Bloch-Messiah decomposition and Magnus expansion for parametric down-conversion with monochromatic pump: role of the gain
Univ. Lille, CNRS, UMR 8523 -PhLAM -Physique des Lasers Atomes et Molécules, F-59000 Lille, France
2 B. I. Stepanov Institute of Physics, NASB, Nezavisimosti Ave. 68, Minsk 220072 Belarus
* e-mail: Tobias.Lipfert@univ-lille.fr
Published online: 15 January 2019
We consider the effect of different orders of Magnus expansion for the field transformation in type-I parametric down-conversion with a monochromatic pump. The exact solution, existing in this case, allows us to analyze the convergence of the Magnus expansion for the spectrum of squeezing and the angle of squeezing. We demonstrate how the convergence of the Magnus series depends on the parametric gain for various values of the phase mismatch. For each phase-mismatch angle we find the gain, which is the exact upper bound for the convergence of the Magnus series.
© The Authors, published by EDP Sciences, 2019
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