Abstract
An analytical treatment is provided of some different classes of two atoms having two or three energy levels whose dynamics show the presence of different entanglement. The phenomenon of sudden death of entanglement is investigated subject to different initial states settings. We find that for an initial Fock state, the presence of one or more photons in the cavity is a necessary condition for the sudden death of entanglement. Further examination allows us to formulate additional conditions for detecting entanglement and purity of the different systems. We conclude by showing howthe methods used here can be extended to find entanglement in systems of more than two atoms.