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Frequency ratio measurements at 18-digit accuracy using an optical clock network

Nature volume 591, pages 564–569 (2021)Cite this article

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Abstract

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics1. Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10−18 level, two orders of magnitude beyond their microwave predecessors2. Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained 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 fractional uncertainties at or below 8 × 10−18. Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields9,10. Our optical clock network utilizes not just optical fibre11, but also a 1.5-kilometre free-space link12,13. This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws1, perform relativistic geodesy14 and substantially improve international timekeeping15.

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Fig. 1: System overview of the Boulder Atomic Clock Optical Network (BACON).
Fig. 2: Ratio measurement results.
Fig. 3: Comparison of measured frequency ratios with previous results.
Fig. 4: Constraints on ultralight dark matter.

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Data availability

The data presented here are available from the corresponding authors on reasonable request.

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Acknowledgements

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 careful reading of the manuscript. This work was supported by the National Institute of Standards and Technology, the Defense Advanced Research Projects Agency, the Air Force Office for Scientific Research, the National Science Foundation (NSF grant no. PHY- 1734006), the Office of Naval Research (ONR grant no. N00014-18-1-2634), NASA Fundamental Physics, and a Department of Energy, Office of Science HEP QuantISED award.

Author information

Author notes

  1. Samuel M. Brewer

    Present address: Department of Physics, Colorado State University, Fort Collins, CO, USA

  2. Sarah L. Bromley

    Present address: Department of Physics, Durham University, Durham, UK

  3. Jwo-Sy Chen

    Present address: IonQ Inc., College Park, MD, USA

  4. Holly Leopardi

    Present address: Space Dynamics Laboratory, North Logan, UT, USA

  5. Stefania Romisch

    Present address: Northrup Grumman Mission Systems, Woodland Hills, CA, USA

  6. Stefan A. Schäffer

    Present address: Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Amsterdam, The Netherlands

Authors and Affiliations

  1. National Institute of Standards and Technology, Boulder, CO, USA

    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

  2. JILA, University of Colorado, Boulder, CO, USA

    Tobias Bothwell, Sarah L. Bromley, Dhruv Kedar, Colin J. Kennedy, William R. Milner, Eric Oelker, John M. Robinson, Lindsay Sonderhouse & Jun Ye

  3. Department of Physics, University of Colorado, Boulder, CO, USA

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

  4. Consultation OctoSig Inc., Quebec City, Quebec, Canada

    Jean-Daniel Deschênes

Consortia

Boulder Atomic Clock Optical Network (BACON) Collaboration*

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

Contributions

All authors contributed to the design of the experiment, collection of data and revision of the manuscript. During the measurement campaign, Al+ clock operation was conducted by S.M.B., J.-S.C., D.B.H. and D.R.L.; Sr clock operation was conducted by T.B., S.L.B., D.K., C.J.K., W.R.M., E.O., J.M.R., L.S. and J. Ye; Yb clock operation was conducted by K.B., R.J.F., Y.S.H., A.D.L., W.F.M., D.N., S.A.S. and X.Z.; comb metrology laboratory operation was conducted by T.M.F. and H.L.; maser operation and comparison with UTC-NIST was conducted by T.E.P., S.R., J.A.S. and J. Yao; O-TWTFT system operation including the free-space link was conducted by M.I.B., J.-D.D., S.A.D., I.K., N.R.N., L.C.S. and W.C.S.; network interconnections excluding the free-space link were maintained by H.L., W.R.M., E.O. and J.M.R. Ratio data analysis and preparation of the manuscript were performed by T.M.F., D.B.H., D.K., C.J.K., A.K., H.L., L.C.S. and X.Z.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Andrei Derevianko, Nils Nemitzand the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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

Extended data figures and tables

Extended Data Fig. 1 Diagram of the Boulder Atomic Clock Optical Network (BACON).

The Al+ ion optical clock (blue shaded area), the Yb optical lattice clock (orange shaded area), the Er:fibre comb (light grey shaded area) and the Ti:S comb (light grey shaded area) are located in Building 81 of NIST. The Sr optical lattice clock (pink shaded area) is located in the basement of JILA. The free space link (grey shaded area) includes two parts (split by the dashed line): one part is located in the NIST Building 1 penthouse and another part is located at the 11th floor of the Gamow tower at the University of Colorado. The Er:fibre comb and the Ti:S comb at NIST are locked to the Yb optical clock. The Er:fibre comb in the Sr optical clock lab is locked to the Si cavity and is used to transfer the Si cavity stability to the Sr clock laser. Free space Er:fibre combs are locked to the Yb optical clock through the Er:fibre comb at NIST and the Sr optical clock through the Si cavity, respectively. All AOM frequencies in the network are referenced to a hydrogen maser at NIST, which is transferred to JILA through an optical fibre link. The frequency shifts of optical clocks due to calibrated systematic effects are added to the optical frequency ratio calculations in post-processing. FNC, fibre-noise cancellation. In key at bottom right: f0, carrier-envelope offset frequency; fb, beatnote frequency; Tis, Ti:sapphire; fsp, free space.

Extended Data Fig. 2 Long-term stability of concatenated ratio data as characterized by the overlapping Allan deviation.

The data plotted include all measurements that were taken at the nominal operating conditions over the course of the measurement campaign with total measurement durations as follows: 165,240 s, 94,760 s and 167,140 s for Al+/Yb, Al+/Sr and Yb/Sr, respectively. For the Al+/Yb ratio, in addition to the data that contributed to the final ratio, we include two extra days of data (27 February 2018 and 2 March 2018) that were used in the evaluation of the Al+ second-order Zeeman shift as described in ref. 6. Although acquired in very similar experimental conditions, these datasets are excluded from frequency ratio estimate to avoid statistical correlation between the systematic shift evaluation and the frequency ratio measurement. Because the data were taken in short segments over many months, the time series is dominated by periods of dead-time such that the noise spectrum cannot be identified unambiguously. Fits (solid lines) use a white frequency noise model: \({\sigma }_{y}(\tau )={\sigma }_{1s}/{(\tau /s)}^{1/2}\), where σ1s is the extrapolated 1-s instability. These include all data beyond the τ = 100 s bin size with weights equal to the number of bins contributing to each point. Although it is not directly related to the stability, for reference, the total systematic uncertainty evaluated for each ratio is indicated by a corresponding dashed line. Error bars indicate 68% confidence intervals based on a white frequency noise model.

Extended Data Fig. 3 Results of the Bayesian analysis.

a, Posterior distributions for the ratio values μ (top row) expressed here as a fractional offset from the current recommended CIPM values15, and for the between-day variability ξ (bottom row). Left column, ratio Al+/Yb; middle column, ratio Al+/Sr; right column, ratio Yb/Sr. The blue dashed lines denote our estimate for these parameters, the posterior mean. The shaded areas and blue lines on the bottom of each plot denote the 95% credible intervals and the red dotted lines denote the static uncertainties due to systematic effects. The posterior distributions for ξ have mass concentrated on values closer to zero and widths comparable to their means. More comparison days would be needed to further constrain these parameters. b, Prior distribution for ξ. c, Trace plots for the between-day variability ξ for the Al+/Yb measurements. The x axis is the MCMC iteration number (plotting every 1,000th sample) and the y axis is the value of the parameter. Trace plots are used as a convergence diagnostic for MCMC; these plots show that the chains are mixing well.

Extended Data Fig. 4 Correlation analysis for daily measurements of all ratio pairs.

a, Al+/Sr versus Al+/Yb; b, Al+/Sr versus Yb/Sr; and c, Al+/Yb versus Yb/Sr. 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 plotted. There is no statistically significant linear relationship between these ratios, indicating that the present clock data, with only seven overlapping days of data, are not precise enough to identify a source of daily fluctuations. The slopes (dashed black lines) and 95% confidence intervals (shaded areas) for the three plots are: a, 0.17 (−0.08, 0.53), b, −0.34 (−1.90, 1.19), and c, −1.07 (−3.09, 0.72).

Extended Data Table 1 Clock operating parameters
Full size table
Extended Data Table 2 Numerical results for μ and ξ
Full size table
Extended Data Table 3 Fractional ratio uncertainties
Full size table

Supplementary information

Supplementary Information

This file contains (1) Measurement overview, and (2) Ratio calculations, including Supplementary Tables 1-3 and additional references.

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Boulder Atomic Clock Optical Network (BACON) Collaboration*. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021). https://doi.org/10.1038/s41586-021-03253-4

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