Radium Ion Optical Clock

Abstract: We report the first operation of a Ra$^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}$Ra$^{+}$ ion and operates on the $7s\ ^2S_{1/2}\rightarrow$ $6d\ ^2D_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1$\times10^{-13}$/$\sqrt{\tau}$, where $\tau$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be ${\Delta \nu / \nu = 9 \times 10^{-16}}$. Using the clock, we realize the first measurement of the ratio of the $D_{5/2}$ state to the $S_{1/2}$ state Land\'{e} $g$-factors: $g_{D}/g_{S}$ = 0.5988053(11). A Ra$^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\dot \alpha / \alpha$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.