Fig. 1. Experimental setup for an ultra-cold atoms trapped inside a high-finesse optical cavity driven by a pump laser in the z direction. While, a nanomechanical oscillator interacts with the optical cavity in the x direction. 将超冷原子囚禁在超精细的光腔内, 在z方向注入一束泵浦光, 并且在x方向外加一个与光腔发生相互作用的纳米机械振子

Fig. 2. The average photon number as a function of the atom-field coupling strength . 平均光子数 随原子-场的集体耦合强度 变化的示意图

Fig. 3. The average photon number’s phase diagram of the atom-field collective coupling strength and the temperature for different atom-light nonlinear interaction strength with the disappeared phonon-photon coupling constant . 原子-光场非线性相互作用影响下, 平均光子数随原子-场集体耦合强度和温度变化的相图 , 其中声子-光子耦合强度

Fig. 4. The phase diagram about the average photon number of atom-field collective coupling strength and the nonlinear photon-phonon interaction for different atoms-light nonlinear interaction strength with different finite temperature (1) and (2). 原子-光非线性相互作用影响下, 平均光子数关于原子-场耦合强度和声子-光子非线性相互作用强度 的相图, 其中有限温度分别为 (1)和 (2)

Fig. 5. The phase diagram about the average photon number of the atoms-light nonlinear interaction and temperature for different atoms-field collective coupling strength, where the nonlinear photon-phonon interaction . 在不同的原子-场集体耦合强度下, 平均光子数关于原子-光非线性相互作用和温度( )的相图, 其中声子-光子非线性相互作用

Fig. 6. Variations of the average photon number with respect to the atom-light nonlinear interaction . The given parameters are the atom-field coupling strength (a) and (b) , the temperature and the photon-phonon nonlinear coupling strength . 平均光子数 随原子-光非线性相互作用 变化的示意图, 给定的参数是: 原子-场耦合强度. (a) 和(b) , 温度 和光子-声子非线性耦合强度

Fig. 7. The average energy as a function of the atom-field collective coupling strength. 平均能量 随原子-场集体耦合强度 的变化

Fig. 8. Entropy as a function of the atom-field coupling strength . 熵 随原子-场集体耦合强度 的变化