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Topical Meeting on Optical Bistability (OB)

Optical Bistability, Chaos in the Coherent Two Photon Processes:

G. S. Agarwal, Surendra Singh

Published Jan 1, 1983• 0 citations
Publisher

Abstract

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-Block 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 atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.

DOI
10.1364/obi.1983.wha3

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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-Block 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 atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.
We describe a system comprising two circularly polarized ring-cavity modes coupled via a J=½ to J=½ transition. Both modes are equally excited by a linearly polarized incident laser. The steady-state transmission of the cavity shows optical tristability and polarization switching as predicted by Kitano et al.(1) and recently observed.(2) We generalise the model of Kitano et al. with the inclusion of saturation and absorption. In addition to optical tristability we find quadrastability (four stable output configurations for the same input intensity), self-oscillation, and chaos.(3) We have studied the chaotic region numerically as the incident laser intensity and the detuning of the cavity modes is varied. The routes to chaos appear to be analogous to those in the Lorenz equations. For a decreasing incident intensity the passage to chaos involves a new period doubling sequence of periodic windows embedded in chaos, where in each periodic window conventional period-doubling of the Feigenbaum type is observed. We have estimated the experimental parameters required to observe chaos in this system and find that power requirements are modest, although the limitations imposed by the adiabatic elimination and single-mode assumptions used in our theory cause some difficulties -- chaos may well remain, however, when these theoretical restrictions are relaxed.
We present nonlinear dynamical features of two-photon double-cavity optical bistability exhibited by a three-level ladder system in the mean-field limit at low input light levels. The system exhibits a hump-like feature in the lower branch of the bistable response, wherein a region of instability develops. The system displays a range of dynamical features varying from normal stable switching to periodic self-pulsing and chaos. The inclusion of two competing cooperative atom-field couplings leads to such rich, nonlinear dynamical behavior. We provide a domain map that clearly delineates the various regions of stability, as well as bifurcation diagrams with associated supporting evidence that identifies the period-doubling route to chaos.
We derive equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The dynamic equations of such a system are derived by using the technique of quantum Langevin operators, and then are studied numerically under different driving conditions. The results show that under certain conditions the cascade two-photon laser can generate chaotic, period doubling, periodic, stable and bistable states. Chaos can be inhibited by atomic populations, atomic coherences, and injected classical field. In addition, no chaos occurs in optical bistability.
We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.
Abstract In this paper we investigate the nonlinear dynamics for optical bistabile (OB) model of homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity in the presence of a Kerr-nonlinear blackbody (KNB) radiation reservoir. We show the impact of the relative temperature of the reservoir on the transition between the dynamical states via bifurcation diagrams that represents the relation between maximum values of the output field and the relative temperature for fixed input field. Specifically, decreasing the relative temperature (T b ) causes the system to bifurcate from periodic to chaotic behavior and in turn reverts back to periodic behavior with further decrease of T b . Varying atomic detuning leads to a change in the nature of the dynamic transition between the system’s states from self pulsing to chaotic behavior.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to photons statistics are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1) -- equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. We take into account parametric pumping. Corresponding equations of motion are received without the rotation-wave approximation. It was demonstrated the scenario of transition to chaos, realized by doubling frequencies mechanism with growing of 'atom + field' coupling constant. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values of order of the atomic frequency, the calculation of the maximal Lyapunov coefficient for the dynamics of many two- level atoms interacting with photon cavity mode as function of 'atoms + field' interaction constant is performed. An influence of possible parametric instabilities of nonlinear media and effects of dissipation for atoms are discussed.