chaos in a media that includes quantum inference effects confined in a micro-ring resonator

We present the nonlinear dynamics of the output field from a micro-ring resonator filled with media that includes quantum inference effects. the quantum interference effects we consider, is a three-level atomic media whose levels are coupled by two laser beams under the λ-type configuration. under beyond fast-response condition. actually we take into account the population dynamics in the mean field limit, and the analysis of the nonlinear dynamics of the system is the main focus of our work in this research. this dynamical system is driven to chaos through period-doubling route by scanning the resonator detuning from the input frequency, as control parameter. these instabilities arise when the atomic states involved in the bistable transition are leaky and have substantial population, where the incoherent processes directly hinder the cooperative preparation of the atomic ensemble. we provide a bifurcation diagrams with associated supporting evidence that identifies the period-doubling route to chaos.