Stationary three-dimensional entanglement via dissipative Rydberg pumping

We extend the recent result of bipartite Bell singlet [Carr and Saffman, Phys. Rev. Lett. {\bf111}, (2013)] to a stationary three-dimensional entanglement between two-individual neutral Rydberg atoms. This proposal makes full use of the coherent dynamics provided by Rydberg mediated interaction and the dissipative factor originating from the spontaneous emission of Rydberg state. The numerical simulation of the master equation reveals that both the target state negativity ${\cal N}(\hat\rho_{\infty})$ and fidelity ${\cal F}(\hat\rho_{\infty})$ can exceed 99.90%. Furthermore, a steady three-atom singlet state $|S_3\rangle$ is also achievable based on the same mechanism.