Absolute frequency measurements of the D ₁ lines in ³⁹ K, ⁸⁵ Rb, and ⁸⁷ Rb with ∼ 0.1 ppb uncertainty

We report values for the D 1 -line frequencies with 0.13 ppb uncertainty in the alkali atoms 39 K, 85 Rb, and 87 Rb. The frequencies are measured using an evacuated ring-cavity resonator whose length is calibrated against a reference laser locked to the D 2 line in 87 Rb. The measured frequencies, along with sub-ppb measurement of the atomic masses reported previously, form important links in a possible high-precision determination of the fine-structure constant using the photon-recoil shift measured in an atom interferometer. We also obtain, with improved precision, the hyperfine-coupling constants in the P 1/2 state of these atoms, and the fine-structure interval in the 5 P state of Rb.