  Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap
is the prerequisite for quantum information experiments with trapped ions. With
resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we
have cooled one and two 40Ca+ ions to the ground state of vibration with up to
99.9% probability. With a novel cooling scheme utilizing electromagnetically
induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous
ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the
motional ground state we have demonstrated coherent quantum state manipulation
on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations
within 1.4 ms have been observed in the motional ground state and in the n=1
Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along
the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more
than 5 micron for up to 4 ions. We are able to cool two ions to the ground
state in the trap and individually address the ions with laser pulses through a
special optical addressing channel.
