  We propose and analyze an approach for preparation of high fidelity
entanglement and antiferromagnetic states using Rydberg mediated interactions
with dissipation. Using asymmetric Rydberg interactions the two-atom Bell
singlet is a dark state of the Rydberg pumping process. Master equation
simulations demonstrate Bell singlet preparation fidelity $\mcF=0.998$.
Antiferromagnetic states are generated on a four spin plaquette in agreement
with results found from diagonalization of the transverse field Ising
Hamiltonian.
