Nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics

We show that photons in two tunnel-coupled microwave resonators each containing a single superconducting qubit undergo a sharp nonequilibrium delocalization-localization (self-trapping) transition due to strong photon-qubit coupling. We find that self-trapping of photons in one of the resonators (spatial localization) forces the qubit in the opposite resonator to remain in its initial state (energetic localization). This allows for an easy experimental observation of the transition by local readout of the qubit state. Dissipation of photons and decoherence of the qubit favor the self-trapped regime.