Helen S. Margolis

Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the 10 − 18 level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from 7.7 × 10 − 18 to 6.1 × 10 − 17 . Among the results, the Yb + 171 ( E 3 ) clocks at NPL and PTB demonstrated agreement within an uncertainty of 7.7 × 10 − 18 , marking the first international verification of two independently developed optical clocks below one part in 10 17 . The operation of the Hg 199 clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with Yb + 171 ( E 3 ) , Yb 171 , and Sr 87 optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.

Optical atomic clocks based on laser-cooled trapped ions and atoms have advanced rapidly over the past decade. With fractional frequency uncertainties now surpassing 10 ⁻¹⁸ , they are some of the most precise measurement tools ever built. Yet researchers are still pursuing new avenues of research to explore the fundamental limits to their stability, accuracy, and reproducibility. In this mini-review, we provide a survey of the current state of the art by describing the fundamental principles and techniques that underpin this progress, the architectures used to realize optical clocks, and the supporting laser technologies that are essential to their operation. We also examine the progress that has been made toward a redefinition of the second in the International System of Units and the inclusion of optical clocks into the global time and frequency metrology infrastructure. Finally, we discuss emerging applications of optical clocks and look at the prospects for making their precision more readily accessible to end users.

Optical clocks provide ultraprecise frequency references that are vital for international metrology as well as for tests of fundamental physics. To investigate the level of agreement between different clocks, we simultaneously measured the frequency ratios between ten optical clocks in six different countries, using fiber and satellite links. This is the largest coordinated comparison to date, from which we present a subset of 38 optical frequency ratios and an evaluation of the correlations between them. Four ratios were measured directly for the first time to our knowledge, while others had significantly lower uncertainties than previously achieved, supporting the advance toward a redefinition of the second and the use of optical standards for international time scales.

A full evaluation of the uncertainty budget for the ytterbium ion optical clock at the National Physical Laboratory (NPL) was performed on the electric octupole (E3) 2 S 1 / 2 → 2 F 7 / 2 transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of 2.2 × 10 − 18 . Furthermore, the absolute frequency of the E3 transition of the ¹⁷¹Yb⁺ ion was measured between 2019 and 2023 via a link to International Atomic Time (TAI) and against the local caesium fountain NPL-CsF2. The absolute frequencies were measured with fractional standard uncertainties between 3.7 × 10 − 16 and 1.1 × 10 − 15 , and all were in agreement with the 2021 BIPM recommended frequency.

This paper gives a detailed account of the analysis underpinning the 2021 update to the list of standard reference frequency values recommended by the International Committee for Weights and Measures. This update focused on a subset of atomic transitions that are secondary representations of the second (SRS) or considered as potential SRS. As in previous updates in 2015 and 2017, methods for analysing over-determined data sets were applied to make optimum use of the worldwide body of published clock comparison data. To ensure that these methods were robust, three independent calculations were performed using two different algorithms. The 2021 update differed from previous updates in taking detailed account of correlations among the input data, a step shown to be important in deriving unbiased frequency values and avoiding underestimation of their uncertainties. It also differed in the procedures used to assess input data and to assign uncertainties to the recommended frequency values, with previous practice being adapted to produce a fully consistent output data set consisting of frequency ratio values as well as absolute frequencies. These changes are significant in the context of an anticipated redefinition of the second in terms of an optical transition or transitions, since optical frequency ratio measurements will be critical for verifying the international consistency of optical clocks prior to the redefinition. In the meantime, the reduced uncertainties for optical SRS resulting from this analysis significantly increases the weight that secondary frequency standards based on these transitions can have in the steering of International Atomic Time.

This paper gives a detailed account of the analysis underpinning the 2021 update to the list of standard reference frequency values recommended by the International Committee for Weights and Measures (CIPM). This update focused on a subset of atomic transitions that are secondary representations of the second (SRS) or considered as potential SRS. As in previous updates in 2015 and 2017, methods for analysing over-determined data sets were applied to make optimum use of the worldwide body of published clock comparison data. To ensure that these methods were robust, three independent calculations were performed using two different algorithms. The 2021 update differed from previous updates in taking detailed account of correlations among the input data, a step shown to be important in deriving unbiased frequency values and avoiding underestimation of their uncertainties. It also differed in the procedures used to assess input data and to assign uncertainties to the recommended frequency values, with previous practice being adapted to produce a fully consistent output data set consisting of frequency ratio values as well as absolute frequencies. These changes are significant in the context of an anticipated redefinition of the second in terms of an optical transition or transitions, since optical frequency ratio measurements will be critical for verifying the international consistency of optical clocks prior to the redefinition. In the meantime, the reduced uncertainties for optical SRS resulting from this analysis significantly increases the weight that secondary frequency standards based on these transitions can have in the steering of International Atomic Time (TAI).

This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth’s gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10⁻¹⁸uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.

Main text: Six lasers from six national metrological institutes (NMIs) were compared in the year 2023 as part of the CCL-K11 ongoing key comparison, initiated by the 13th meeting of the Comité Consultative des Longueurs (CCL) in 2007. The absolute frequency of theses lasers was measured in three different node laboratories following the technical protocol for CCL-K11. All are practical realisations of the definition of the metre according to the MeP for the definition of the metre. Five standards are He-Ne-lasers stabilized on the f component of the R(127) 11-5 transitions of molecular iodine 127I2 with a wavelength of approximately 633 nm. The sixth standard is a fibre laser stabilized to the P(16) (ν1+ν3) transition of molecular acetylene 13C2H2 with a wavelength of approximately 1542 nm. The technical protocol was deliberately designed to accommodate artefacts of different wavelengths in a common framework. The results of these measurements are compiled in the present report. The comparison reports, as communicated by each participant, are included in the main document. This document constitutes the thirteenth final report for the ongoing key comparison CCL-K11. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/. The final report has been peer-reviewed and approved for publication by the CCL, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on⁸⁷Sr,¹⁷¹Yb⁺and¹³³Cs, we set bounds on parameters controlling the variation of the fine-structure constant,α, and the electron-to-proton mass ratio,µ. We consider variations on timescales ranging from a minute to almost a day. In addition, we use our results to derive some of the tightest limits to date on the parameter space of models of ultralight dark matter and axion-like particles.