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Physical Review A

Phase properties of real field states: The Garrison-Wong versus Pegg-Barnett predictions

Ts. Gantsog, Adam Miranowicz, R. Tanaś

Published Sep 1, 1992• 21 citations
Publisher

Abstract

A comparison is made of predictions for the phase variances and the phase distribution functions obtained from the Garrison-Wong and Pegg-Barnett formalisms for real field states that include number states, coherent states, and squeezed vacuum states. It is shown that both approaches lead to qualitatively different phase distributions. The Garrison-Wong approach predicts an anisotropy of the phase distribution that is inconsistent with the symmetry of the Wigner and Q functions.

DOI
10.1103/physreva.46.2870

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A comparison is made of predictions for the phase variances and the phase distribution functions obtained from the Garrison-Wong and Pegg-Barnett formalisms for real field states that include number states, coherent states, and squeezed vacuum states. It is shown that both approaches lead to qualitatively different phase distributions. The Garrison-Wong approach predicts an anisotropy of the phase distribution that is inconsistent with the symmetry of the Wigner and Q functions.
The phase distribution obtained within the Pegg–Barnett Hermitian phase formalism is compared to the phase distributions obtained from the s -parametrized quasiprobability distributions integrated over the "radial" variable for some real states of the field. Exact analytical formulas for the s -parametrized phase distributions of coherent states, squeezed states, and displaced number states are obtained. A general formula relating the s -parametrized phase distributions to the Pegg–Barnett distribution is derived. Numerical examples illustrating the similarities and differences are presented in a graphical form.
Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.
The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg—Barnett formalism. Then, two nonclassical features, i.e., squeezing in the number and phase operators, as well as the number—phase Wigner function of the generalized squeezed states are investigated. Due to some actual physical situations, the present approach is applied to two classes of generalized squeezed states: solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions. Finally, the time evolution of the nonclassical properties of the considered systems has been numerically investigated.