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 mirrors 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 $692pm20~textrm{pW}$ 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 $7.2pm0.2~%$ 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.
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