Abstract
In this paper we consider the problem of the interaction between two SU(2) quantum systems namely: two-level atom and multi-level atoms. The evolution operator is obtained and used to calculate the time-dependent dynamical operators. It has shown that the atomic inversion is sensitive to the change in the detuning parameter a, the quantum numbers jk as well as the atomic angles. The atomic squeezing is also considered and the phenomenon of squeezing is observed in both quadrature variances, however, with a periodic exchange between the quadratures. The degree of entanglement is examined by employing von Neumann entropy. It has shown that an increase in the value of the detuning parameter leads to a decrease in the degree of entanglement. However, for a weak coupling parameter the system shows reduction in the entropy. In the meantime the maximum entanglement can be reached when we increase the value for the quantum numbers jk. Also it has shown that the atomic angles play a role for controlling the degree of entanglement.