  We investigate photon-mediated transport processes in a hybrid circuit-QED
structure consisting of two double quantum dots coupled to a common microwave
cavity. Under suitable resonance conditions, electron transport in one double
quantum dot is facilitated by the transport in the other dot via
photon-mediated processes through the cavity. We calculate the average current
in the quantum dots, the mean cavity photon occupation, and the current
cross-correlations with both a full numerical simulation and a recursive
perturbation scheme that allows us to include the influence of the cavity
order-by-order in the couplings between the cavity and the quantum dot systems.
We can then clearly identify the photon-mediated transport processes.
