The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal

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.

Complex Energies of the Coherent Logitudinal Optical Phonon-plasmon Coupled Mode According to Dynamic Mode Decomposition Analysis

“…The effective Hamiltonian H with the complex frequencies of Eqs. ( 4) to ( 6) obtains two LOPC eigenmodes with complex eigenfrequencies, z n = ν n − iγ n , where the real and imaginary parts denote the renormalized frequency shifts and decay rates of the eigenmodes, respectively 43 . The LB and UB are identified by the lower and upper real values, respectively, of the complex eigenfrequencies.…”