A single ${\mathrm{Ca}}^{+}$ ion in a Paul trap has been cooled to the ground state of vibration with up to $99.9\%$ probability. Starting from this Fock state $|n=0\mathrm{}〉$ we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations with 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the $|n=1\mathrm{}〉$ Fock state. The coherence of optical state manipulation is limited only by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.

• Received 3 September 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.4713