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

Department of Physical Science, Osaka Prefecture University, Gakuen-cho 1-1, Sakai 599-8531, Japan
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Physics 2020, 2(1), 34-48; https://doi.org/10.3390/physics2010005
Received: 22 December 2019 / Revised: 4 February 2020 / Accepted: 4 February 2020 / Published: 7 February 2020
(This article belongs to the Special Issue The Quantum Vacuum)
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. View Full-Text
Keywords: dynamical Casimir effect; parametric amplification of vacuum fluctuation; floquet method; complex spectral analysis dynamical Casimir effect; parametric amplification of vacuum fluctuation; floquet method; complex spectral analysis
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MDPI and ACS Style

Tanaka, S.; Kanki, K. The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal. Physics 2020, 2, 34-48. https://doi.org/10.3390/physics2010005

AMA Style

Tanaka S, Kanki K. The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal. Physics. 2020; 2(1):34-48. https://doi.org/10.3390/physics2010005

Chicago/Turabian Style

Tanaka, Satoshi; Kanki, Kazuki. 2020. "The Dynamical Casimir Effect in a Dissipative Optomechanical Cavity Interacting with Photonic Crystal" Physics 2, no. 1: 34-48. https://doi.org/10.3390/physics2010005

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