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    Atomic Clock Frequency Ratios with Fractional Uncertainty ≤3.2×10−18

    Alexander Aeppli1,2,*, Willa J. Arthur-Dworschack2,3, Kyle Beloy3, Caitlin M. Berry4, Tobias Bothwell3,†, Angela Folz2,4, Tara M. Fortier3, Tanner Grogan2,3, Youssef S. Hassan2,3,* et al. (BACON Collaboration)

    Youssef S. Hassan2,3,*, Zoey Z. Hu1,2, David B. Hume2,3, Benjamin D. Hunt2,3, Kyungtae Kim1,2,‡, Amanda Koepke4, Dahyeon Lee1,2, David R. Leibrandt2,3,§, Ben Lewis1,2, Andrew D. Ludlow2,3,5, Mason C. Marshall3,∥, Nicholas V. Nardelli2,3,¶,**, Harikesh Ranganath3,5, Daniel A. Rodriguez Castillo2,3, Jeffrey A. Sherman3, Jacob L. Siegel2,3,††, Suzanne Thornton4,6, William Warfield1,2, and Jun Ye1,2 (BACON Collaboration)

    • *Present address: Atom Computing, Boulder, Colorado, USA.
    • †Present address: Infleqtion, Boulder, Colorado, USA.
    • ‡Contact author: kyungtae.kim@colorado.edu
    • §Present address: Department of Physics and Astronomy, University of California, Los Angeles, California, USA.
    • ∥Contact author: mason.marshall@nist.gov
    • Present address: The University of Adelaide, Adelaide, South Australia, Australia.
    • **Contact author: nicholas.nardelli@colorado.edu
    • ††Contact author: jacob.siegel-1@colorado.edu

    Phys. Rev. Lett. 137, 033201 – Published 14 July, 2026

    DOI: https://doi.org/10.1103/g865-9mk1

    Abstract

    We report high-precision frequency ratio measurements between optical atomic clocks based on Al+27, Yb171, and Sr87. With total fractional uncertainties at or below 3.2×10−18, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in Sr87 ratios at approximately 1×10−16 and the Al+/Yb ratio at 1.6×10−17 in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key upgrade from our previous work is the use of a common ultrastable reference delivered to all clocks via a 3.6-km phase-stabilized fiber link between two institutions, enabling better accuracy and stability in frequency transfer. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2–3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10−16 at 1 s. Identifying individual clock stabilities with a three-corner-hat measurement, we demonstrate the most stable optical lattice and trapped-ion clocks used in a multispecies comparison. By enabling faster comparisons, this stability will improve sensitivity to nonwhite noise processes and other underlying limits of state-of-the-art optical frequency standards.

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