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

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Abstract
We report values for the D1-line frequencies with 0.13 ppb uncertainty in the alkali atoms 39K, 85Rb, and 87Rb. The frequencies are measured using an evacuated ring-cavity resonator whose length is calibrated against a reference laser locked to the D2 line in 87Rb. 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 P1/2 state of these atoms, and the fine-structure interval in the 5P state of Rb.