Spontaneous emission induced entanglement and steady entanglement in two atomic system

We report possibility of generating entanglement between two atoms in free space when their spatial separation is on the order of wavelength or less. We show that these two atoms get coupled by photon exchange due to spontaneous decay, which in turn generates the atomic entanglement. By introducing the incoherent pumping, one can obtain the steady entanglement, and the incoherent pumping can overcome the decay of the atoms. Moreover, one can obtain the larger value of steady entanglement via proper tuning the incoherent pumping.