A photonic crystal realization of a phase driven two-level atom

We propose a set of photonic crystals that realize a nonlinear quantum Rabi model equivalent to a two-level system driven by the phase of a quantized electromagnetic field. The crystals are exactly solvable in the weak-coupling regime; their dispersion relation is discrete and the system is diagonalized by normal modes similar to a dressed state basis. In the strong-coupling regime, we use perturbation theory and find that the dispersion relation is continuous. We give the normal modes of the crystal in terms of continued fractions that are valid for any given parameter set. We show that these photonic crystals allow state reconstruction in the form of coherent oscillations in the weak-coupling regime. In the strong-coupling regime, the general case allows at most partial reconstruction of single waveguide input states, and non-symmetric coherent oscillations that show partial state reconstruction of particular phase-controlled states.