A classical simulation of nonlinear Jaynes--Cummings and Rabi models in photonic lattices

TL;DR

This paper presents a method to classically simulate nonlinear quantum optics models, like the Jaynes-Cummings and Rabi models, using photonic lattices, enabling the study of complex quantum interactions through classical optical setups.

Contribution

The authors propose a novel approach to simulate nonlinear quantum optics models with photonic lattices, extending the range of feasible experimental realizations beyond linear couplings.

Findings

Successfully simulate Buck-Sukumar model classically

Reconstruct quantum measurement averages from classical outputs

Enable study of nonlinear quantum interactions via photonic lattices

Abstract

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.