@article{115f1f08343244fda70249543971333d,
title = "Degenerate parametric amplification of squeezed photons: Explicit solutions, statistics, means and variances",
abstract = "In the Schr{\"o}dinger 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.",
keywords = "Ermakov-type system, Ince equation, Kovacic algorithm, Time-dependent Schr{\"o}dinger equation, Wigner function, degenerate parametric amplifier, differential Galois theory, interaction picture",
author = "Acosta-Hum{\'a}nez, {P. B.} and Kryuchkov, {S. I.} and E. Suazo and Sergei Suslov",
note = "Funding Information: We would like to thank Albert Boggess for help and encouragement. This research was partially supported by AFOSR Grant No. FA9550-11-1-0220. The first named author was partially supported by MICIIN/FEDER MTM2012-31714 and by Ecos Funding Information: Nort Project C12M0l. Erwin Suazo was partially supported by a grant from the Simons Foundation (#316295) and by the AMS-Simons Travel Grants. Sergei Suslov thanks Marlan O. Scully, Wolfgang Schleich and M. Suhail Zubairy for valuable discussions during his visit to Institute for Quantum Science and Engineering, Texas A&M University. We are grateful to Victor V. Dodonov, Vladimir I. Man{\textquoteright}ko, Geza Giedke, Boris A. Malomed, Paulina Marian, Giuseppe Ruoso, Christoph Koutschan, Jos{\'e} M. Vega-Guzm{\'a}n and Andreas Ruffing for valuable comments and important references and to Kamal Barley for graphics enhancement.",
year = "2015",
month = jun,
day = "7",
doi = "10.1142/S0218863515500216",
language = "English (US)",
volume = "24",
journal = "Journal of Nonlinear Optical Physics and Materials",
issn = "0218-8635",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",
}