NONDEGENERATE PARAMETRIC INTERACTIONS AND NONCLASSICAL EFFECTS

We consider the classical and quantum-mechanical processes of three-wa ve interactions in different phase regimes and present numerical calcu lations for the quantum case, where all three modes are sizably excite d from the beginning. These excitations are coherent so that various i mportant phase regimes can be adjusted. In addition, one mode can also be prepared in a squeezed or Kerr state. The classical solutions are well known and are briefly summarized, but certain phase regimes are c lassically unexplored and we show here that they give interesting and surprising results. In the out-of-phase regime (where the photon numbe rs do not change in the first order of time) we get, with an initial K err state, strongly sub-Poissonian photon statistics in the signal aft er a short interaction time. This effect is limited by the classically described phase shifts that are present even in the parametric approx imation. This nonclassical phenomenon (due to the Kerr state) helps us to understand similar nonclassical effects generated by entangled sta tes of the pump and signal during sum-frequency generation.