Dynamical creation of entanglement and steady entanglement between two spatially separated Λ-type atoms

We report possibility of generating entanglement and steady entanglement between two identical atoms in free space with a very natural way when their spatial separation is on the order of wavelength or less. We show a dynamical creation of entanglement and steady entanglement due to the radiative coupling with different separable initial atomic states and study the entanglement properties about this atomic subsystem. Not only the creation of steady state entanglement is decided by the initial atomic states, but also the magnitude of the entanglement and the steady state entanglement are found to be strongly dependent on the initial states. We derive a master equation for the atomic subspace and solve it analytically to show how the spontaneous emission from the two atoms system induces entanglement and steady entanglement, the crossing coupling terms in master equation can enhance the entanglement value.