The mean photon number, the second-order coherence and the distribution of this optical cat state are derived in this paper and some properties of this state are presented.

Based on the second-order coherence function theory, authors have studied nonlinear effects of third-and fifth-order on polarization beats in a cascade three-level system (TPBCTS and FPBCTS).

It is proved that the average photon Numbers and the second-order quantum coherence are dramatically influenced by the entangled degree of the atoms.