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

## TL;DR

This paper presents a detailed uncertainty evaluation of an $^{171}$Yb optical lattice clock, achieving a fractional uncertainty of 3.6×10⁻¹⁶, by refining measurements of light and magnetic field shifts to improve clock accuracy.

## Contribution

The study improves the accuracy of sensitivity coefficients for hyperpolarizability and Zeeman shifts, enhancing the systematic uncertainty evaluation of Yb lattice clocks.

## Key findings

- Total fractional uncertainty of 3.6×10⁻¹⁶ achieved.
- Improved sensitivity coefficients for hyperpolarizability and Zeeman shifts.
- Refined measurements reduce systematic uncertainties in Yb lattice clocks.

## Abstract

We report an uncertainty evaluation of an $^{171}$Yb optical lattice clock with a total fractional uncertainty of $3.6\times10^{-16}$, 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 $\mathrm{6s^{2}\,^{1}S_{0}-6s6p\,^{3}P_{0}}$ 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 $\mathrm{6s6p^{3}P_{0}-6s8p^{3}P_{0}}$, $\mathrm{6s8p^{3}P_{2}}$, and $\mathrm{6s5f^{3}F_{2}}$. The obtained values are $d=-1.1(4)$ $\mathrm{\mu}$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.