Comparing a mercury optical lattice clock with microwave and optical frequency standards

In this paper we report the evaluation of an optical lattice clock based on neutral mercury down to a relative uncertainty of $1.7\times 10^{-16}$. Comparing this characterized frequency standard to a Cs atomic fountain we determine the absolute frequency of the $^1S_0 \rightarrow \phantom{}^3P_0$ transition of $^{199}$Hg as $\nu_{\mathrm{Hg}} = 1 128\,575\,290\,808\,154.62\,$Hz $\pm\,0.19\,$Hz (statistical) $\pm\,0.38\,$Hz (systematic), limited solely by the realization of the SI second. Furthermore, by comparing the mercury optical lattice clock to a Rb atomic fountain, we determine for the first time to our knowledge the ratio between the $^{199}$Hg clock transition and the $^{87}$Rb ground state hyperfine transition. Finally we present a direct optical to optical measurement of the $^{199}$Hg/$^{87}$Sr frequency ratio. The obtained value of $\nu_{\mathrm{Hg}}/\nu_{\mathrm{Sr}}=2.629\,314\,209\,898\,909\,15$ with a fractional uncertainty of $1.8\times10^{-16}$ is in excellent agreement with the same measurement obtained by Yamanaka et al. (arXiv:1503.07941). This makes this frequency ratio one of the few physical quantities agreed upon by different laboratories to this level of uncertainty. Frequency ratio measurements of the kind of those reported in this paper have a strong impact for frequency metrology but also for fundamental physics as they can be used to monitor putative variations of fundamental constants.