Interaction between two SU(1,1) quantum systems and a two-level atom

•The interaction between quantum system and two-level atom is considered.•The atomic inversion and entanglement are examined.•The entropy and the variance squeezing, as well as the correlation function are also considered.

We consider a two-level atom interacting with two coupled quantum systems that can be represented in terms of su(1,1) Lie algebra. The wave function that is obtained using the evolution operator for the atom is initially in a superposition state and the coupled su(1,1) systems in a pair coherent Barut–Girardello coherent state. We then discuss atomic inversion, where more periods of revivals are observed and compared with a single su(1,1) quantum system. For entanglement and squeezing phenomena, the atomic angles coherence and phase as well as the detuning are effective parameters. The second-order correlation function displays Bunching and anti-Bunching behavior.