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We discuss the basic properties of a recently proposed hybrid light-mattersystem of strongly interacting photons in an array of coupled cavities eachdoped with a single two level system. Using the non-linearity generated fromthe photon blockade effect, we predict strong correlations between the hoppingphotons in the array, and show the possibility of observing a phase transitionfrom a polaritonic insulator to a superfluid of photons. In the Mott phase,this interaction can be mapped to an array of spins. We show how the remainingHamiltonian, in conjunction with individual spin manipulation, can thus be usedfor simulating spin chains (useful for state transfer protocols) and clusterstate quantum computation.

Many body effects and cluster state quantum computation in strongly interacting systems of photons