Geodesic
Exactly solvable boson model with cubic nonlinearity
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 289-296

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The model of phase matched parametric amplifier, Hamiltonian of which has a cubic nonlinearity with respect to the Bose-field, is assumed. Exact operator solution is obtained. Evolution of the photon intensity and the corresponding variance is examined Conditions, defining the sub-Poissonian charachter of the number destribution and the squeezing of quantum fluctuations of modequadraturs, are obtained. 
@article{TMF_1994_98_2_a8,
     author = {A. B. Gordiets and W. Chmielowski},
     title = {Exactly solvable boson model with cubic nonlinearity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {289--296},
     publisher = {mathdoc},
     volume = {98},
     number = {2},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a8/}
}
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A. B. Gordiets; W. Chmielowski. Exactly solvable boson model with cubic nonlinearity. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 289-296. http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a8/