  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.
