Absolute Frequency Measurements of theHg+and Ca Optical Clock Transitions with a Femtosecond Laser

Abstract

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 ${f}_{\mathrm{Hg}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1064721609899143(10)\mathrm{Hz}$ and ${f}_{\mathrm{Ca}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}455986240494158(26)\mathrm{Hz}$, 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 $|(\ensuremath{\partial}{f}_{\mathrm{Ca}}/\ensuremath{\partial}t){/f}_{\mathrm{Ca}}|\ensuremath{\le}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\mathrm{yr}}^{\ensuremath{-}1}$ and $|(\ensuremath{\partial}{f}_{\mathrm{Hg}}/\ensuremath{\partial}t){/f}_{\mathrm{Hg}}|\ensuremath{\le}30\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\mathrm{yr}}^{\ensuremath{-}1}$.