Frequency Ratio Measurements with 18-digit Accuracy Using a Network of Optical Clocks
Boulder Atomic Clock Optical Network, Collaboration, :, K. Beloy, Martha I. Bodine, Tobias Bothwell, Samuel M. Brewer, Sarah Bromley, Jwo-Sy Chen, Jean-Daniel Deschênes, Scott A. Diddams, Robert Fasano, Tara M. Fortier, Youssef S. Hassan, David B. Hume, Dhruv Kedar, Colin J. Kennedy, Isaac H. Khader, Koepke, Amanda, David R. Leibrandt, Holly Leopardi, Andrew D. Ludlow, William F. McGrew, William R. Milner, Nathan R. Newbury, Daniele Nicolodi, Eric Glenn Oelker, T.E. Parker, John Martin Robinson, Stefania Romisch, Stefan Alaric Schäffer, Jeff A. Sherman, Laura C. Sinclair, Lindsay Sonderhouse, William C. Swann, Jian Yao, Jun Ye, Xiaogang Zhang
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 $^{27}$Al$^+$, $^{171}$Yb and $^{87}$Sr 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 $6\times10^{-18}$ and $8\times10^{-18}$, 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.
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 27Al+, 171Yb and 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 6×10−18 and 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.
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.
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.
Cryogenic optical lattice clocks with a relative frequency difference of 1×10−18
Time and frequency are the most accurately measurable quantities, providing foundations for science and modern technologies. The accuracy relies on the SI (Systeme International) second that refers to Cs microwave clocks with fractional uncertainties at 10−16. Recent revolutionary progress of optical clocks aims to achieve 1×10−18 uncertainty, which however has been hindered by long averaging-times or by systematic uncertainties. Here, we demonstrate optical lattice clocks with 87Sr atoms interrogated in a cryogenic environment to address the blackbody radiation-induced frequency-shift, which remains the primary source of clocks' uncertainties and has initiated vigorous theoretical and experimental investigations. The quantum-limited stability for N∼1,000 atoms allows investigation of the uncertainties at 2×10−18 in two hours of clock operation. After 11 measurements performed over a month, the two cryo-clocks agree to within (−1.1±1.6)×10−18. Besides its contribution to fundamental science and the redefinition of the SI second, such a speedy comparison of accurate clocks provides a means for relativistic geodesy.
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.
Cryogenic optical lattice clocks with a relative frequency difference of 1×10−18
Time and frequency are the most accurately measurable quantities, providing foundations for science and modern technologies. The accuracy relies on the SI (Systéme International) second that refers to Cs microwave clocks with fractional uncertainties at 10−16. Recent revolutionary progress of optical clocks aims to achieve 1×10−18 uncertainty, which however has been hindered by long averaging-times or by systematic uncertainties. Here, we demonstrate optical lattice clocks with 87Sr atoms interrogated in a cryogenic environment to address the blackbody radiation-induced frequency-shift, which remains the primary source of clocks' uncertainties and has initiated vigorous theoretical and experimental investigations. The quantum-limited stability for N∼1,000 atoms allows investigation of the uncertainties at 2×10−18 in two hours of clock operation. After 11 measurements performed over a month, the two cryo-clocks agree to within (−1.1±1.6)×10−18. Besides its contribution to fundamental science and the redefinition of the SI second, such a speedy comparison of accurate clocks provides a means for relativistic geodesy.