Statistical properties of two-mode parametric amplifier interacting with a single atom

In the present work we introduce a Hamiltonian model consisting of two fields injected simultaneously within a perfect cavity to interact with a single atom. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. The model can be regarded as a generalization of the Jaynes–Cummings model as well as a generalization of the parametric amplifier model. Under a certain condition, which is carefully selected, the exact solution for the Heisenberg equations of motion is obtained. Employing this solution we managed to discuss some statistical properties such as the atomic inversion, the photon number distribution, the squeezing phenomenon, the Glauber second-order correlation function and Phase distribution. Also the Q-function is considered