Dissipative dynamical Casimir effect in terms of the complex spectral analysis in the symplectic-Floquet space

TL;DR

This paper presents a theoretical analysis of the dissipative dynamical Casimir effect in an optomechanical cavity interacting with a photonic crystal, using complex spectral analysis in symplectic-Floquet space to understand photon amplification and emission.

Contribution

It introduces a non-Hermitian effective Floquet-Liouvillian approach incorporating dissipation, revealing new stationary eigenmodes influenced by indirect virtual transitions.

Findings

Identification of nonequilibrium stationary eigenmodes with zero imaginary parts.

Discovery of nonlocal stationary eigenmodes caused by indirect virtual transitions.

Reduction of external field frequency needed for DCE via finite bandwidth photonic band.

Abstract

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.