Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Intrinsic phase operator of the Noh-Fougères-Mandel experiments

Berthold‐Georg Englert, Krzysztof Wódkiewicz, Peter Riegler

Published Aug 1, 1995• 9 citations
Publisher

Abstract

We find the intrinsic Hermitiean phase operator associated with the Noh-Foug\`eres-Mandel apparatus. This is achieved by first identifying the corresponding phasor basis. Previous, alternative approaches are shown to be equivalent. Quantum analogs of trigonometric functions are discussed with the aid of their Glauber and Wigner representations.

DOI
10.1103/physreva.52.1704

Related papers

Operational Phase Operators and Hermitian Phase Operators

K. Kakazu

It is shown that there exist two kinds of operational (or measured) phase operators, those of the Hradil type [Phys. Rev. A 47 (1993), 4532], defined on the entire Hilbert space, and those of the Noh-Fougères-Mandel type [Phys. Rev. A 45 (1992), 424], defined only on a subspace. As a consequence, strictly speaking, the Noh-Fougères-Mandel measured phase cannot be defined in the case of, for example, coherent states, squeezed states and the vacuum. The difference between these operators is made clear by using the concept of the Bargmann distance between a quantum state and its “reduced” state. Since Noh et al. did not use the correct variances of the Susskind-Glogower and Pegg-Barnett phase operators when they compared their data with the results predicted through use of these operators, the correct expressions in that case are presented. Comparing the measured operators with the Hermitian phase operator in the extended Susskind-Glogower formalism, we show that the quantum phase given by the Hermitian phase operator is more appropriate than the measured phases. The variance of the Hermitian operator in the vacuum is consistent with the complementarity of the photon number and phase, which implies that the vacuum has a uniform phase distribution. Hradil's measured operator does not have such a property. Although the Noh-Fougères-Mandel operator has such a property in a particular limit, this operator does not represent, in principle, a meaningful measure of the phase measurement in a typical quantum region, because the Bargmann distance becomes large in such a region.

Progress of Theoretical Physics•Oct 1, 2003•0 citations

Phase measurements

Stephen Mark Barnett, David Thomas Pegg

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.

Physical Review A•May 1, 1993•17 citations

Fock representation for two-mode quantum phase operators' eigenstates

Hong-Yi Fan, Min Xiao

The quantum phase description of Noh, Fougères and Mandel (NFM) leads to a two-mode theory of phase in the strong local oscillator limit. We show that the explicit form of the eigenstates of the sine and the cosine phase operators in two-mode Fock space can be constructed. This brings great convenience to the NFM quantum phase approach.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1996•5 citations

Comment on ‘‘Further investigations of the operationally defined quantum phase’’

Z. Hradil, J. Bajer

The normalization of the phase experiment of the scheme 1 in the paper of Noh, Foug\`eres, and Mandel [Phys. Rev. A 46, 2840 (1992)] is inappropriate. The correct treatment of this measurement tends to the same result as in their scheme 2.

Physical Review A•Aug 1, 1993•6 citations

Photon counting, quantum phase, and phase-space distributions

Matthias Freyberger, Wolfgang P. Schleich

We analyze a recent proposal for a new phase operator along with the experiment [J. W. Noh, A. Foug\`eres, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991)] using phase-space functions. We show that the measured dispersion in phase results from a phase distribution given by the appropriate Wigner function integrated over radius. We relate this experiment to a different phase operator [H. Paul, Fortschr. Phys. 22, 657 (1974)] and the integrated Q function.

Physical Review A•Jan 1, 1993•107 citations

Two-mode quantum phase

Matthias Freyberger, Martin Heni, Wolfgang P. Schleich

The authors review the operational quantum phase description of Noh, Fougeres and Mandel (1991-3) (NFM) and show that in the strong local oscillator limit it leads us to a two-mode theory of phase. This two-mode description contains the quantum phase of Paul (1993) as a special case. Furthermore this approach connects directly with a generalized and measurable phase space distribution.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1995•36 citations
We find the intrinsic Hermitiean phase operator associated with the Noh-Foug`eres-Mandel apparatus. This is achieved by first identifying the corresponding phasor basis. Previous, alternative approaches are shown to be equivalent. Quantum analogs of trigonometric functions are discussed with the aid of their Glauber and Wigner representations.
It is shown that there exist two kinds of operational (or measured) phase operators, those of the Hradil type [Phys. Rev. A 47 (1993), 4532], defined on the entire Hilbert space, and those of the Noh-Fougères-Mandel type [Phys. Rev. A 45 (1992), 424], defined only on a subspace. As a consequence, strictly speaking, the Noh-Fougères-Mandel measured phase cannot be defined in the case of, for example, coherent states, squeezed states and the vacuum. The difference between these operators is made clear by using the concept of the Bargmann distance between a quantum state and its “reduced” state. Since Noh et al. did not use the correct variances of the Susskind-Glogower and Pegg-Barnett phase operators when they compared their data with the results predicted through use of these operators, the correct expressions in that case are presented. Comparing the measured operators with the Hermitian phase operator in the extended Susskind-Glogower formalism, we show that the quantum phase given by the Hermitian phase operator is more appropriate than the measured phases. The variance of the Hermitian operator in the vacuum is consistent with the complementarity of the photon number and phase, which implies that the vacuum has a uniform phase distribution. Hradil's measured operator does not have such a property. Although the Noh-Fougères-Mandel operator has such a property in a particular limit, this operator does not represent, in principle, a meaningful measure of the phase measurement in a typical quantum region, because the Bargmann distance becomes large in such a region.
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.