Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 4 February 2020 / Approved: 6 February 2020 / Online: 6 February 2020 (16:20:18 CET)

A peer-reviewed article of this Preprint also exists.

Tanaka, S.; Kanki, K. The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal. Physics 2020, 2, 34-48. Tanaka, S.; Kanki, K. The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal. Physics 2020, 2, 34-48.

Journal reference: Physics 2020, 2, 5
DOI: 10.3390/physics2010005

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.

Subject Areas

Dynamical Casimir effect; parametric amplification of vacuum fluctuation; Floquet method; complex spectral analysis

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