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Physical Review A

Two-mode intelligent SU(1,1) states

Christopher C. Gerry, R. Grobe

Published May 1, 1995• 55 citations
Publisher

Abstract

Using the two-mode realization of the su(1,1) Lie algebra, we define new states that equalize the su(1,1) uncertainty relation. We refer to these as two-mode intelligent SU(1,1) states. Due to strong correlations between modes, these states exhibit nonclassical properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, squeezing in the superposition of the modes, and sum squeezing. We also study the phase distributions of the states and propose a mechanism by which they may be generated.

DOI
10.1103/physreva.51.4123

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Using the two-mode realization of the su(1,1) Lie algebra, we define new states that equalize the su(1,1) uncertainty relation. We refer to these as two-mode intelligent SU(1,1) states. Due to strong correlations between modes, these states exhibit nonclassical properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, squeezing in the superposition of the modes, and sum squeezing. We also study the phase distributions of the states and propose a mechanism by which they may be generated.
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.
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.
We have constructed a new kind of two-mode bosonic realization of SU (1,1) Lie algebra, on the basis of which the SU (1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU (1,1) coherent states, which are called uncorrelated two-mode SU (1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy-Schwarz inequality and two-mode squeezing.
Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.