Testing the Stability of Fundamental Constants with theHg+199Single-Ion Optical Clock
Over a two-year duration, we have compared the frequency of the $^{199}\mathrm{H}\mathrm{g}^{+}$ $5{d}^{10}6s\text{ }^{2}S_{1/2}(F=0)\ensuremath{\leftrightarrow}5{d}^{9}6{s}^{2}\text{ }^{2}D_{5/2}(F=2)$ electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral $^{133}\mathrm{C}\mathrm{s}$. These measurements show that any fractional time variation of the ratio ${\ensuremath{\nu}}_{\mathrm{C}\mathrm{s}}/{\ensuremath{\nu}}_{\mathrm{H}\mathrm{g}}$ between the two frequencies is smaller than $\ifmmode\pm\else\textpm\fi{}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{y}\mathrm{r}}^{\ensuremath{-}1}$ ($1\ensuremath{\sigma}$ uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of ${g}_{\mathrm{C}\mathrm{s}}({m}_{e}/{m}_{p}){\ensuremath{\alpha}}^{6.0}$ at the same level.