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Acta Physica Sinica (Overseas Edition)

Nonclassical properties of photon-added pair coherent states

H. Lu, Guo Guang-Can

Published Aug 1, 1999• 23 citations
Publisher

Abstract

The two-mode photon-added state defined by |?, q; m>?=?a+mb+m|?, q> up to a normalization constant is introduced, where |?, q> is a pair coherent state and m an integer. It is shown that the fields in such a state have remarkable quantum features such as sub-Poissonian statistics, violations of Cauch-Schwarz inequalities, correlations in the number fluctuations and squeezing. We examine the influence of photon-adding on the properties of pair coherent state, and propose a method of generating two-mode photon-added states in the context of cavity quantum electrodynamics.

DOI
10.1088/1004-423x/8/8/004

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The two-mode photon-added state defined by |?, q; m>?=?a+mb+m|?, q> up to a normalization constant is introduced, where |?, q> is a pair coherent state and m an integer. It is shown that the fields in such a state have remarkable quantum features such as sub-Poissonian statistics, violations of Cauch-Schwarz inequalities, correlations in the number fluctuations and squeezing. We examine the influence of photon-adding on the properties of pair coherent state, and propose a method of generating two-mode photon-added states in the context of cavity quantum electrodynamics.
We examine the nonclassical properties of the pair coherent states defined as the simultaneous eigenstates of the operator that annihilates photons in pairs and of the operator that gives the relative occupation number in the two modes. We show that fields in such states have remarkable quantum features such as sub-Poissonian statistics correlations in the number fluctuations, squeezing, and violations of Cauchy–Schwarz inequalities. We show how such pair coherent states can be generated by the competition of different nonlinear processes in a two-photon medium. The quantam features occur not only in the transient domain but also survive in the steady state because of the balance between nonlinear processes.
The photon-added odd pair coherent states and photon-added even pair coherent states are constructed,and their nonclassical properties are studied with numeric simulation method.The results show that the constructed states are new quantum optical fields that exhibit the nonclassical properties such as the sub-poissonian distribution characters of photon statistics and the antibunching effect.When the photons are added to the two modes of the odd(even) pair coherent states,the sub-poissonian distribution characters of photon statistics can be obviously enhanced.
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 mode of a photon-added double-mode SU(2) coherent state｜M,ξ;m〉=A_(Mξm)a~(+m)｜M,ξ〉is introduced and its quantum statistics property is investigated with numeric method. The results exhibit that when the photons are added to the mode aof the double mode SU(2) coherent state, the two field modes can preserve anti-relation character. The violation of Cauchy-Schwartz inequality, the sub-Poissonian photon statistics property of mode aand anti-bunching effect of mode bare enhanced, but the sub-Poissonian photon statistics property of mode band anti-bunching effect of mode a are weakened.
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.