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Localization to the ground state of axial motion is demonstrated for asingle, trapped atom strongly coupled to the field of a high finesse opticalresonator. The axial atomic motion is cooled by way of coherent Ramantransitions on the red vibrational sideband. An efficient state detectionscheme enabled by strong coupling in cavity QED is used to record the Ramanspectrum, from which the state of atomic motion is inferred. We find that thelowest vibrational level of the axial potential with zero-point energy 13uK isoccupied with probability P0~0.95.Comment: 5 pages, 4 figure

Cooling to the Ground State of Axial Motion for One Atom Strongly Coupled to an Optical Cavity