Abstract
The dynamical Casimir effect (DCE) is a conversion of virtual photons into directly observable real photons
by the parametric amplification of quantum vacuum fluctuations. After briefly reviewing previous
studies on DCE, we introduce our theory on photon emissions from DCE in terms of the complex spectral
analysis. We solved the Heisenberg equation of the whole system in which a parametric oscillator is
coupled to a photonic crystal and calculated the photon emission spectrum. In situations where a pair of
complex eigenvalues of the Liouvillian (complex eigenfrequencies) is in the first Riemann sheet, the
photon number of every mode increases exponentially. Otherwise, parametric amplification is suppressed
by the effect of dissipation, and the photon number of the parametric oscillator is kept constant
and stationary photon emission occurs. We also found a qualitative change in the photon emission process
at the parametric bifurcation point.
