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Physical Review A

Spectrum of single-atom fluctuations in cooperative systems

G. S. Agarwal

Published Jul 1, 1982• 2 citations
Publisher

Abstract

The spectrum of single-atom fluctuations in cooperative situations such as in the context of optical bistability and tristability is calculated by applying the method of system size expansion. The correlation functions of the fluctuating forces in quantum Langevin equations for any pair of atoms are found to be of order $\frac{1}{N}$. The relaxation matrix for single-atom fluctuations is shown to have the same structure as in the noncooperative situation but with an effective field determined by the state equation for multistability.

DOI
10.1103/physreva.26.680

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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.
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