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Physical Review A

Comparison of Vogel-Schleich phase theory with quantum phase measurements

Robert Lynch

Published Feb 1, 1993• 11 citations
Publisher

Abstract

The predictions of the Vogel-Schleich (VS) phase theory are compared to the recent experimental quantum phase measurements of Noh, Foug\`eres, and Mandel (NFM) [Phys. Rev. Lett. 67, 1426 (1991)]. Agreement is found to be excellent over the expected range of validity of the VS theory. Hence it appears that, contrary to the view of NFM, an abstract phase theory can predict their results independently of the detailed experimental configuration.

DOI
10.1103/physreva.47.1576

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The predictions of the Vogel-Schleich (VS) phase theory are compared to the recent experimental quantum phase measurements of Noh, Foug`eres, and Mandel (NFM) [Phys. Rev. Lett. 67, 1426 (1991)]. Agreement is found to be excellent over the expected range of validity of the VS theory. Hence it appears that, contrary to the view of NFM, an abstract phase theory can predict their results independently of the detailed experimental configuration.
We address the problem of identifying an operational prescription for quantum phase measurements. As is known, different experiments can lead to different measured phase operators. However, we show that ambiguities of interpretation can arise even if a single experiment, such as that of Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991)], is chosen as defining a phase measurement. We show by reference to a simple but fundamental example that it is not possible to deduce a unique phase difference from the measurements.
In papers by Lynch [ Phys. Rev. A 41 2841 (1990)] and Gerry and Urbanski [ Phys. Rev. A 42 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [ Phys. Lett. 49A 119 (1974)] are in good agreement with the variance of the Pegg–Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase ϕ 0 of the Pegg–Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Fougères and Mandel [ Phys. Rev. A 46 2840 (1992)] relative phase experiment in terms of the Pegg–Barnett phase taking post-selection conditions into account.
Generalizing a recent theoretical result obtained by Freyberger and Schleich [Phys. Rev. A 47, R30 (1993)], we show that the phase-measurement scheme proposed and realized by Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992)] amounts to measuring the Q function for the light under investigation, provided the reference beam (used for homodyne detection) is a very strong coherent field so that it can be described classically. The desired phase distribution follows from the Q function by averaging over the field amplitude. Since an analysis of an earlier proposal by Bandilla and Paul [Ann. Phys. (Leipzig) 23, 323 (1969)] to measure phase distributions via amplification led to just the same result, a perfect physical equivalence of those two approaches has thus been established.