  In order to use a collection of trapped ions for experiments where a well
defined preparation of vibrational states is necessary, all vibrational modes
have to be cooled to ensure precise and repeatable manipulation of the ions'
quantum states. A method for simultaneous sideband cooling of all axial
vibrational modes is proposed. By application of a magnetic field gradient the
absorption spectrum of each ion is modified such that sideband resonances of
different vibrational modes coincide. The ion string is then irradiated with
monochromatic electromagnetic radiation, in the optical or microwave regime,
for sideband excitation. This cooling scheme is investigated in detailed
numerical studies. Its application for initializing ion strings for quantum
information processing is extensively discussed.
