Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays

The non-interacting nature of light makes the observation of photonic quantum phase transitions an impossible task. We demonstrate how a photonic insulator type of phase(Mott phase) can arise in an array of coupled high Q electromagnetic cavities and show how to drive the system to a superfluid state. Each cavity site is coupled resonantly to a 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.