In the present communication we investigate the usual Jaynes–Cummings Hamiltonian model, describing two-level atom interacting with an electromagnetic field, in the presence of the second harmonic generation (degenerate parametric amplifier). Exact solutions of the wave function in the Schrödinger picture have been obtained for two different cases. In the first case the field frequency ω is not equal to the splitting photon frequency ε, where the canonical transformation has been invoked to obtain the solution of the wave function. In the second case, we considered both frequencies are equal (ε = ω) and the system is taken to be at exact resonance. Both solutions have been used to discuss the atomic inversion as well as the entropy squeezing. It has been shown that the system is sensitive to any change in the coupling parameter responses of the second harmonic generation as well as to the atomic phase angle.