Direct measurement of the frequency ratio for Hg and Yb optical lattice clocks and closure of the Hg/Yb/Sr loop

We performed the first direct measurement of the frequency ratio between a mercury ( 199 Hg) and an ytterbium ( 171 Yb) optical lattice clock to find ν Hg / ν Yb = 2.177 473 194 134 565 07(19) with the fractional uncertainty of 8.8 × 10 −17 . The ratio is in excellent agreement with expectations from the ratios ν Hg / ν Sr and ν Yb / ν Sr obtained previously in comparisons against a strontium ( 87 Sr) optical lattice clock. The completed closure ( ν Hg / ν Yb )( ν Yb / ν Sr )( ν Sr / ν Hg ) − 1 = 0.4(1.3) × 10 −16 tests the frequency reproducibility of the optical lattice clocks beyond what is achievable in comparison against the current realization of the second in the International System of Units (SI).