Search for Temporal Variation of Fundamental Constants With Hg+ and Al+ Optical Clocks

\newcommand{\ratioAlHg}{$\sepnum{.}{\,}{\,}{1.052871833148990438} (55)$} \newcommand{\uncertaintyAlHg}{$5.2\times10^{-17}$} \newcommand{\uncertaintyAl}{$2.3\times10^{-17}$} \newcommand{\uncertaintyHg}{$1.9\times10^{-17}$} \newcommand{\uncertaintyHgCs}{$6.5\times10^{-16}$} \newcommand{\uncertaintyStat}{$4.3\times10^{-17}$} \newcommand{\absolutefreqAl}{$\sepnum{.}{\,}{\,} {1121015393207857.4}(7)$ Hz} \newcommand{\Al}{$^{27}$Al$^+$ } \newcommand{\Alns}{$^{27}$Al$^+$} \newcommand{\Be}{$^{9}$Be$^+$ } \newcommand{\Bens}{$^{9}$Be$^+$} \newcommand{\Hg}{$^{199}$Hg$^+$ } \newcommand{\Hgns}{$^{199}$Hg$^+$} \newcommand{\ratioName}{$\nu_{Al^+}/\nu_{Hg^+}$ } \newcommand{\alphadotConstraint}{$\dot{\alpha}/\alpha = (-1.6 \pm 2.4) \times 10^{-17} /$year} We measure the ratio of aluminum and mercury single-ion optical clock frequencies with a fractional uncertainty of \uncertaintyAlHg, comprising a statistical measurement uncertainty of \uncertaintyStat, and systematic uncertainties of \uncertaintyHg$ $ and \uncertaintyAl$ $ in the mercury and aluminum frequency standards, respectively. This frequency ratio is the best known physical constant that is not a simple integer. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant of \alphadotConstraint.