The generation of a superposition state of a single-mode or two-mode coherent state is always an attractive topic. We propose schemes to generate the Schrödinger cat state and entangled coherent state of a mechanical oscillator in a hybrid optomechanical system. By introducing time-dependent coupling between the atom and photon, an effective Hamiltonian is deduced, where a tripartite interaction with time-dependent coupling is achieved. The effect of relatively high free energy can be cancelled so that we can obtain a relatively large average phonon number. Including dissipation, we derive an analytic solution of the system and further discuss the decoherence and disentanglement. In addition, a steady phonon laser can be reached.

中文翻译：

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在混合光机械系统中生成宏观量子叠加和声子激光

单模或双模相干态的叠加状态的产生始终是一个吸引人的话题。我们提出了在混合光机械系统中生成机械振荡器的薛定ding猫状态和纠缠相干状态的方案。通过在原子和光子之间引入时间相关的耦合，推导了有效的哈密顿量，其中实现了与时间相关的耦合的三重相互作用。可以抵消相对较高的自由能的影响，以便我们可以获得相对较大的平均声子数。包括耗散，我们导出了系统的解析解，并进一步讨论了退相干和解纠缠。另外，可以达到稳定的声子激光。