Dark entangled steady states of interacting Rydberg atoms.

We propose a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.