Production of photons by the parametric resonance in the dynamical Casimir effect

Abstract

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n{\ensuremath{\omega}}_{1}$ $(n=1,2,3,\dots{}),$ which is a generalization of other works considering only $2{\ensuremath{\omega}}_{1}$, where ${\ensuremath{\omega}}_{1}$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time evolution of quantum fields, we introduce a method that is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.