Atomic Clock Frequency Ratios with Fractional Uncertainty ≤ 3.2 × 10 − 18
Alexander Aeppli, Willa J. Arthur-Dworschack, K. Beloy, Caitlin M. Berry, Tobias Bothwell, Angela Folz, Tara M. Fortier, Thomas M. Grogan, Youssef S. Hassan, Zoey Hu, David B. Hume, B. D. Hunt, Kyungtae Kim, Amanda A. Koepke, Dahyeon Lee, David R. Leibrandt, Ben Lewis, Andrew D. Ludlow, Mason C. Marshall, Nicholas V. Nardelli, Harikesh Ranganath, Daniel A. Rodriguez Castillo, Jeff A. Sherman, Jacob L. Siegel, Suzanne Thornton, William Warfield, Jun Ye
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 3.2×10^{-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 1×10^{-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.
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 3.2×10^{-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 1×10^{-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.
Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18
We report high-precision frequency ratio measurements between optical atomic clocks based on 27Al+, 171Yb, and 87Sr. 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 87Sr 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 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 1.3×10−16 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.
International atomic clock comparison achieving 5×10−18 uncertainty
Two single-ion optical clocks, located in the United Kingdom and in Germany, are compared remotely via a 2220\,km long optical fiber link. Both clocks are based on the 2S1/2(F=0)↔2F7/2(F=3) electric octupole (E3) transition in 171Yb+. Using more than 106 seconds of measurement data, we determine a fractional frequency difference of 1.0(4.8)×10−18, demonstrating agreement of the independently developed systems. To our knowledge, this constitutes the first international clock comparison reaching a fractional uncertainty below 5×10−18, an important milestone towards an anticipated optical redefinition of the SI second. The measurement uncertainty is dominated by that of the relativistic redshift correction between the two sites, which includes time-varying gravity potential differences. We exploit the large baseline between the two clocks to search for violations of Lorentz invariance. In the absence of statistically significant modulations, we improve constraints on the Robertson-Mansouri-Sexl parameter α by approximately a factor of five in the uncertainty, and provide limits on corresponding parameters within the Standard-Model Extension framework.
An Al+ clock with 1.6×10−18 systematic uncertainty and its frequency ratios
Advances in optical clocks motivate a redefinition of the second, requiring rigorous evaluations of systematic uncertainties and robust consistency among the clocks. Here, we report the full evaluation of the systematic frequency shifts of an 27Al+ single-ion clock, and the measurement of its absolute frequency and frequency ratio with a 87Sr optical lattice clock at PTB. The evaluated total systematic fractional frequency uncertainty is 1.6×10−18, mainly limited by the accuracy of the relevant atomic coefficients and by background gas collisions. The absolute frequency of the clock has been measured to be νAl+=1121015393207859.19(24)Hz, obtained by comparison with two primary caesium fountain clocks at PTB. The frequency ratio between the Al and Sr optical clocks has been determined to be νAl+/ν87Sr=2.611701431781462668(36), limited by the accuracy of the Sr clock. This ratio differs by 8.6σ and 1.2σ from the 2021 and 2025 frequency ratio published by the BACON collaboration, respectively. These results represent an important contribution toward a future redefinition of the second using optical clocks, and underscore the importance of independent measurements of clock-candidate frequency ratios across different institutions.
Interspecies clock comparison below 5×10−18 uncertainty with a transportable clock
We report a measurement of the optical frequency ratio between the 2S1/2(F=0)--2F7/2(F=3) electric-octupole (E3) transition of 171Yb+ and the 1S0--3P0 transition of 87Sr, νYb+/νSr=1.4959916185449005881(65). Reaching a fractional uncertainty of 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 10−18 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.
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 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 $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.
We report a single-ion optical atomic clock with a fractional frequency uncertainty of 5.5×10^{-19} and fractional frequency stability of 3.5×10^{-16}/sqrt[τ/s], based on quantum logic spectroscopy of a single ^{27}Al^{+} ion. A cotrapped ^{25}Mg^{+} ion provides sympathetic cooling and quantum logic readout of the ^{27}Al^{+}^{1}S_{0}↔^{3}P_{0} clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous ^{27}Al^{+} clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the rf ion trap, eliminating systematic uncertainty due to field orientation.