Strong photon nonlinearities and photonic mott insulators

We show that photon nonlinearities in an electromagnetically induced transparency can be at least 1 order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that in this regime they give rise to very strong photon-photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultrahigh-Q microcavities.