Resonance Photon Generation in a Vibrating Cavity

V. V. Dodonov

doi:10.1088/0305-4470/31/49/008

paper

Resonance Photon Generation in a Vibrating Cavity

arXiv:quant-ph/9810077 · doi:10.1088/0305-4470/31/49/008

Abstract

The problem of photon creation from vacuum due to the nonstationary Casimir effect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls is solved in the resonance case, when the frequency of vibrations is close to the frequency of some unperturbed electromagnetic mode: $ω_{w} = p (π c / L_{0}) (1 + δ)$ , $∣ δ ∣ ≪ 1$ , (p=1,2,...). An explicit analytical expression for the total energy in all the modes shows an exponential growth if $∣ δ ∣$ is less than the dimensionless amplitude of vibrations $ε ≪ 1$ , the increment being proportional to $p ε^{2} - δ^{2}$ . The rate of photon generation from vacuum in the (j+ps)th mode goes asymptotically to a constant value $c p^{2} sin^{2} (π j / p) ε^{2} - δ^{2} / [π L_{0} (j + p s)]$ , the numbers of photons in the modes with indices p,2p,3p,... being the integrals of motion. The total number of photons in all the modes is proportional to $p^{3} (ε^{2} - δ^{2}) t^{2}$ in the short-time and in the long-time limits. In the case of strong detuning $∣ δ ∣ > ε$ the total energy and the total number of photons generated from vacuum oscillate with the amplitudes decreasing as $(ε / δ)^{2}$ for $ε ≪ ∣ δ ∣$ . The special cases of p=1 and p=2 are studied in detail.

23 pages, Latex2e with iopart.cls, no figures, to appear in J. Phys. A

Resonance Photon Generation in a Vibrating Cavity

Abstract

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