In this study, we consider three interacting atoms, one of them represented
by N-level atom based on SU(2) Lie algebra and the other represented by a
two two-level atom in presence of the external field. The effect of the
external field on the dynamics of the proposed system is discussed in detail
for certain values for the external field. The dynamical expression of the
observable operators is obtained by using the Heisenberg equation of motion.
The general solution via solving Schrodinger equation is obtained. The
fidelity and concurrence formula as a measure of entanglement between two
two-level atom are calculated and discussed in detail. We explore the sudden
death and sudden birth phenomena with and without the presence of external
field. Finally, we compare the results of the fidelity, concurrence and
second-order correlation function for some values of the initial state and
the external field parameters.