Quantum state engineering on an optical transition and decoherence in a Paul trap

A single Ca+ ion in a Paul trap has been cooled to the ground state of vibr ation with up to 99.9% probability. Starting from this Fock state \n = 0] w e have demonstrated coherent quantum state manipulation on an optical trans ition. 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] Fock state. The coherence of optical state manipulation is limited on ly by laser and ambient magnetic field fluctuations. Motional heating has b een measured to be as low as one vibrational quantum in 190 ms.