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International Journal of Modern Physics B

NONCLASSICAL PROPERTIES AND HOLE BURNING IN THE REAL AND IMAGINARY BINOMIAL STATES

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

Published Jun 20, 2001• 1 citation
Publisher

Abstract

We study the nonclassical properties of the real and imaginary binomial states formed by a superposition of the binomial states of Stoler et al. Their sub-Poissonian statistics and squeezing properties are studied in detail. These states have holes in the photon-number distribution, due to quantum interference between the two conjugate components. The corresponding ladder operator formalisms of these states are given.

DOI
10.1142/s0217979201005696

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We study the nonclassical properties of the real and imaginary binomial states formed by a superposition of the binomial states of Stoler et al. Their sub-Poissonian statistics and squeezing properties are studied in detail. These states have holes in the photon-number distribution, due to quantum interference between the two conjugate components. The corresponding ladder operator formalisms of these states are given.
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.
“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 investigate the nonclassical properties of the single-mode binomial states of the quantized electromagnetic field. We concentrate our analysis on the fact that the binomial states interpolate between the coherent states and the number states, depending on the values of the parameters involved. We discuss their statistical properties, such as squeezing (second and fourth order) and sub-Poissonian character. We show how the transition between those two fundamentally different states occurs, employing quasiprobability distributions in phase space, and we provide, at the same time, an interesting picture for the origin of second-order quadrature squeezing. We also discuss the phase properties of the binomial states using the Hermitian-phase-operator formalism.
New states of electromagnetic field, generalized excited negative binomial states are introduced here. These states interpolate between the superposition of two excited coherent states and number states. The non-classical properties for these states are discussed, such as, second order correlation function, squeezing phenomena [normal squeezing and amplitude squared squeezing], phase properties in Pegg–Barnett formalism and the quasi-probability distribution functions (Q-function and Wigner function).