  We consider the problem of photon creation from vacuum inside an ideal cavity
with vibrating walls in the resonance case, taking into account the interaction
between the resonant field mode and a detector modeled by a quantum harmonic
oscillator. The frequency of wall vibrations is taken to be twice the cavity
normal frequency, modified due to the coupling with the detector. The dynamical
equations are solved with the aid of the multiple scales method. Analytical
expressions are obtained for the photon mean numbers and their variances for
the field and detector modes, which are supposed to be initially in the vacuum
quantum states. We analyze different regimes of excitation, depending on the
ratio of the modulation depth of the time-dependent cavity eigenfrequency to
the coupling strength between the cavity mode and detector. We show that
statistical properties of the detector quantum state (variances of the photon
numbers, photon distribution function, and the degree of quadrature squeezing)
can be quite different from that of the field mode. Besides, the mean number of
quanta in the detector mode increases with some time delay, compared with the
field mode.
