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Journal of the Optical Society of America B

Binomial states of the quantized radiation field: comment

G. Dattoli, Juan Carlos Gallardo, A. Torre

Published Feb 1, 1987• 72 citations
Publisher

Abstract

Following a recent suggestion that binomial states exist in the quantized radiation field [ D. Stoles B. E. A. Saleh M. Teich , Opt. Acta32, 345 ( 1985)], we discuss a simple physical model that leads to binomial probability distribution. We also point out the relation between the binomial states and the generalized SU2 coherent states.
DOI
10.1364/josab.4.000185

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We introduce the binomial state of the quantized radiation field, which is a state that yields a binomial counting probability distribution. It reduces to the coherent state and to the number state in different limits. The binomal state is quantum mechanical in nature, and we show that it produces light that is antibunched, sub-poissonian, and squeezed for certain parameter ranges. A mixed binomial state is also defined. Particular attention is devoted to the mixed Bernoulli state which is an important special case. The properties of this mixed state indicate that squeezing might be present in individual atomic emissions.
We introduce an intermediate state of the light field which is alternative to the binomial state introduced by Stoler et al., thus interpolating bet seen the number state \\n > and the coherent state \\alpha >. A comparison between their properties shows that the amount of nonclassical effects obtained in the present state can be greater than that obtained in the binomial state, depending on the values of the interpolating parameters and the excitations n and <(n)over bar (alpha)>. Quantum coherence effect exhibited by the present state is also discussed.
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.``