  We investigate the spontaneous emission of one atom placed near an
oscillating reflecting plate. We consider the atom modeled as a two-level
system, interacting with the quantum electromagnetic field in the vacuum state,
in the presence of the oscillating mirror. We suppose that the plate oscillates
adiabatically, so that the time-dependence of the interaction Hamiltonian is
entirely enclosed in the time-dependent mode functions, satisfying the boundary
conditions at the plate surface, at any given time. Using time-dependent
perturbation theory, we evaluate the transition rate to the ground-state of the
atom, and show that it depends on the time-dependent atom-plate distance. We
also show that the presence of the oscillating mirror significantly affects the
physical features of the spontaneous emission of the atom, in particular the
spectrum of the emitted radiation. Specifically, we find the appearance of two
symmetric lateral peaks in the spectrum, not present in the case of a static
mirror, due to the modulated environment. The two lateral peaks are separated
from the central peak by the modulation frequency, and we discuss the
possibility to observe them with actual experimental techniques of dynamical
mirrors and atomic trapping. Our results indicate that a dynamical (i.e.
time-modulated) environment can give new possibilities to control and
manipulate also other radiative processes of two or more atoms or molecules
nearby, for example their cooperative decay or the resonant energy transfer.
