Abstract
In this article, we present the analytical solution for the pair of entangled two three-level atoms in the cascade configuration with and without the atomic motion effect. The effects of time dependent coupling and photon multiplicity on the evolution of the nonlocal correlation between the two atoms are examined. It is shown that the amount of atom-atom entanglement increases for one photon transition when the atomic motion effect is considered. Also, the entanglement between the two atoms decreases by increasing the photons multiplicity when the time dependent coupling effect is ignored. Finally, the results explored very important phenomena such as entanglement sudden death and entanglement sudden birth.