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Physical Review A

Reply to ‘‘Comment on ‘Operational approach to the phase of a quantum field’ ’’

J. W. Noh, A. Fougères, L. Mandeļ

Published May 1, 1993• 16 citations
Publisher

Abstract

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 ${\mathit{n}}_{3}$=${\mathit{n}}_{4}$ and ${\mathit{n}}_{5}$=${\mathit{n}}_{6}$ can lead to meaningless results. Moreover, Hradil's Eq. (5) for obtaining ${\mathit{D}}^{2}$ from the measured variance leads to disagreement with experiment. Finally, it is possible to obtain a continuous spectrum of phases with our technique.

DOI
10.1103/physreva.47.4535

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In response to the Comment by Barnett and Pegg [preceding paper, Phys. Rev. A 47, 4537 (1993)] it is pointed out that their objection is really based on a different measurement scheme. If our measurement procedure is repeated many times with different phase shifters inserted at one input port, the method yields an almost continuous probability density.

Physical Review A•May 1, 1993•8 citations
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.
Interpretational difficulties of a quantum measurement [J. W. Noh, A. Foug\`eres, and L. Mandel, Phys. Rev. A 45, 424 (1992)] are pointed out. The nonunitarity of the respective exponential phase operator reflects an enhanced noise, which can be reduced by discarding ambiguous output data. Consequently, dispersion of such measurements does not represent a meaningful performance measure relevant to the input state. Moreover, the proposed model of quantum phase measurements provides a discrete spectrum of the quantum phase operator, whereas the phase-shift parameter is continuous.
Recently, we introduced [C. Ufrecht and E. Giese, Phys. Rev. A 101, 053615 (2020)] a technique to calculate the phase of light-pulse atom interferometers caused by the presence of perturbation potentials and underlined its power by an illustrative example. In the preceding Comment [B. Dubetsky, Phys. Rev. A 102, 027301 (2020)], it was pointed out that other, less idealized situations could have been calculated as well. Our Reply emphasizes that our method is correct, the results from our example can be trivially generalized to other perturbations, and intricate effects of local environments can be even more prominent but also treated by our technique.