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An approach to fast entanglement generation based on Rydberg dephasing ofcollective excitations (spin-waves) in large, optically thick atomic ensemblesis proposed. Long-range $1/r^3$ atomic interactions are induced by microwavemixing of opposite-parity Rydberg states. Required long coherence times areachieved via four-photon excitation and read-out of long wavelength spin-waves.The dephasing mechanism is shown to have favorable, approximately exponential,scaling for entanglement generation.

Dephasing of multiparticle Rydberg excitations for fast entanglement generation