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arXiv:quant-ph/9801052 · Journal de Physique II

Transverse Effects on Squeezing with Atoms

Astrid Lambrecht, Jean-Michel Courty, Serge Reynaud

Published Aug 1, 1996• 4 citations
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Abstract

We evaluate the squeezing of a probe beam with a transverse Gaussian profile interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and noise functions. The transverse structure is accounted for by averaging atomic functions over the intensity profile. The results of the plane-wave and Gaussian-wave theories are compared. When large squeezing is predicted we find the prediction of the plane-wave model not to be reliable outside the Kerr domain. We give an estimate of the squeezing degradation due to the Gaussian transverse structure.

DOI
10.1051/jp2:1996121

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We evaluate the squeezing of a probe beam with a transverse Gaussian profile interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and noise functions. The transverse structure is accounted for by averaging atomic functions over the intensity profile. The results of the plane-wave and Gaussian-wave theories are compared. When large squeezing is predicted we find the prediction of the plane-wave model not to be reliable outside the Kerr domain. We give an estimate of the squeezing degradation due to the Gaussian transverse structure.
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We investigate the effect of a spatially varying field mode on the squeezing generated by two-level atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good- and bad-cavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standing-wave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.
We analyze nonlinear transverse mode coupling in a Kerr medium placed in an optical cavity and its influence on bistability and different kinds of quantum noise reduction. Even for an input beam that is perfectly matched to a cavity mode, the nonlinear coupling produces an excess noise in the fluctuations of the output beam. Intensity squeezing seems to be particularly robust with respect to mode coupling, while quadrature squeezing is more sensitive. However, it is possible to find a mode whose quadrature squeezing is not affected by the coupling. \textcopyright{} 1996 The American Physical Society.
The steady state behaviour of a bistable system of a homogeneously/inhomogeneously broadened two-level atomic medium in contact with a squeezed vacuum field and placed in a ring cavity driven by a coherent field is analysed within the mean field limit where the transverse effect of the radiation field is taken into account within the single-transverse-mode model. Effects on the input–output relation and the critical value of the cooperative parameter C crit are examined and compared with these results in the plane wave approximation. The 'cooperative switching effect' between the output states of the system due to variation of the cooperative parameter C is also investigated. Linear stability analysis for the model Maxwell–Bloch equations is presented in the homogeneously broadened case.
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