  As photons do not interact with each other, it is interesting to ask whether
photonic systems can be modified to exhibit the phases characteristic of
strongly coupled many-body systems. We demonstrate how a Mott insulator type of
phase of excitations can arise in an array of coupled electromagnetic cavities,
each of which is coupled resonantly to a {\em single} two level system
(atom/quantum dot/Cooper pair) and can be individually addressed from outside.
In the Mott phase each atom-cavity system has the same integral number of net
polaritonic (atomic plus photonic) excitations with photon blockade providing
the required repulsion between the excitations in each site. Detuning the
atomic and photonic frequencies suppresses this effect and induces a transition
to a photonic superfluid. We also show that for zero detuning, the system can
simulate the dynamics of many body spin systems.
