Ground state cooling, quantum state engineering and study of decoherence   of ions in Paul traps
  We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum 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. 
F. Schmidt-Kaler, Ch. Roos, H. C. Naegerl, H. Rohde, S. Gulde, A.   Mundt, M. Lederbauer, G. Thalhammer, Th. Zeiger, P. Bart...