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Journal of Modern Optics

SU(1, 1) and SU(2) Squeezing in Trilinear Optical Processes

Igor Jex, G. Drobný

Published May 1, 1992• 6 citations
Publisher

Abstract

The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.

DOI
10.1080/09500349214551061

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The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.
The properties of correlated two-mode SU(1, 1) coherent states are studied. These states are a generalization of the two-mode squeezed vacuum states and are generated by applying the two-mode squeeze operator to a state in which there are initially q photons in one mode, |q, 0〉, the squeezed vacuum (q = 0) obviously being a special case. For these states the photon-number distribution and the nonclassical properties of photon antibunching, enhanced phase fluctuations, violations of the Cauchy–Schwarz inequality, two-mode squeezing, and sum squeezing are studied. A Q-function quasi-probability distribution for these states is also presented.
The squeezing properties of optical field and atomic laser are studied in the system of two-mode SU (1, 1) coherent states interacting with two-level atomic BEC. The results show that two quadrature components of optical field can be squeezed periodically. The frequency of squeezing of optical field depends closely on both the interaction among atoms in BEC and the coupling constant between optical field and atoms. The maximum depth of squeezing is closely correlated to the two-mode SU (1, 1) coherent states parameters. The two quadrature components of atomic laser also can be squeezed, but it is difficult to squeeze. The maximum depth of squeezing is determined by the initial optical field.
We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.
The theory of generalized coherent states associated with the SU(2) and SU(1,1) Lie algebras is discussed and applied in an investigation of possible reductions of fluctuations. In the framework of a system of N two-level atoms the squeezing of angular-momentum [SU(2)] fluctuations is exhibited for optical coherent transients involving the photon echo. The SU(1,1) fluctuations are discussed and established for general two-photon processes involving dynamical variables different from the creation and annihilation operators.