  We theoretically investigated the ground states of coupled arrays of cavity
quantum electrodynamical (cavity QED) systems in presence of two photon modes.
Within the Gutzwiller-type variational approach, we found the first-order
quantum phase transition between Mott insulating and superfluid phases as well
as the conventional second-order one. The first-order phase transition was
found only for specific types of emitter models, and its physical origin is
clarified based on the analytic arguments which are allowed in the perturbative
and semiclassical limits. The first-order transition of the correlated photons
is accompanied with discontinuous change in the emitter states, not only with
the appearance of inter-cavity coherence in the superfluid phase. We also
discuss the condition for the first-order transition to occur, which can lead
to a strategy for future design of quantum optical switching devices with
cavity QED arrays.
