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Topical Meeting on Optical Bistability (OB)

Critical Quantum Fluctuations in Optical Bistability

P. D. Drummond

Published Jan 1, 1983• 1 citation
Publisher

Abstract

Intrinsic optical bistable elements that have been investigated to date typically are either high-Q devices dominated by the interferometer relaxation, or else are fast switching devices dominated by relatively slow population transfers. In the case of the one-mode quantum theory of optical bistability with two-level atoms, these limits can be treated in a unified way with a single Fokker-Planck equation.

DOI
10.1364/obi.1983.wd3

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Intrinsic optical bistable elements that have been investigated to date typically are either high-Q devices dominated by the interferometer relaxation, or else are fast switching devices dominated by relatively slow population transfers. In the case of the one-mode quantum theory of optical bistability with two-level atoms, these limits can be treated in a unified way with a single Fokker-Planck equation.
We solve numerically the simplest Fokker-Planck equation which describes the effects of amplitude noise in absorbitive optical bistability. When the semiclassical solution exhibits critical slowing down, the probability distribution becomes two-peaked in a sizable time interval during the approach to the one-peaked steady-state distribution. The switching time undergoes considerable fluctuations, and on the average it is shorter than predicted by semiclassical theory. These noise effects seem accessible to experimental observation.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
A generalized Fokker-Planck equation is used to study the problem of single-atom optical bistability in the good-cavity limit. The effects of quantum fluctuations are investigated by linearizing fluctuations around the steady-state value. It is shown that in the good-cavity limit, quantum fluctuations are relatively small, and hence there exist both absorptive and dispersive single-atom bistability. By comparing our single-atom Fokker-Planck equation with the N-atom Fokker-Planck equation, we find that in the good-cavity limit, these two different Fokker-Planck equations reduce to identical equations. We therefore come to an important conclusion that the results obtained from the many-atom Fokker-Planck equation in the good-cavity limit are also valid for a single atom. \textcopyright{} 1996 The American Physical Society.
We specialize the quantum-statistical theory of optical bistability developed in "Optical Bistability. II" to a low-QQQ cavity. From a linearized Fokker-Planck equation derived in the positive PPP representation, the steady-state correlation matrix and spectrum of fluctuations are calculated. Expressions which normally assume a positive-definite diffusion matrix are shown to be valid for nonpositive-definite diffusion. For absorptive bistability we find agreement with results derived previously by quite different methods. More generally we extend previously published results by including atomic and cavity detunings. We compare the transmitted spectrum for dispersive bistability with that for absorptive bistability, and photon antibunching in dispersive bistability is discussed.