Dissipative dynamical Casimir effect in terms of complex spectral analysis in the symplectic Floquet space
Dissipative dynamical Casimir effect in terms of complex spectral analysis in the symplectic Floquet space
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DOI：
10.1093/ptep/ptaa129
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Satoshi Tanaka;K. Kanki
中科院分区：
文献类型：
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作者：
Satoshi Tanaka;K. Kanki
在辛-Floquet空间中，利用Floquet-Liouvillian复谱分析方法，研究了光机腔与一维光子晶体相互作用的动态Casimir效应.腔内模的量子真空涨落通过镜边界的周期性运动被参量放大，被放大的光子自发地发射到光子带。在辛-Floquet空间中，利用Brillouin-Wigner-Feshbach投影方法，从Liouvillian系统导出了非厄米有效Floquet-Liouvillian系统.利用与能量有关的自能，考虑了光子从腔中发射的微观耗散过程。我们通过非微扰求解有效Floquet-Liouvillian的非线性复本征值问题，得到了整个系统的离散本征模，其中本征模由多模Bogoliubov变换表示.基于微观动力学理论，将非平衡稳态本征模定义为虚部为零的本征模，这是由于参量放大和耗散效应之间的平衡。我们发现，当腔模与光子带之间的混合由间接虚跃迁引起时，会出现非局域稳态本征模，其中使用有限带宽的光子带可以大大降低引起VCE的外场频率。
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.