Optical Bistability, Chaos in the Coherent Two Photon Processes
The cooperative behavior of a system of atoms contained in a ring cavity is investigated under the condition that the fundamental atomic transition is a two photon transition1. Maxwell-Bloch equations are used to obtain the input vs. output relation by adiabatically eliminating all the atomic variables. The fundamental equation that results is a complex two dimensional map--which in the mean field limit reduces to the standard bistability equations. The characteristics of the two dimensional map are numerically investigated. Such a map is shown to lead to chaotic behavior following the Feigenbaum2 scenario. The sequence of events following first regime of chaos is a set of period halving bifurcations. The characteristics of the power spectrum in the region of chaos are presented. The effect of noise on the period doubling bifurcations in the present model, is also investigated and the connection with the theoretical predictions3 is established. The changes in the dynamical characteristics of the system when the atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.
KeywordsChaotic Behavior Output Relation Fundamental Equation Cooperative Behavior Ring Cavity