Frequency evaluation of the doubly forbidden ${}^1{S}_0\to {}^3{P}_0$ transition in bosonic ${}^{174}\mathrm{Yb}$

We report an uncertainty evaluation of an optical lattice clock based on the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ transition in the bosonic isotope ${}^{174}\mathrm{Yb}$ by use of magnetically induced spectroscopy. The absolute frequency of the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ transition has been determined through comparisons with optical and microwave standards at NIST. The weighted mean of the evaluations is $\nu \left({}^{174}\mathrm{Yb}\right)=518294025309217.8\left(0.9\right)\mathrm{Hz}$. The uncertainty due to systematic effects has been reduced to less than $0.8\mathrm{Hz}$, which represents $1.5\times {10}^{-15}$ in fractional frequency.

Figure 1

(Color online) Systematic shifts of the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ transition in Yb optical lattice clock. (a) Measurement of the second-order Zeeman shift. The second-order coefficient is evaluated $\beta =-6.12\left(10\right)\mathrm{Hz}∕{\mathrm{mT}}^2$. (b) Probe ac linear Stark shift. The coefficient $\kappa =15\left(3\right)\mathrm{mHz}∕(\mathrm{mW}∕{\mathrm{cm}}^2)$ is in agreement with the theoretical estimation (see text). (c) Density shift. The data points are consistent with zero density shift with a total deviation of $0.6\mathrm{Hz}$. (d) Servo error. The frequency offset due to uncompensated linear drift of the reference cavity is shown $[\mathrm{slope}=1.82(10)\mathrm{Hz}∕(\mathrm{Hz}∕\mathrm{s}\left)\right]$. With periodic manual correction of the feed-forward system used to remove the linear cavity drift this uncertainty can be made negligible.

Figure 2

(Color online) Frequency comparison of ${}^{174}\mathrm{Yb}$ against a maser calibrated to NIST-F1 (left) and ${\mathrm{Hg}}^{+}$ (right) through use of the optical fequency comb [9, 10]. Histograms and Allan deviation generated from series of $1\mathrm{s}$ gate interval frequency counts. The linear fit on the two Allan deviations give a slope of $2\times {10}^{-13}{\tau }^{-1∕2}$ and $5.5\times {10}^{-15}{\tau }^{-1∕2}$, respectively. The statistical uncertainties for the two measurements are 0.9 and $0.10\mathrm{Hz}$.

Figure 3

(Color online) Frequency evaluation of Yb clock transition. Two measurements were against ${\mathrm{Hg}}^{+}$ $(•)$ and the other two measurements were against a calibrated maser $(▲)$. The weighted mean of all the evaluations is $\nu \left({}^{174}\mathrm{Yb}\right)=518294025309217.8\left(0.9\right)\mathrm{Hz}$ (shaded area is the one $\sigma$ confidence interval).