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Journal of Modern Optics

On a new intermediate state of the quantized radiation field

Andreísa Fabri Lima, B. Baseia, Gil C. Marques

Published Apr 1, 1996• 14 citations
Publisher

Abstract

In a recent paper we introduced the intermediate number-phase state (INPS) of the quantized radiation field, which interpolates between the number state |n> and the phase state |θ >. Various non-classical properties of the light field in this state (sub-Poissonian statistics, antibunching and squeezing effects) were investigated. Here, looking for a criterion characterizing the INPS as a “good” interpolating state, we investigate the influence of the interpolating parameters upon the variances and uncertainty relation involving the number and phase operators in this state.

DOI
10.1080/09500349608232779

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In a recent paper we introduced the intermediate number-phase state (INPS) of the quantized radiation field, which interpolates between the number state |n> and the phase state |θ >. Various non-classical properties of the light field in this state (sub-Poissonian statistics, antibunching and squeezing effects) were investigated. Here, looking for a criterion characterizing the INPS as a “good” interpolating state, we investigate the influence of the interpolating parameters upon the variances and uncertainty relation involving the number and phase operators in this state.
Recently, a new state of the quantized radiation field — the intermediate number squeezed state (INSS) — has been introduced in the literature: it interpolates between the number state |n> and the squeezed state |z, α>=Ŝ(z)|α>, and exhibits interesting nonclassical properties as antibunching, sub-Poissonian statistics and squeezing. Here we introduce a slight modification in the previous definition allowing us a proposal to generate the INSS. Nonclassical properties using a new set of parameters are also studied.
This thesis is divided into 3 chapters supported by extensive Appendices. The first chapter gives a brief discussion on the need for the quantization of the electromagnetic field, and an introduction to its quantized form. In the second chapter, starting with a discussion on Coherent state representation, we give a brief account of some of the ‘non-classical’ properties of the radiation field, like, antibunching, sub-Poissonian statistics and squeezing, necessary for a good understanding of the material in Chapter(3).In the third and the final chapter, we analyze the effects of LASER plasma interaction on the radiation field from a Lie algebraic stand. Particularly, we analyze the emergence of non-classicality in the radiation field due to the interaction. Some of the results presented in this chapter are original and, to the extent of our knowledge, are not present in the literature.
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 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.
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.