“…The Hamiltonian (113) describes the two-photon down-conversion process in the crystal (one photon of frequency ω a is absorbed, and two photons of frequencies ω b , ω c are emitted), and the sum-frequency generation (two photons of frequencies ω b , ω c are absorbed and one photon of frequency ω a is emitted). Several aspects of model (113) have been thoroughly studied in the literature [143,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161]. The first description of the parametric amplifier and frequency converter, without the classical approximation for the pumping field, was performed by Walls and Barakat [147], who solved exactly the quantum-mechanical problem by the technique of the integrals of motion.…”