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On the quantum phase problem

J. M. Vargas-Martínez, H. M. Moya-Cessa

Published Apr 24, 2003• 2 citations
OpenAlex

Abstract

We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $\\pi^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.

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Physica Scripta•Jan 1, 1993•30 citations
We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value pi2/3\\pi^2/3pi2/3 which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.
We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value π2/3π^2/3π2/3 which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.
The expectation value and variance of a new phase operator introduced recently by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and by Barnett and Pegg [J. Mod. Opt. 36, 7 (1989)] is calculated for a coherent state. The values for the variance so obtained are compared with the phase-fluctuation measurements of Gerhardt, B\"uchler, and Liftin [Phys. Lett. 49A, 119 (1974)] and Gerhardt, Welling, and Frolich [Appl. Phys. 2, 91 (1973)]. Agreement is found to be good, provided that account is taken of the details of the experimental values.
The problem of defining a Hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions have been proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we make an explicit connection between two of the most prominent approaches by proving that the probability distribution of phase in the Paul formalism follows exactly from the Pegg-Barnett formalism by combining the latter with the quantum-limited amplifier channel. Our findings suggest that the Paul framework may be viewed as a semiclassical limit of the Pegg-Barnett approach.
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.