Absolute frequency measurement of the In⁺ clock transition with a mode-locked laser

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The absolute frequency of the In⁺ 5s² ¹S₀ - 5s5p³P₀ clock transition at 237 nm was measured with an accuracy of 1.8 parts in 10¹³. Using a phase-coherent frequency chain, we compared the ¹S₀ - ³P₀ transition with a methane-stabilized He-Ne laser at 3.39 μm which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the He-Ne standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In⁺ clock transition was found to be 1 267 402 452 899.92 (0.23) kHz, the accuracy being limited by the uncertainty of the He-Ne laser reference. This represents an improvement in accuracy of more than 2 orders of magnitude on previous measurements of the line and now stands as the most accurate measurement of an optical transition in a single ion.