Dynamical Casimir effect in dissipative optomechanical cavity interacting with photonic crystal

TL;DR

This paper presents a theoretical study of the dynamical Casimir effect in an optomechanical cavity coupled with a photonic crystal, highlighting the impact of dissipation and the potential for easier experimental observation.

Contribution

It introduces a rigorous theoretical framework incorporating microscopic dissipation effects into the analysis of the dynamical Casimir effect in a photonic crystal-embedded optomechanical cavity.

Findings

Identification of two competing instabilities affecting the stationary mode.

Discovery of a non-local multimode dynamical Casimir effect.

Reduction of required pump frequency for observing DCE in narrow band photonic crystals.

Abstract

We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy-dependent self-energy. The obtained effective Floquet-Liouvillian exhibits the two competing instabilities, i.e., parametric and resonance instabilities, which determine the stationary mode as a result of the balance between them in the dissipative DCE. Solving the complex eigenvalue problem of the Floquet-Liouvillian, we have determined the stationary mode with vanishing values of the imaginary parts of the eigenvalues. We find a new non-local multimode DCE represented by a multimode Bogoliubov transformation of the cavity mode and the photon band. We show the practical advantage for the observation of DCE in that we can largely reduce the pump frequency when the cavity system is embedded in a narrow band photonic crystal with a bandgap.