Lu⁺ optical frequency references with accuracy verified at the 19th digit

Optical atomic frequency references¹ have far surpassed their microwave frequency predecessors, leading to an anticipated redefinition of the SI (International System of Units) second². However, as the scientific community seeks consensus on a new standard, and several state-of-the-art optical standards now report evaluated fractional uncertainties below 10^-18, verification by same-species comparisons to comparable levels remains an outstanding challenge. Here we report two ¹⁷⁶Lu⁺ single-ion optical frequency references, each with evaluated fractional frequency uncertainty near 1 × 10^-19, which are directly compared by correlation spectroscopy and demonstrate agreement, with a measured relative frequency difference of [-0.1 ± (5.7)_stat ± (1.0)_sys] × 10^-19, where 'stat' and 'sys' indicate the statistical and systematic uncertainty, respectively. Our optical references have been comprehensively assessed with evaluated uncertainties below 10^-18, supported by a same-species comparison of independent systems to the 5.7 × 10^-19 level. This accuracy, achieved in practical room-temperature systems, will contribute to improving international timekeeping and towards chronometric levelling^3,4 at the millimetre scale, as well as tests of fundamental physics⁵ such as Lorentz invariance⁶, general relativity⁷, searches for dark matter^8,9 and variation of fundamental constants^10,11.