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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Nearly ideal squeezing in degenerate two-photon optical bistability in three-level atoms

Alice Sinatra, D. Zibetti, F. Castelli, Luigi A. Lugiato

Published Dec 1, 1996• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1355-5111/8/6/008

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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.
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The squeezing spectrum for a cavity field mode interacting with an ensemble of three-level ``\ensuremath{\Lambda}-configuration'' atoms by an effective two-photon transition is calculated. The advantage of the three-level \ensuremath{\Lambda} system as a squeezing medium, that is, optical nonlinearity without atomic saturation, has recently been pointed out by Reid, Walls, and Dalton. We predict perfect squeezing at the turning points for dispersive optical bistability and good squeezing for a range of other cases. Three-level ladder atoms interacting by an effective two-photon transition are also shown to give perfect squeezing in the dispersive limit.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.