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Physical Review A

Comment on ‘‘Langevin equation for the squeezing of light by means of a parametric oscillator’’

Paul Kinsler, P. D. Drummond

Published Dec 1, 1991• 22 citations
Publisher

Abstract

We comment on statements made about quantum representation theory in the paper by T. W. Marshall and E. Santos [Phys. Rev. A 41, 1582 (1990)]. Results are presented which show that correct results can be obtained from Langevin equations derived from the positive-P representation, even when those obtained by truncation of the Wigner time-evolution equation give incorrect results.

DOI
10.1103/physreva.44.7848

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Reply to ‘‘Comment on ‘Langevin equation for the squeezing of light by means of a parametric oscillator’ ’’

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We try to place the preceding Comment by Kinsler and Drummond [Phys. Rev. A 44, 7848 (1991)] in an overall scientific context.Received 30 April 1991DOI:https://doi.org/10.1103/PhysRevA.44.7851©1991 American Physical Society

Physical Review A•Dec 1, 1991•2 citations

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We disagree with the conclusions of the preceding Comment [Janszky and Yushin, Phys. Rev. A 39, 5437 (1989)]. It is shown in this Reply that a squeeze operator can also serve as the time evolution operator for a Franck-Condon transition, and that our previous interpretation is correct. It is also pointed out that the model Hamiltonian used in the preceding Comment is not appropriate for a Franck-Condon transition.

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Degenerate parametric amplification of squeezed photons: Explicit solutions, statistics, means and variances

Primitivo B. Acosta-Humánez, Sergey Kryuchkov, Erwin Suazo +1 more

In the Schrödinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multi-parameter squeezed input photons. The corresponding photon statistics and Wigner's function are also derived in coordinate representation. Their time evolution is investigated in detail. The unitary transformation and an extension of the squeeze/evolution operator are briefly discussed.

arXiv:1311.2479•Journal of Nonlinear Optical Physics & Materials•Jun 1, 2015•7 citations
We comment on statements made about quantum representation theory in the paper by T. W. Marshall and E. Santos [Phys. Rev. A 41, 1582 (1990)]. Results are presented which show that correct results can be obtained from Langevin equations derived from the positive-P representation, even when those obtained by truncation of the Wigner time-evolution equation give incorrect results.
We show that the Langevin equation for a nonlinear-optical system may be obtained directly from the Heisenberg equation of motion for the annihilation operators, provided a certain linearization procedure is valid. We apply the technique to the parametric oscillator used to generate squeezed light and compare our results to those obtained from Fokker-Planck-type equations. We argue that, only when the Wigner, as opposed to the P or Q, representation of quantum optics is used, do we get a correct description of the underlying stochastic process. We show how the linearization procedure may be carried out to describe the operation of the parametric oscillator both below threshold, where a squeezed vacuum state results, and above threshold, where we find a squeezed coherent state. In the region of the threshold a heuristic extension of the method leads to a possible description of the system by means of a nonlinear Langevin equation.