Entanglement properties between two spatially separated atoms in free space reinforced by incoherent pumping

We report on the generation of entanglement between two spatially separated identical atoms in free space. We show that the evolution of the entanglement occurs due to the radiative coupling between the two atoms via the retarded dipole-dipole interaction. The magnitude of the entanglement is found to be strongly dependent on the initial states and the distance between the two atoms. We also study the different effects on the entanglement of the dipole-dipole collective parameters in the master equation. By introducing incoherent pumping, a steady entanglement can be acquired, and the condition for generating steady entanglement is also obtained.