We theoretically investigate the generation of steady-state entanglement in a levitated optomechanical system with a cascade three-level atomic medium and a dielectric nanosphere. There are two cavity modes, driven by two external laser beams with different frequencies, which are responsible for trapping and cooling the nanosphere. Atoms prepared in coherent superposition are injected into the cavity to manipulate the optical fields and the effective optomechanical coupling. We show that the entanglement between the nanosphere and the cavity modes can be enhanced by selecting properly the initial population of the lower atomic level. In particular, when the atoms are prepared at that level, the corresponding optomechanical entanglement increases with the increase of the atom-field coupling strength. We also investigate in detail the influence of the effective cavity field detunings, the atomic detunings, the driving power, and the nanosphere's radius and found that there exist optimal values of the effective cavity field detuning and the driving power that maximize the optomechanical entanglement. By selecting the system's parameters properly, we further demonstrate the generation of genuine tripartite entanglement between three degrees of freedom in the system. The findings here may help flexible control of the steady-state entanglement in hybrid optomechanical systems.

中文翻译：

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在混合悬浮光机系统中通过三能级原子操纵稳态纠缠

我们理论上研究了具有级联三能级原子介质和介电纳米球的悬浮光机系统中稳态纠缠的产生。有两种腔模式，由具有不同频率的两个外部激光束驱动，它们负责捕获和冷却纳米球。将以相干叠加方式制备的原子注入腔中，以操纵光场和有效的光机械耦合。我们表明，纳米球和腔模之间的缠结可以通过选择适当的下原子水平的初始群体来增强。特别地，当以该水平制备原子时，相应的光机械缠结随着原子-场耦合强度的增加而增加。我们还详细研究了有效腔场失谐，原子失谐，驱动力和纳米球半径的影响，发现存在有效腔场失谐和驱动力的最佳值，这些最优值可使光机械纠缠最大化。通过适当地选择系统的参数，我们进一步证明该系统真正三方纠缠的三个自由度之间产生。此处的发现可能有助于灵活控制混合光机械系统中的稳态纠缠。通过适当地选择系统的参数，我们进一步证明该系统真正三方纠缠的三个自由度之间产生。此处的发现可能有助于灵活控制混合光机械系统中的稳态纠缠。通过正确选择系统的参数，我们进一步证明了系统中三个自由度之间真正的三方纠缠的产生。此处的发现可能有助于灵活控制混合光机械系统中的稳态纠缠。