It is shown that the classical and quantum mechanical description of first and second order nonlinear optical processes (including squeezing) are equivalent in the sense that in both cases an initial phase space distribution transforms in the same manner. We investigate in detail the degenerate three wave mixing, which is a third order process, and point out that the classical and quantum descriptions give essentially different results. This process yields three-pointed star states. It is pointed out that the efficiency of the star state in a three photon process is superior to that of a coherent state with two orders of magnitude.
"Star states in multi-photon processes", Proc. SPIE 3573, OPTIKA '98: 5th Congress on Modern Optics, (19 August 1998); doi: 10.1117/12.320979; https://doi.org/10.1117/12.320979