Route to chaos in a coupled microresonator system with gain and loss

TL;DR

This paper investigates how chaos emerges in a coupled microresonator system with gain and nonlinear absorption, revealing routes to chaos and the effectiveness of Galerkin approximation in describing complex dynamics.

Contribution

It demonstrates the routes to chaos in a non-Hermitian coupled resonator system and shows that Galerkin approximation effectively captures the system's key behaviors.

Findings

Identification of routes to chaos in the system

Galerkian approximation accurately models system dynamics

Connection between continuous and discrete system representations

Abstract

We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates, optical waveguides or atomic Bose-Einstein condensates of ultra-cold atoms placed in a circular-shaped trap. From the theoretical point of view this system is attractive due to its modulational instability and rich structure, including various types of spontaneous symmetry breaking, period doubling bifurcations, eventually leading to chaotic regime. It is described by set of partial differential equations but we show that the so called Galerkin approximation can explain most of the system characteristics mapping it on the dynamics of few coupled oscillator modes. The main goal of present study is to investigate various routes to chaos in our non-hermitian system and to show the correspondence between the continuous operator problem and its discrete representation.