  We study the electronic transport through a pair of distant nanosystems
($S_a$ and $S_b$) embedded in a single-mode cavity. Each system is connected to
source and drain particle reservoirs and the electron-photon coupling is
described by the Tavis-Cummings model. The generalized master equation approach
provides the reduced density operator of the double-system in the
dressed-states basis. It is shown that the photon-mediated coupling between the
two subsystems leaves a signature on their transient and steady-state currents.
In particular, a suitable bias applied on subsystem $S_b$ induces a
photon-assisted current in the other subsystem $S_a$ which is otherwise in the
Coulomb blockade. We also predict that a transient current passing through one
subsystem triggers a charge transfer between the optically active levels of the
second subsystem even if the latter is not connected to the leads. As a result
of back-action, the transient current through the open system develops Rabi
oscillations (ROs) whose period depends on the initial state of the closed
system.
