${}^{176}$Lu${}^{+}$ clock comparison at the ${10}^{-18}$ level via correlation spectroscopy

We experimentally demonstrate agreement between two ${}^{176}$Lu${}^{+}$ frequency references using correlation spectroscopy. From a comparison at different magnetic fields, we obtain a quadratic Zeeman coefficient of $-4.89264(88)\mathrm{H}\mathrm{z}\mathrm{/}\mathrm{m}{\mathrm{T}}^2$, which gives a corresponding fractional frequency uncertainty contribution of just $2.5\times {10}^{-20}$ for comparisons at typical operating fields of 0.1,mT. A subsequent comparison with both systems at 0.1,mT, demonstrates a fractional frequency difference of $(-2.0\pm (3.7{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm (0.9{)}_{\mathrm{s}\mathrm{y}\mathrm{s}})\times {10}^{-18}$, where stat' and sys’ indicate statistical and systematic uncertainty, respectively.