In this work we have shown 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. We also show that dissipation of photons and decoherence of the qubit do not destroy the self-trapping regime, but actually favor it.
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