Dynamics of nonclassical properties of a SU(3) system interacting with two open parametric amplifier modes

We introduce an analytical description of an open bimodal cavity containing a3-type three-level atom.We explore the effect of the atom-cavity nonlinear interaction, the cavity dissipation, and the initial coherent intensity on the dynamics of the nonclassical correlations for a cavity prepared initially in a superposition of nonlinear coherent states. The nonlinear interaction generates a regular entanglement between the subsystems, and populates the energy atomic states.We show that the collapse phenomenon is a good indicator of the generated quantum coherence. The growth of the entropy is used to explore the generated entanglement (if the dissipation is absent) and mixedness (in the presence of the dissipation). It is found that the generation and the robustness of the quantum synchronization and the correlations between the subsystems are very sensitive to the dissipation, the superposition, and the coherent intensity of the initial Barut-Girardello coherent states.