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Volume 591, Pages 564 569 (2021) Cite this article

Atomic clocks are critical to a wide variety of technologies and experiments, including basic physics testing1. Clocks that operate at optical frequencies have now shown fractional stability and reproducibility at the 10-18 level, two orders of magnitude above their microwave predecessors2. Frequency ratio measurements between optical clocks are the basis for many applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has been largely unchanged for more than a decade3,4,5. Here we operate a network of optical clocks based on 27Al (Ref. 6), 87Sr (Ref. 7) and 171Yb (Ref. 8) and measure their frequency ratios with fracture uncertainties at or below 8 × 10 ×? 18. Taking advantage of this precision, we derive improved restrictions for the possible coupling of ultralight bosonic dark matter to standard model fields9,10. Our optical clock network not only uses fiber optics11, but also a 1.5 kilometer open space connection12,13. This progress in the measurement of the frequency ratio forms the basis for future networks of mobile, airborne and remote-controlled optical clocks, with which physical laws1 are tested, relativistic geodesy is carried out14 and international time measurement is significantly improved15.

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We thank J. Bergquist, E. Clements, A. Hankin, S. Kolkowitz, J. Scott, and B. Toman for technical contributions, and A. Possolo, C. Sanner, and A. Wilson for carefully reading the manuscript . This work was supported by the National Institute for Standards and Technology, the Agency for Advanced Defense Research Projects, the Air Force Scientific Research Agency, the National Science Foundation (NSF Grant No. PHY-1734006), and the Bureau of Naval Research (ONR Grant) No. N00014 -18-1-2634), NASA Fundamental Physics, and a Department of Energy, Office of Science, HEP QuantISED Award.

Kyle Beloy, Martha I. Bodine, Samuel M. Brewer, Jwo-Sy Chen, Scott A Diddams, Robert J. Fasano, Tara M. Fortier, Youssef S. Hassan, David B. Hume Colin J. Kennedy, Isaac Khader, Amanda Koepke, David R. Leibrandt, Holly Leopardi, Andrew D. Ludlow, William F. McGrew , Nathan R. Newbury, Daniele Nicolodi, Eric Oelker Thomas E. Parker, Stefania Romisch, Stefan A. Schäffer, Jeffrey A. Sherman, Laura C. Sinclair, William C. Swann, Jian Yao, Jun Ye & Xiaogang Zhang

Jwo-Sy Chen, Scott A. Diddams, Robert J. Fasano, Youssef S. Hassan, David R. L eibrandt, Holly Leopardi, William F. McGrew, Daniele Nicolodi, Jun Ye & Xiaogang Zhang

All authors contributed to the design of the experiment, the data acquisition and the revision of the manuscript. During the measurement campaign, the Al-Clock operation was checked by S.M.B., J.-S.C., D.B.H. and D. R. L .; The Sr cycle operation has been developed by T.B., S.L.B., D.K., C.J.K., W.R.M., E.O., J.M.R., L.S. and J. Ye; The Yb cycle operation was developed by K.B., R.J.F., Y.S.H., A.D.L., W.F.M., D.N., S.A.S. and X.Z .; The operation of the comb metrology laboratory was carried out by T.M.F. and H. L .; The maser operation and the comparison with UTC-NIST were made by T.E.P., S.R., J.A.S. and J. Yao; The operation of the O-TWTFT system including the free space connection has been reviewed by M.I.B., J.-D.D., S.A.D., I.K., N.R.N., L.C.S. and W. C. S .; Network connections without the free space connection have been made by H.L., W.R.M., E.O. and J.M.R. Ratio data analysis and manuscript preparation were carried out by T.M.F., D.B.H., D.K., C.J.K., A.K., H.L., L.C.S. and X.Z.

correspondence

Tara M. Fortier or David B. Hume or Colin J. Kennedy or Amanda Koepke or Holly Leopardi or Laura C. Sinclair or Xiaogang Zhang.

Peer-reviewed information Nature thanks Andrei Derevianko, Nils Nemitz, and the other anonymous reviewers for their contribution to the peer review of this work. Peer-reviewed reports are available.

Editor’s note Springer Nature remains neutral with regard to jurisdiction claims in published maps and institutional affiliations.

The Al-ion optical clock (shaded blue area), the Yb optical clock Lattice clock (orange shaded area), the Er: fiber comb (light gray shaded area), and Ti: S comb (light gray shaded area) are located in Building 81 of NIST. The optical lattice clock Sr (pink shaded area) is located in the basement of JILA. The open space connection (shaded gray area) consists of two parts (separated by the dashed line): one part is located in the penthouse of NIST Building 1 and another part is located on the 11th floor of the Gamow Tower at the University of Colorado. The Er: Fiber Comb and the Ti: S Comb at NIST are tied to the Yb optical clock. The Er: fiber comb in the Sr optical clock laboratory is bound to the Si cavity and is used to transfer the stability of the Si cavity to the Sr clock laser. Free space Er: fiber combs are bound by the Er: fiber comb at NIST and the optical Sr clock through the Si cavity to the optical Yb clock. All AOM frequencies in the network relate to a hydrogen maser at NIST, which is transmitted to JILA via a fiber optic link. The frequency shifts of optical clocks due to calibrated systematic effects are added to the calculations of the optical frequency ratio during post-processing. FNC, fiber noise reduction. In the lower right key: f0, offset frequency of the carrier envelope; fb, beat note frequency; Tis, Ti: sapphire; fsp, free storage space.

The recorded data include all measurements that were carried out under the nominal operating conditions in the course of the measurement campaign with the following total measurement times: 165,240 s, 94,760 s and 167,140 s for Al / Yb, Al / Sr and Yb / Sr. For the Al / Yb ratio, in addition to the data that contributed to the final ratio, we include two additional days of data (February 27, 2018 and March 2, 2018) for evaluating the second order Al Zeeman displacement as used have been described in ref. 6. Although these data sets were collected under very similar experimental conditions, they are excluded from the frequency ratio estimation in order to avoid a statistical correlation between the systematic displacement assessment and the frequency ratio measurement. Since the data was recorded over many months in short segments, the time series is dominated by dead times, so that the noise spectrum cannot be clearly identified. Adjustments (solid lines) use a white frequency noise model: ({ sigma} _ {y} ( tau) = { sigma} _ {1s} / {( tau / s)} ^ {1/2} ) , where Ï ?? 1s is the extrapolated 1s instability. This includes all data that exceeds the container size of = ?? = 100 s, where the weights correspond to the number of containers that contribute to each point. Although this is not directly related to stability, the total systematic uncertainty assessed for each ratio is indicated by a corresponding dashed line as a reference. Error bars indicate 68% confidence intervals based on a white frequency noise model.

a, Posterior distributions for the ratio values Î¼ (top row), expressed as a fractional offset from the currently recommended CIPM values15, and for the inter-day variability Î¾ ( bottom row). Left column, Al / Yb ratio; middle column, ratio Al / Sr; right column, ratio Yb / Sr. The blue dashed lines indicate our estimate for these parameters, the rear mean. The shaded areas and blue lines at the bottom of each graph indicate the 95% believable intervals, and the red dotted lines indicate the static uncertainties due to systematic effects. The posterior distributions for Î¾ have a mass that focuses on values closer to zero and latitudes comparable to their means. Further comparison days would be required to further restrict these parameters. b, previous distribution for Î¾. c, trace diagrams for the inter-day variability Î¾ for the Al / Yb measurements. The x-axis is the MCMC iteration number (plotting every 1000th sample) and the y-axis is the value of the parameter. Trace plots are used as a convergence diagnosis for MCMC. These graphs show that the chains mix well.

a, Al / Sr versus Al / Yb; b, Al / Sr versus Yb / Sr; and c, Al / Yb versus Yb / Sr. The data are offset by their mean and error bars account for known correlations between the x and y uncertainties as described in the methods. All days with simultaneous ratio measurements from each pair are recorded. There is no statistically significant linear relationship between these ratios, indicating that the present clock data, with only seven days of data overlapping, is not precise enough to identify a source of daily variation. The slopes (dashed black lines) and 95% confidence intervals (shaded areas) for the three graphs are: a, 0.17 (0.08, 0.53), b, 0.34 (0.034). 1.90, 1.19) and c 1.07 (3.09, 0.72).

This file contains (1) measurement overview and (2) ratio calculations, including supplementary Tables 1-3 and additional references .

Collaboration of the Boulder Optical Atomic Clock Network (BACON) *., Beloy, K., Bodine, MI et al. 18-digit accuracy frequency ratio measurements using an optical clock network.

Nature 591, 564 & ndash; 569 (2021). https://doi.org/10.1038/s41586-021-03253-4

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