Probing phases of interacting polaritons in circuit QED setups

Circuit QED systems pose a new paradym for reaching the strong coupling regime of photonic and atomic degrees of freedom and are thus ideal candidates for quantum simulation and computation. We are investigating one-dimensional arrays of transmission-line cavities, where each cavity is coupled to a transmon-qubit. This system can be used as a quantum many-body simulator, lowering the experimental requirements for prescission control with respect to the use as a quantum computing device. We exploit the intermediate qubit-harmonic oscillator regime of the transmon to simulate Bose-Hubbard physics. As a suitable experimental setup we consider a system where the first cavity is driven by a classical microwave source and the output voltage is monitored, with respect to signatures of a quantum phase transition, at the last cavity.