Author: ALEJANDRO ZARATE CARDENAS
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.
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.