Quantum interaction of SU(1,1) Lie group with entangled a two 2-level atoms

In present contribution, we consider a two two-level atoms in non-resonance case interacting with a quantum system. The wave function is obtained via solving the Schrödinger equation. The initial density operator is assumed, with respect to the quantum system starts in a Barut-Girardello state. We use the numerical results to describe the entanglement between the subsystem. Some statistical aspects, the atomic inversion, the squeezing phenomena and negatively are discussed in details. We study the effective of the detuning parameter on the population inversion and the squeezing phenomenon. Finally the negativity for different values of the detuning parameter are examined. It is shown that the effects of the detuning parameter changes the region of the entanglement sudden death and sudden birth phenomena.