A radium ion optical clock*

We report the operation of a ${}^{226}\mathrm{Ra}^+$ single ion optical clock with a frequency instability of $\SI{1.1e-13}{}/\sqrt{\tau}$ and systematic fractional uncertainty of $\SI{9e-16}{}$. With the clock, we measured the ratio of the $D_{5/2}$ state to the $S_{1/2}$ Land\'{e} $g$-factors, $g_{D}/g_{S}$ = $\SI{0.5988053\pm.0000011}{}$. The radium ion has a small negative differential scalar polarizability that reduces leading systematic effects such as the black-body radiation shift, and transition wavelengths that are suitable for integrated photonics. These properties make the radium ion clock promising for a transportable optical clock. The radium ion clock could also improve limits on the time variation of the fine structure constants in an optical frequency comparison.