Absolute Frequency Measurements of the ${\mathrm{Hg}}^{+}$ and Ca Optical Clock Transitions with a Femtosecond Laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the ${\mathrm{Hg}}^{+}$ and Ca optical standards with respect to the SI second. We find the transition frequencies to be $f_{\mathrm{Hg}}=1\mathrm{}064721609899143\left(10\right)\mathrm{Hz}$ and $f_{\mathrm{Ca}}=455\mathrm{}986240494158\left(26\right)\mathrm{Hz}$, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the ${\mathrm{Hg}}^{+}$ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of $|(\partial f_{\mathrm{Ca}}/\partial t){/f}_{\mathrm{Ca}}|\le 8\times {10}^{-14\mathrm{}}{\mathrm{yr}}^{-1\mathrm{}}$ and $|(\partial f_{\mathrm{Hg}}/\partial t){/f}_{\mathrm{Hg}}|\le 30\times {10}^{-14\mathrm{}}{\mathrm{yr}}^{-1\mathrm{}}$.