腔能使系统稳定点增多,运动模式增加,混沌加剧.

英文摘要：

From the Schrodinger equations of the Bose-Fermi mixture in a double well coupled with a cavity,the time evolution expressions for the particle and the photon operator were given.An effective classical Hamiltonian for this system was derived,and its dynamics was investigated from the perspective of the phase portrait.It was shown that the strong condensate-cavity interplay did alter the dynamics of the system drastically.We found that the evolution of the relative number difference could be controlled by the interaction between fermions and the ones between bosons and fermions,respectively,and that the coupling with the cavity could make the system appear with more fixed points.The motional mode increased and the chaos could be enhanced accordingly.