Entanglement preservation in a system of two dipole-dipole interacting two-level atoms coupled with single mode cavity

We address the problem of atom-atom entanglement dynamics control in a system of two different two-level atoms with dipole-dipole interaction coupled to a common single mode cavity with different coupling strengths. The control of entanglement dynamics is based on the parity kick method, and we use the antisymmetry properties of the Hamiltonian of the system to maintain atom-atom entanglement. We classify the possible controllable cases of this system. The control procedure is carried out with a sequence of cyclic evolution; accordingly, the entanglement of the system is protected for any given initial state with any desired precision and long duration.