Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb

With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of $2\times {10}^{-13} \mathrm{in} 5 \mathrm{s}$, to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the ${\mathrm{Hg}}^{+}$ clock transition with an improvement in accuracy of $\sim {10}^5$ compared with its best previous measurement.