Optical clocks with accuracy validated at the 19th digit

TL;DR

This paper presents a detailed evaluation of systematic uncertainties in two $^{176}$Lu$^+$ optical clocks, achieving unprecedented accuracy levels validated through direct comparison, demonstrating stability and agreement at the 19th digit.

Contribution

It provides the first comprehensive uncertainty analysis and direct frequency comparison of $^{176}$Lu$^+$ optical clocks at the 10^-19 level.

Findings

Total systematic uncertainty around 1.1-1.4×10^-19.

Relative frequency agreement within 2.4×10^-19.

Measurement stability of 4.8×10^-16 over time.

Abstract

We report a comprehensive evaluation of all known sources of systematic uncertainty for two independent $^{176}$Lu$^+$ single-ion optical references, finding total systematic uncertainty of $1.1\times10^{-19}$ and $1.4\times10^{-19}$ for the two individual systems and $9.6\times10^{-20}$ for the difference. Through direct comparison via correlation spectroscopy, we demonstrate a relative frequency agreement of $-2.4\pm(5.7)_\mathrm{stat}\pm(1.0)_\mathrm{sys}\times10^{-19}$, where `stat' and `sys' indicate the statistical and systematic uncertainty, respectively. The comparison uncertainty is statistically limited after approximately 200 hours of averaging with a measurement instability of $4.8\times10^{-16}(\tau/\mathrm{s})^{-1/2}$.