Uncertainty evaluation of an ${}^{171}$Yb optical lattice clock at NMIJ

Abstract

We report an uncertainty evaluation of an ${}^{171}$Yb optical lattice clock with a total fractional uncertainty of $3.6\times 10^{-16}$, which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the $6{\mathrm{s}}^2{}^1{\mathrm{S}}_0-6s6p{}^3{\mathrm{P}}_0$ clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift $d$ incorporated in a widely-used light shift model by RIKEN and the second-order Zeeman shift $a_{\mathrm{Z}}$ are improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient $d$ is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions $6s6{\mathrm{p}}^3{\mathrm{P}}_0-6s8{\mathrm{p}}^3{\mathrm{P}}_0$, $6s8{\mathrm{p}}^3{\mathrm{P}}_2$, and $6s5{\mathrm{f}}^3{\mathrm{F}}_2$. The obtained values are $d=-1.1(4)$ $\mu$Hz and $a_{\mathrm{Z}}=-6.6(3)$ Hz/mT${}^2$. These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

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