  We model theoretically the time-dependent transport through an asymmetric
double quantum dot etched in a two-dimensional wire embedded in a FIR photon
cavity. For the transient and the intermediate time regimes the currents and
the average photon number are calculated by solving a Markovian master equation
in the dressed-states picture, with the Coulomb interaction also being taken
into account. We predict that in the presence of a transverse magnetic field
the interdot Rabi oscillations appearing in the intermediate and transient
regime coexist with slower non-equilibrium fluctuations in the occupation of
states for opposite spin orientation. The interdot Rabi oscillation induces
charge oscillations across the system and a phase difference between the
transient source and drain currents. We point out a difference between the
steady-state correlation functions in the Coulomb blocking and the
photon-assisted transport regimes.
