We show that photons in two tunnel-coupled microwave resonators each
containing a single superconduct- ing qubit undergo a sharp non-equilibrium
delocalization-localization (self-trapping) transition due to strong
photon-qubit coupling. We find that dissipation favors the self-trapped regime
and leads to the possibility of observing the transition as a function of time
without tuning any parameter of the system. Furthermore, 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 read-out of the qubit state.Comment: 4 pages, 5 figure
