  We report on the demonstration of a light-matter interface coupling light to
a single $^{174}\textrm{Yb}^+$ ion in free space. The interface is realized
through a parabolic mirror partially surrounding the ion. It transforms a
Laguerre-Gaussian beam into a linear dipole wave converging at the mirror's
focus. By measuring the non-linear response of the atomic transition we deduce
the power required for reaching an upper-level population of $1/4$ to be
$692\pm20~\textrm{pW}$ at half linewidth detuning from the atomic resonance.
Performing this measurement while scanning the ion through the focus provides a
map of the focal intensity distribution. From the measured power we infer a
coupling efficiency of $7.2\pm0.2~\%$ on the linear dipole transition when
illuminating from half solid angle, being among the best coupling efficiencies
reported for a single atom in free space.
