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We have observed resonant energy transfer between cold Rydberg atoms in spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s atoms in one cylinder to the 49p state while the 41d atoms in the second cylinder are transferred down to the 42p state. We have measured the production of the 49p state as a function of separation of the cylinders (0-80 microm) and the interaction time (0-25 micros). In addition, we measured the width of the electric field resonances. A full many-body quantum calculation reproduces the main features of the experiments.

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