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Journal of Optics B Quantum and Semiclassical Optics

Superpositions of negative binomial states

Jing Liao, Xiaoguang Wang, Ling-An Wu, Shaohua Pan

Published Jul 31, 2000• 12 citations
Publisher

Abstract

The states formed by a superposition of the negative binomial states are introduced. The sub-Poissonian statistics and squeezing properties of the superposition states are studied in detail. Moreover, we obtain the ladder operator formalism of the superposition state and find that this state is a type of two-photon nonlinear coherent state. A scheme for the generation of the superposition state is also discussed.

DOI
10.1088/1464-4266/2/4/313

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The states formed by a superposition of the negative binomial states are introduced. The sub-Poissonian statistics and squeezing properties of the superposition states are studied in detail. Moreover, we obtain the ladder operator formalism of the superposition state and find that this state is a type of two-photon nonlinear coherent state. A scheme for the generation of the superposition state is also discussed.
The real and imaginary negative binomial states formed by a superposition of the negative binomial states are introduced. The sub-Poissonian statistics, Wigner function and squeezing properties of the real and imaginary states are studied in detail. The oscillatory character of the photon distribution due to the quantum interference between the two components is shown. Moreover, we find that these states are real and imaginary nonlinear Schrödinger cat states and give the corresponding ladder operator formalisms. We also discuss how to generate these general real quantum superposition states based on the intensity-dependent Jaynes-Cummings model.
We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov's su(1,1) coherent states via its Holstein-Primakoff realisation. These states exhibit strong squeezing effect and they obey the super-Poissonian statistics. A method to generate these states is proposed.
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schrodinger cat states in a certain limit.The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras.It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.``
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schrödinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.
From the photon-added one-photon nonlinear coherent states a†m|α, ƒ〉, we introduce a new type of nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states |m〉 and |0〉, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail. Finally, we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions. PACS Nos.: 42.50Dv, 03.65Fd