Satoshi Tanaka

Department of Physical Science
Osaka Prefecture University
Japan

Quantum vacuum amplification of a dissipative optomechanical cavity in terms of the complex spectral analysis of Floquet-Liouvillian

We study the quantum vacuum amplification of a dissipative optomechanical cavity with a photonic crystal in terms of complex spectral analysis of Floquet-Liouvillian. The quantum vacuum fluctuation of the cavity mode is parametrically amplified by a coherent oscillation of the mirror boundary, while a spontaneous photon emission from the cavity gives rise to dissipation. The energy gain-loss balance between the parametric amplification and spontaneous emission determines the stationary state of the cavity system. Applying the Floquet method to the time-dependent Heisenberg equation, we have obtained the non-Hermitian effective Liouvillian, which clearly shows the virtual transition and resonance singularity are the different origins of the non-Hermiticity of the effective Liouvillian. The dissipation process is taken into account in terms of an energy-dependent self-energy in the effective Liouvillian, making the eigenvalue problem of the effective Liouvillian nonlinear in the sense that the effective Liouvillian depends on its eigenvalue. We have found that both the parametric instability and the dissipation instablitity appear in the bifurcation of the normal modes, which emerge as the exceptional points of the non-Hermitian effective Liouvillian. We have also found that when the cavity frequency is in resonance with the photonic band continuum across the Floquet mode, a non-local stationary state emerges, where a strongly-mixed multimode squeezing state appears.