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arXiv:quant-ph/9611047 · Journal of Physics A Mathematical and General

Pólya states of quantized radiation fields, their algebraic characterization and non-classical properties

Hong-Chen Fu

Published Mar 7, 1997• 7 citations
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Abstract

Pólya states of a single-mode radiation field are proposed and their algebraic characterization and non-classical properties are investigated. They degenerate to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1) coherent) states in two different limits and further to the number, the ordinary coherent and Susskind - Glogower phase states. The algebra involved turns out to be a two-parameter deformation of both su(2) and su(1,1). Non-classical properties are investigated in detail.

DOI
10.1088/0305-4470/30/5/002

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Pólya states of a single-mode radiation field are proposed and their algebraic characterization and non-classical properties are investigated. They degenerate to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1) coherent) states in two different limits and further to the number, the ordinary coherent and Susskind - Glogower phase states. The algebra involved turns out to be a two-parameter deformation of both su(2) and su(1,1). Non-classical properties are investigated in detail.
Polya states of single mode radiation field are proposed and their algebraic characterization and nonclassical properties are investigated. They degenerate to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1) coherent) states in two different limits and further to the number, the ordinary coherent and Susskind-Glogower phase states. The algebra involved turn out to be a two-parameter deformation of both su(2) and su(1,1). Nonclassical properties are investigated in detail.
We study the non-classical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their non-classical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail.
“Hypergeometric states,” which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to the coherent and number states are studied. The ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one-parameter deformation of su(2) algebra. These states exhibit highly nonclassical properties, like sub-Poissonian character, antibunching, and squeezing effects. The quasiprobability distributions in phase space, namely the Q and the Wigner functions are studied in detail. These remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics.
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical 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 a same eigenvalue equation with a same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such states are proposed.
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.