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Physical Review A

Reply to ‘‘Jackiw state and higher-order squeezing of the electromagnetic field’’

Cao Hong, L. Mandeļ

Published Jun 1, 1986• 7 citations
Publisher

Abstract

In response to the preceding Comment by Lynch, it is pointed out that squeezing does not require that the uncertainty product be a minimum, but for higher-order squeezing two field components that differ in phase by less than \ensuremath{\pi}/2 may be more appropriate as canonical conjugates than the two quadratures.
DOI
10.1103/physreva.33.4432

Related papers

Finite fourth-order squeezing of both quadrature phase components

Robert Lynch

In a previous Comment on recent papers by Hong and Mandel, I was able to show that the ``Jackiw state,'' which is infinitesimally different from the coherent state, displays fourth-order squeezing (as defined by Hong and Mandel's criterion) of both quadrature field components; the magnitude of such squeezing is, however, infinitesimal. In this paper an explicit perturbation calculation is given which results in a state with finite fourth-order squeezing of both quadrature components.

Physical Review A•Nov 1, 1987•4 citations

sComment on 'Puri's criterion and higher-order squeezing'

Xia Yunjie, Yan Ke-zhu, Kong Xianghe

The result that Lynch and Mavromatis [Phys. Rev. A 52, 55 (1995)] obtained by Puri's definition of squeezing has no relation to Hong and Mandel"s higher-order squeezing [Phys. Rev. Lett. 54, 323 (1985)]. We also point out that, for an electromagnetic field, the nonclassicality of the squeezed state defined according to Puri's general uncertainty relation is not preserved.

Physical Review A•Feb 1, 1997•4 citations

Reply to “Comment on ‘Puri’s criterion and higher-order squeezing’ ”

Harry A. Mavromatis

The paper of Yunjie, Kezhu, and Xianghe [Phys. Rev. A 55, 1548 (1997)] points out an error in the conclusions of Lynch and Mavromatis [Phys. Rev. A 52, 55 (1995)]. In the present paper it is shown how, with the appropriate modifications, the results of Lynch and Mavromatis may still be used.

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Reply to the Comment on On the uncertainty relations and squeezed states for the quantum mechanics on a circle

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In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity $Δ^2(\hatϕ)$ introduced by us representing the uncertainty of the angle is not a proper measure of the position uncertainty and therefore the proposed inequalities can hardly be qualified as a relevant uncertainty relations on a circle; and that (ii) the most suitable uncertainty relations on a circle are those based on the Gram-Robertson matrix. It is shown by examples that both points are erroneous.

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In response to the objection raised by Pegg and Vaccaro [the preceding Comment] we point out that their example is not a difficulty in directly representing the phase difference by the ${\mathrm{\ensuremath{\Phi}}}_{12}$ operator. In fact, we argue that it is a property common to a wide range of phase descriptions, including the Pegg-Barnett formalism.

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

J. W. Noh, A. Fougères, L. Mandeļ

It is pointed out in response to Hradil and Bajer [preceding Comment, Phys. Rev. A 48, 1717 (1993)] that C${\mathrm{^}}_{\mathit{M}}$ and S${\mathrm{^}}_{\mathit{M}}$ cannot both be measured together by scheme 1, whereas they can by scheme 2. There is no phase angle whose cosine and sine both vanish, and putting C+iS equal to zero for certain measurement outcomes breaks the connection with phase.

Physical Review A•Aug 1, 1993•6 citations
In a previous Comment on recent papers by Hong and Mandel, I was able to show that the ``Jackiw state,'' which is infinitesimally different from the coherent state, displays fourth-order squeezing (as defined by Hong and Mandel's criterion) of both quadrature field components; the magnitude of such squeezing is, however, infinitesimal. In this paper an explicit perturbation calculation is given which results in a state with finite fourth-order squeezing of both quadrature components.
In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity Δ2(ϕ^)Δ^2(\hatϕ)Δ2(ϕ^​) introduced by us representing the uncertainty of the angle is not a proper measure of the position uncertainty and therefore the proposed inequalities can hardly be qualified as a relevant uncertainty relations on a circle; and that (ii) the most suitable uncertainty relations on a circle are those based on the Gram-Robertson matrix. It is shown by examples that both points are erroneous.