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Physical Review A

Reply to ‘‘Comment on ‘Phase properties of the quantized single-mode electromagnetic field’’

David Thomas Pegg, Stephen Mark Barnett

Published Mar 1, 1991• 12 citations
Publisher

Abstract

We assess the objections raised by Ma and Rhodes [preceding Comment, Phys. Rev. A 43, 2576 (1991)]. These objections seem to arise from a misinterpretation of our theory and a confusion between states of precise phase and states of precise field.
DOI
10.1103/physreva.43.2579

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We show that the approach by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] to construct a phase operator through a limiting procedure does not give a satisfactory description of the phase properties of the quantized electromagnetic field. We refute the claim that their approach predicts the same results of physical experiments on phase properties as the conventional Hilbert space approach. Their procedure could only be used as a definition of the phase, but it is not a good definition because the ``phase'' states they used to construct their ``phase'' operator are not of precisely defined phase contrary to their assertion.
In response to Hradil's Comment [preceding Comment, Phys. Rev. A 47, 4532 (1993)], we point out that his prescription for putting both the cosine and sine equal to zero when the data yield n3{\mathit{n}}_{3}n3​=n4{\mathit{n}}_{4}n4​ and n5{\mathit{n}}_{5}n5​=n6{\mathit{n}}_{6}n6​ can lead to meaningless results. Moreover, Hradil's Eq. (5) for obtaining D2{\mathit{D}}^{2}D2 from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.