Phase-space motion in parametric three-wave interaction

We study the interaction of three modes in phi((2)) media in the classical as well as in the quantum picture. We show that it is possible to distinguish two basic forms of phase-space motion depending on the value of the integral of motion Gamma in the classical formulation or the (initial) mean value of the interaction Hamiltonian in the quantum formulation. The quantum and classical pictures are compared using a simulation of the Husimi Q function via classical trajectories for an ensemble of phase-space points. The very good correspondence between the two pictures is shown to last for a significant interaction time and can be investigated for arbitrary initial intensities.