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 (Hg) and an ytterbium (Yb) optical lattice clock to find ν/ν = 2.177 473 194 134 565 07(19) with the fractional uncertainty of 8.8 × 10. The ratio is in excellent agreement with expectations from the ratios ν/ν and ν/ν obtained previously in comparisons against a strontium (Sr) optical lattice clock. The completed closure (ν/ν)(ν/ν)(ν/ν) - 1 = 0.4(1.3) × 10 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).