Dynamical Casimir effect of the optomechanical cavity interacting with one-dimensional photonic crystal is theoretically investigated in terms of the complex spectral analysis of Floquet-Liouvillian in the symplectic-Floquet space. The quantum vacuum fluctuation of the intra-cavity mode is parametrically amplified by a periodic motion of the mirror boundary, and the amplified photons are spontaneously emitted to the photonic band. We have derived the non-Hermitian effective Floquet-Liouvillian from the total system Liouvillian with the use of the Brillouin-Wigner-Feshbach projection method in the symplectic-Floquet space. The microscopic dissipation process of the photon emission from the cavity has been taken into account by the energy-dependent self-energy. We have obtained the discrete eigenmodes of the total system by non-perturbatively solving the nonlinear complex eigenvalue problem of the effective Floquet-Liouvillian, where the eigenmodes are represented by the multimode Bogoliubov transformation. Based on the microscopic dynamics, the nonequilibrium stationary eigenmodes are identified as the eigenmodes with vanishing values of their imaginary parts due to the balance between the parametric amplification and dissipation effects. We have found that the nonlocal stationary eigenmode appears when the mixing between the cavity mode and the photonic band is caused by the indirect virtual transition, where the external field frequency to cause the DCE can be largely reduced by using the finite bandwidth photonic band.

中文翻译：

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辛-Floquet空间中复谱分析方面的耗散动力学卡西米尔效应

光机腔与一维光子晶体相互作用的动力学卡西米尔效应从辛-弗洛奎特空间中弗洛奎特-刘维利安的复杂光谱分析的角度进行了理论研究。腔内模式的量子真空涨落通过镜面边界的周期性运动进行参数放大，放大后的光子自发发射到光子带。我们在辛 Floquet 空间中使用 Brillouin-Wigner-Feshbach 投影方法从总系统 Liouvillian 导出了非 Hermitian 有效 Floquet-Liouvillian。依赖于能量的自能已经考虑了从腔中发射光子的微观耗散过程。我们通过非微扰求解有效 Floquet-Liouvillian 的非线性复特征值问题，获得了整个系统的离散特征模，其中特征模由多模 Bogoliubov 变换表示。基于微观动力学，由于参数放大和耗散效应之间的平衡，非平衡平稳本征模被识别为虚部值为零的本征模。我们发现当腔模和光子带之间的混合由间接虚拟跃迁引起时，会出现非局部平稳本征模，其中使用有限带宽光子带可以大大降低引起 DCE 的外场频率。其中本征模由多模 Bogoliubov 变换表示。基于微观动力学，由于参数放大和耗散效应之间的平衡，非平衡平稳本征模被识别为虚部值为零的本征模。我们发现当腔模和光子带之间的混合由间接虚拟跃迁引起时，会出现非局部平稳本征模，其中使用有限带宽光子带可以大大降低引起 DCE 的外场频率。其中本征模由多模 Bogoliubov 变换表示。基于微观动力学，由于参数放大和耗散效应之间的平衡，非平衡平稳本征模被识别为虚部值为零的本征模。我们发现当腔模和光子带之间的混合由间接虚拟跃迁引起时，会出现非局部平稳本征模，其中使用有限带宽光子带可以大大降低引起 DCE 的外场频率。由于参数放大和耗散效应之间的平衡，非平衡平稳本征模被识别为虚部值为零的本征模。我们发现当腔模和光子带之间的混合由间接虚拟跃迁引起时，会出现非局部平稳本征模，其中使用有限带宽光子带可以大大降低引起 DCE 的外场频率。由于参数放大和耗散效应之间的平衡，非平衡平稳本征模被识别为虚部值为零的本征模。我们发现当腔模和光子带之间的混合由间接虚拟跃迁引起时，会出现非局部平稳本征模，其中使用有限带宽光子带可以大大降低引起 DCE 的外场频率。