Dynamical behavior of entanglement, purity and energy for two atoms in the presence of dissipation

Entanglement, purity and energy of two isolated two-level atoms which are initially prepared in Bell state and each interacts with a dissipative thermal cavity field are investigated with considering the atomic motion and the field-mode structure. We give the analytical solution of the atomic state by using the algebraic dynamics approach. The influences of the field-mode structure, the dissipation of the cavities, the strength of the thermal field and the detuning on the entanglement, purity and energy are discussed. We also study the evolution of the atomic state using the entanglement-purity-energy diagrams. Our results suggest that the disentanglement process of the atomic state accompanies with the excitations transferring from atoms to the cavity field modes and with the state converting from a pure one to the mixed ones. When the two atoms become separable, they must be in the mixed states, and their energy decreases with the increase of the purity.