Abstract We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled simultaneously to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tripartite entanglement are realized near the parametric resonances in a coupled system. The model includes dissipation and decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg–Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

中文翻译：

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纳米腔中纠缠费米子-光子-声子态的产生和动力学

摘要 我们开发了描述纠缠量子态的形成和演化的分析理论，费米子量子发射器同时耦合到纳米腔中的量子化电磁场和量子化声子或机械振动模式。该理论适用于广泛的腔量子光力学问题以及与单分子和其他量子发射器耦合的等离子体纳米腔的新兴研究。三方纠缠的最佳条件是在耦合系统中的参数共振附近实现的。该模型包括由于费米子、光子和声子子系统在随机演化方法中耦合到它们的耗散储层而导致的耗散和退相干效应，该方法源自海森堡-朗之万形式主义。我们的理论为量子态和可观测量以及发射光谱的时间演化提供了解析表达式。分析了经典声学泵浦的限制以及参数和标准单光子共振之间的相互作用。