  We consider the general open system problem of a charged quantum oscillator
confined in a harmonic trap, whose frequency can be arbitrarily modulated in
time, that interacts with both an incoherent quantized (blackbody) radiation
field and with an arbitrary coherent laser field. We assume that the oscillator
is initially in thermodynamic equilibrium with its environment, a
non-factorized initial density matrix of the system and the environment, and
that at $t=0$ the modulation of the frequency, the coupling to the incoherent
and the coherent radiation are switched on. The subsequent dynamics, induced by
the presence of the blackbody radiation and the laser field, is studied in the
framework of the influence functional approach. This approach allows
incorporating, in \emph{analytic closed formulae}, the non-Markovian character
of the oscillator-environment interaction at any temperature as well the
non-Markovian character of the blackbody radiation and its zero-point
fluctuations. Expressions for the time evolution of the covariance matrix
elements of the quantum fluctuations and the reduced density-operator are
obtained.
