Free-space read-out and control of single-ion dispersion using quantum interference

We perform a free-space measurement and control of the refractive index of a single trapped ion in the presence of quantum interference effects. The single atom refractive index is characterized by the Faraday rotation of a laser field tightly focused onto a trapped and laser-cooled barium ion. It is tuned using the internal ion state that is optically controlled via a $V$ or a $\ensuremath{\Lambda}$ scheme. Measurements of the phase shift associated with an electromagnetically induced transparency are then performed and the internal state on the qubit transition is read-out with a detection fidelity of ($98\ifmmode\pm\else\textpm\fi{}1$)%.