Non-equilibrium dynamics of non-linear Jaynes-Cummings model in cavity arrays

TL;DR

This paper investigates the complex non-equilibrium behavior of a tunable cavity array system with non-linear interactions, revealing bistability, limit cycles, and phase transitions through analytical and theoretical methods.

Contribution

It provides a detailed mean-field analysis of a non-linear Jaynes-Cummings model in cavity arrays, highlighting new dynamical phenomena and phase transitions.

Findings

Identification of bistable regions in single cavity systems

Discovery of limit cycles via Hopf bifurcations

Observation of Ising-like phase transition at high non-linearity

Abstract

We analyze in detail an open cavity array using mean-field description, where each cavity field is coupled to a number of three-level atoms. Such system is highly tunable and can be described by a Jaynes-Cummings like Hamiltonian with additional non-linear terms. In the single cavity case we provide simple analytic solutions and show, that the system features a bistable region. The extra non-linear term gives rise to a rich dynamical behaviour including occurrence of limit cycles through Hopf bifurcations. In the limit of large non-linearity, the system exhibits an Ising like phase transition as the coupling between light and matter is varied. We then discuss how these results extend to the two-dimensional case.