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Topical Meeting on Optical Bistability (OB)

The Squeezing Spectrum in Optical Bistability

L. A. Lugiato, M. Vadacchino, F. Castelli

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.1364/obi.1988.fc.6

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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.
Optical bistability is reexamined as a candidate system for the generation of squeezed states of light. Previous analyses have concluded that significant squeezing can be achieved only in a rather extreme range of parameter space relative to current experimental capabilities and only over a restricted range of frequencies near the carrier.1 By contrast we have identified a new regime in which appreciable squeezing should be obtainable for rather modest operating conditions and without excessive demands on the stability of external control parameters. Following the treatment by Carmichael,2 we have conducted a theoretical search for optimal squeezing in optical bistability in the general case without adiabatic elimination of atomic or cavity variables. Our analysis is based on a linearization of the generalized Fokker-Planck equation for a system of N atoms coupled to a single mode of a high finesse cavity. For comparable atomic and cavity decay rates, there is a mode splitting in the eigenvalue structure of the system which is responsible for the vacuum field Rabi splitting. It is near the spectral features associated with these vacuum field Rabi sidebands that we find significant squeezing. The concepts of optimum squeezing as indicated by Mandel's Q parameter and by the spectrum of squeezing are discussed with reference to the various operating regimes in optical bistability.
A quantum theory describing N two-level atoms in a coherently driven single-mode optical ring cavity is presented. The usual approximation that one may adiabatically eliminate either the cavity or atomic variables is not made. Hence the results are valid for a range of relative cavity and atomic relaxation rates. The theory is based on the linearized equations derived in the positive P representation. A simple analytical solution is presented, including the effect of detunings, for the steady-state transmitted spectrum. The transmitted intensity and squeezing spectra are discussed.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
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.
We perform a systematic comparison between the spectrum of the intensity fluctuations and the spectrum of squeezing optimized with respect to the phase of the local oscillator, for the case of a one-photon single-mode optical bistability. In the bad-cavity limit the quantum noise reduction in the intensity fluctuations becomes comparable to the optimum level of squeezing. We consider also the case of a one-photon, single-mode laser with injected signal and show that under appropriate conditions the system can exhibit a meaningful level of squeezing.