  We study the interaction of a light beams carrying angular momentum with a
single, trapped and well localized ion. We provide a detailed calculation of
selection rules and excitation probabilities for quadrupole transitions. The
results show the dependencies on the angular momentum and polarization of the
laser beam as well as the direction of the quantization magnetic field. In
order to observe optimally the specific effects, focusing the angular momentum
beam close to the diffraction limit is required. We discuss a protocol for
examining experimentally the effects on the S$_{1/2}$ to D$_{5/2}$ transition
using a $^{40}$Ca$^+$ ion. Various applications and advantages are expected
when using light carrying angular momentum: In quantum information processing,
where qubit states of ion crystals are controlled, parasitic light shifts could
be avoided as the ion is excited in the dark zone of the beam at zero electric
field amplitude. Such interactions also open the door to high dimensional
entanglement between light and matter. In spectroscopy one might access
transitions which have escaped excitation so far due to vanishing transition
dipole moments.
