  We consider the spontaneous emission of a two-level quantum emitter, such as
an atom or a quantum dot, in a modulated time-dependent environment with a
photonic band gap. An example of such an environment is a dynamical photonic
crystal or any other environment with a bandgap whose properties are modulated
in time, in the effective mass approximation. After introducing our model of
dynamical photonic crystal, we show that it allows new possibilities to control
and tailor the physical features of the emitted radiation, specifically its
frequency spectrum. In the weak coupling limit and in an adiabatic case, we
obtain the emitted spectrum and we show the appearance of two lateral peaks due
to the presence of the modulated environment, separated from the central peak
by the modulation frequency. We show that the two side peaks are not symmetric
in height, and that their height ratio can be exploited to investigate the
density of states of the environment. Our results show that a dynamical
environment can give further possibilities to modify the spontaneous emission
features, such as its spectrum and emission rate, with respect to a static one.
Observability of the phenomena we obtain is discussed, as well as relevance for
tailoring and engineering radiative processes.
