This thesis reports on the progress of resolved sideband cooling on the S1/2 <-> D5\2 transition of 40Ca+ ions in a Penning trap. We demonstrate cooling of the axial motion of a single ion to the ground state over a wide range of trapping frequencies (67 kHz to 420 kHz) with a mean motional state ranging from nz = 0.07(1)
to nz = 0.015(18). We are also able to cool the radial motion of the ion close to the ground state with mean motional states below one for both the modified cyclotron and magnetron modes. In order to carry out sideband cooling of the radial mode, the ion is initially cooled with Doppler cooling in the presence of an axialisation field. Efficient sideband cooling outside the Lamb-Dicke regime is performed using complex cooling sequences featuring laser pulses at different frequencies.
The sideband cooling technique is extended to one- and two- dimensional ion Coulomb crystals. For a two-ion chain, aligned with the magnetic field, we measure for the centre of mass mode a final mean motional state nc = 0.25(6) and for the breathing mode nb = 0.07(4) with respective heating rates of 11(2) s-1 and 1(1) s-1. Near
ground state cooling of the transverse (axial) modes of two-dimensional planar crystals
made of up to 10 ions is achieved. A coherent drive of the cold ions is demonstrated by the observation of Rabi oscillations.
Ramsey experiments are performed on a single ion to study the coherence of the system. We find a 1/e coherence time of the optical transition S1/2 <-> D5/2 equal to 1.76(7) ms. This was increased to 13.2(6) ms using Uhrig dynamical decoupling. By creating superpositions of the motional states of the ion, we measure the coherence time of the axial motion. A maximum of 565(21) ms is found at 420 kHz.