Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

We investigate single ions of Ca-40(+) in Paul traps for quantum informatio n processing. Superpositions of the S-1/2 electronic ground state and the m etastable D-5/2 state are used to implement a qubit. Laser light on the S-1 /2 <----> D-5/2 transition is used for the manipulation of the ion's quantu m state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state \n = 0], we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190 ms. We also report on ground state cooling of two ions.