中文摘要：

腔光机械系统成为近几年的研究热点之一,它有广泛的应用前景。本文采用泛函路径积分方法研究了与机械振子耦合的光腔中玻色爱因斯坦凝聚体的基态特性,从热力学平衡方程,推导出了原子布居数的表达式。从配分函数推导出了系统平均能的表达式,研究了系统的热力学性质,从中我们可以观察到机械振子对超辐射相的影响。在光子-原子的耦合强度偏小时,机械振子几乎不影响平均光子数的分布;在光子-原子的耦合强度偏大时,平均光子数会随着非线性光子-声子相互作用的逐渐增大而急剧增大。

英文摘要：

As one of the not research fields these years, cavity optomechanics possesses mere practical prospect. In this paper, we investigated the ground-state properties of a Bose-Einstein condensate in an optomechanical cavity. The scaled atomic population was calculated by means of the thermodynamic equilibrium equation. We obtained the average ground-state energy via the partition function and studied the thermodynamic quantities of the system. We observed that the mechanical oscillator had an effect on the superradiant phase（SP）. When the collective atom-photon coupling strength is a little small, the mechanical oscillator almost has no impact on the SP. However, when the collective atom-photon coupling strength is a little big, the average photon number of the system has a sharp increase with the nonlinear photon-phonon interaction constant increasing.