  The recent development of hybrid cQED allows one to study how cavity photons
interact with a system driven out of equilibrium by fermionic reservoirs. We
study here one of the simplest combination : a double quantum dot coupled to a
single mode of the electromagnetic field. We are able to couple resonantly the
charge levels of a carbon nanotube based double dot to cavity photons. We
perform a microwave read out of the charge states of this system which allows
us to unveil features of the out of equilibrium charge dynamics, otherwise
invisible in the DC current. We extract relaxation rate, dephasing rate and
photon number of the hybrid system using a theory based on a master equation
technique. These findings open the path for manipulating other degrees of
freedom e.g. the spin and/or the valley in nanotube based double dots using
microwave light.
