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arXiv:2512.21428

Atomic clock frequency ratios with fractional uncertainty $\leq 3.2 \times 10^{-18}$

Alexander Aeppli, Willa J. Arthur-Dworschack, Kyle Beloy, Caitlin M. Berry, Tobias Bothwell, Angela Folz, Tara M. Fortier, Tanner Grogan, Youssef S. Hassan, Zoey Z. Hu, David B. Hume, Benjamin D. Hunt, Kyungtae Kim, Amanda Koepke, Dahyeon Lee, David R. Leibrandt, Ben Lewis, Andrew D. Ludlow, Mason C. Marshall, Nicholas V. Nardelli, Harikesh Ranganath, Daniel A. Rodriguez Castillo, Jeffrey A. Sherman, Jacob L. Siegel, Suzanne Thornton, William Warfield, Jun Ye

physics.atom-phquant-phSubmitted Dec 24, 2025• Announced Dec 26, 2025
v1 · Dec 24, 2025v2 · Jul 16, 2026
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Abstract

We report high-precision frequency ratio measurements between optical atomic clocks based on $^{27}$Al$^+$, $^{171}$Yb, and $^{87}$Sr. With total fractional uncertainties at or below $3.2 \times 10^{-18}$, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in $^{87}$Sr ratios at approximately $1\times10^{-16}$ and the Al$^+$/Yb ratio at $1.6\times10^{-17}$ in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this 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. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of $1.3 \times 10^{-16}$ at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.

Comments
5 pages main text with 4 figures; 1 page and 1 figure end matter; 9 pages and 7 figures supplemental material

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Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18\leq 3.2 \times 10^{-18}≤3.2×10−18
We report high-precision frequency ratio measurements between optical atomic clocks based on 27^{27}27Al+^++, 171^{171}171Yb, and 87^{87}87Sr. With total fractional uncertainties at or below 3.2×10−183.2 \times 10^{-18}3.2×10−18, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in 87^{87}87Sr ratios at approximately 1×10−161\times10^{-16}1×10−16 and the Al+^++/Yb ratio at 1.6×10−171.6\times10^{-17}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 innovation in this 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. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10−161.3 \times 10^{-16}1.3×10−16 at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.
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An Al+^++ clock with 1.6×10−181.6\times10^{-18}1.6×10−18 systematic uncertainty and its frequency ratios
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Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two 87Sr^{87}\mathrm{Sr}87Sr lattice systems using a laser with a thermal noise floor of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with $\ensuremath{\sim}{10}^{3}$ atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be $\ensuremath{-}3.11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ with an uncertainty of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.
Atomic clocks occupy a unique position in measurement science, exhibiting higher accuracy than any other measurement standard and underpinning six out of seven base units in the SI system. By exploiting higher resonance frequencies, optical atomic clocks now achieve greater stability and lower frequency uncertainty than existing primary standards. Here, we report frequency ratios of the 27^{27}27Al+^++, 171^{171}171Yb and 87^{87}87Sr optical clocks in Boulder, Colorado, measured across an optical network spanned by both fiber and free-space links. These ratios have been evaluated with measurement uncertainties between 6×10−186\times10^{-18}6×10−18 and 8×10−188\times10^{-18}8×10−18, making them the most accurate reported measurements of frequency ratios to date. This represents a critical step towards redefinition of the SI second and future applications such as relativistic geodesy and tests of fundamental physics.
Interspecies clock comparison below 5×10−185 \times 10^{-18}5×10−18 uncertainty with a transportable clock
We report a measurement of the optical frequency ratio between the 2S1/2(F=0)^2\mathrm{S}_{1/2}(F=0)2S1/2​(F=0)--2F7/2(F=3){^2\mathrm{F}_{7/2}(F=3)}2F7/2​(F=3) electric-octupole (E3) transition of 171^{171}171Yb+^{+}+ and the 1S0^1\mathrm{S}_01S0​--3P0{^3\mathrm{P}_0}3P0​ transition of 87^{87}87Sr, νYb+/νSr=1.495 991 618 544 900 588 1(65)ν_{\mathrm{Yb}^{+}}/ν_\mathrm{Sr} = 1.495\,991\,618\,544\,900\,588\,1(65)νYb+​/νSr​=1.4959916185449005881(65). Reaching a fractional uncertainty of 4.3×10−184.3 \times 10^{-18}4.3×10−18, this result improves upon the previous best by more than a factor of three and is among the few that meet the requirements for interspecies clock comparisons specified by the roadmap towards the redefinition of the SI second. The comparison is between a transportable optical lattice clock and a stationary single-ion clock. It spans a period of nearly two years, during which the transportable clock was intermittently operated off-campus. The ratio was reproducibly measured during four separate campaigns, which are consistent within their statistical uncertainties. The results demonstrate reproducible 10−1810^{-18}10−18 level operation of the transportable clock and thus validate its application for chronometric geodesy and as a transfer standard for inter-institute clock comparisons, e.g., in the absence of optical fiber links.