Bloch-Messiah decomposition and Magnus expansion for parametric down-conversion with monochromatic pump

Tobias Lipfert, Dmitri B. Horoshko, Giuseppe Patera, and Mikhail I. Kolobov
Phys. Rev. A 98, 013815 – Published 9 July 2018

Abstract

We discuss the Bloch-Messiah decomposition for the broadband squeezed light generated by type-I parametric down-conversion with a monochromatic pump. Using an exact solution for this process, we evaluate the squeezing parameters and the corresponding squeezing eigenmodes. Next we consider the Magnus expansion of the quantum-mechanical evolution operator for this process and obtain its first three approximation orders. Using these approximated solutions, we evaluate the corresponding approximations for the Bloch-Messiah decomposition. Our results allow us to conclude that the first-order approximation of the Magnus expansion is sufficient for description of the broadband squeezed light for squeezing values below 12.5 dB. For higher degrees of squeezing we show fast convergence of the Magnus series, providing a good approximation for the exact solution already in the third order. We propose a quantitative criterion for this ultrahigh-gain regime of parametric down-conversion when the higher-order terms of the Magnus expansion, known in the literature as the operator-ordering effects, become necessary.

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  • Received 5 March 2018

DOI:https://doi.org/10.1103/PhysRevA.98.013815

©2018 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Tobias Lipfert1,*, Dmitri B. Horoshko1,2,†, Giuseppe Patera1, and Mikhail I. Kolobov1

  • 1Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
  • 2B. I. Stepanov Institute of Physics, NASB, Nezavisimosti Avenue 68, Minsk 220072, Belarus

  • *tobias.lipfert@univ-lille1.fr
  • dmitri.horoshko@univ-lille1.fr

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Issue

Vol. 98, Iss. 1 — July 2018

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