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Physical Review A

Squeezing via optical bistability

M. D. Reid, Daniel F. Walls

Published Jul 1, 1985• 62 citations
Publisher

Abstract

The spectrum of squeezing in the output field for the optically bistable system of an atomic medium in a coherently driven cavity is analyzed. Good squeezing is attainable only in certain limits of atomic parameters and cavity detuning.
DOI
10.1103/physreva.32.396

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We study the spectrum of squeezing in the light transmitted by a system of two-level atoms in an optical cavity driven by a coherent field, as recently observed by Kimble and collaborators. Our analysis does not introduce any restriction on the detuning parameters or on the relative order of magnitude of the atomic and cavity relaxation rates. Using the dressed-mode formalism, we derive explicit analytic expressions for the spectrum of squeezing and for the second-order intensity correlation function. We describe how the spectrum depends on the various parameters of the system; this study provides general indications on how to optimize the conditions to observe squeezing in optical bistability. A special attention is devoted to the changes of the spectrum under variation of the detuning parameters or on the ratio of cavity to atomic damping rate. In all cases, the changes are continuous and smooth, with quantitative variations in the level of squeezing. This indicates the existence of a single avenue to squeezing in this system. The bad-cavity direction is identified as especially convenient to obtain a significant amount of squeezing.
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We discuss the optical bistable behavior of a system of N two-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. We consider the equation of motion for atomic dipole moments, coupled to the cavity field and the squeezed vacuum, and the boundary condition connecting the input and output fields with the atomic lowering operator. A simple analytical expression for the influence of the squeezed vacuum input on the bistable behavior of the output field is derived by this method. The results indicate a strong influence of the squeezed vacuum input on optical bistability. The squeezed (stretched) vacuum input field tends to increase (decrease) the range of optical bistability.
Two-photon bistability in a system of three-level atoms driven by a single-frequency field shows nearly ideal squeezing close to a dynamic instability threshold, occurring in the lower branch of the steady-state bistability curve. The squeezing is maximized and becomes very broad band in the bad cavity limit. Such results which were previously predicted on the basis of an effective two-level model, are demonstrated here and analysed by a full three-level treatment of the atoms. In addition, important restrictions and new features are found.