Unitary decoupling treatment of a quadratic bimodal CQED model

We consider a two-photon quantum model of radiation-matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system the explicit construction of two collective radiation modes, one of which freely evolving and the other one quadratically coupled to the matter subsystem, is reported. Meaning and advantages of such a decoupling treatment are carefully discussed.