Quantum phase transitions with Photons and Polaritons

We show that a system of polaritons - combined atom and photon excitations - in an array of coupled cavities, under an experimental set-up usually considered in electromagnetically induced transparency, is described by the Bose-Hubbard model. This opens up the possibility of using this system as a quantum simulator, allowing for the observation of quantum phase transitions and for the measurement of local properties, such as single site observables. All the basic building blocks of the proposed setting have already been achieved experimentally, showing the feasibility of its realization in the near future.