Fig. 1.

Level scheme of ${}^{174}{\text{Yb}}^{+}$. In the phase-shift experiments, we drive the $\mathit{\pi }$-transition between the $S_{\text{1/2}}$ and the $P_{\text{1/2}}$ state. Furthermore, we use optical pumping to prepare the ion in the metastable $D_{\text{3/2}}$ (dark) state for obtaining a reference phase. The branching ratio from the $P_{\text{1/2}}$ state into the $D_{\text{3/2}}$ state is $0.5\%$ [25]