Optical atomic clocks now individually claim fractional systematic uncertainties at the low 10^-18 level, and frequency ratios between clocks of different species are the primary observable used to validate them. The 2021 Boulder Atomic Clock Optical Network (BACON) collaboration measured the Al+/Yb, Al+/Sr and Yb/Sr ratios with fractional uncertainties of 5.9–8.0×10^-18 but explicitly acknowledged unresolved issues: discrepancies up to ~3σ between its direct optical ratios and earlier ratios derived from absolute-frequency chains (Cs and Hg+ traceability), a disputed multipolar polarizability of the Yb clock transition, poorly constrained between-day variability, correlation treatment when combining measurements across laboratories, and the extension to a global mobile and satellite-capable network. The literature through 2026 shows that the Yb-polarizability discrepancy has been resolved (missing diamagnetic/negative-energy-state contribution to the M1 polarizability, confirmed experimentally in 2024/2025), but the central open question remains and has sharpened — the successor BACON 2026 measurement and an independent PTB Al+ measurement disagree with the 2021 values at up to 14σ and 8.6σ, the physical source is still unidentified, the residual between-day scatter in the Yb/Sr ratio is unexplained, correlation-aware consensus combination of the fast-growing multi-laboratory ratio dataset is not yet established, and 10^-18-accurate intercontinental or satellite-based comparison has not been demonstrated. Solving this problem is the least-advanced mandatory criterion on the roadmap for the planned redefinition of the SI second.

Background

Atomic clocks keep time by interrogating a narrow atomic transition; the best optical clocks (oscillating at hundreds of terahertz) now reach fractional systematic uncertainties of a few 10^-18. Two platforms dominate: optical lattice clocks, in which thousands of neutral Sr or Yb atoms are trapped in a standing-wave laser lattice at the 'magic' wavelength where the differential light shift of the two clock states vanishes, and single-ion clocks such as the 27Al+ quantum-logic clock, in which one clock ion is read out through a co-trapped helper ion. Because different clocks realize different transition frequencies, the natural comparison observable is the frequency ratio between two clock transitions, which cancels the SI definition of the second and can be far more accurate than any absolute frequency. Ratios are transferred between laboratories with optical frequency combs (phase-stabilized pulsed lasers that link optical and microwave frequencies) over phase-stabilized optical fibre or, as demonstrated in the 2021 BACON campaign, over free-space optical two-way time-frequency transfer (O-TWTFT) across a turbulent 1.5 km atmospheric path. Historically, ratios were also obtained indirectly by dividing independently measured absolute frequencies, each traceable to caesium fountain primary standards or to the Hg+ ion clock; such 'absolute-frequency chains' propagate the ~10^-16-level Cs uncertainty and lab-specific systematics. In 2021 the BACON collaboration (NIST/JILA) reported the direct ratios Al+/Yb, Al+/Sr and Yb/Sr with fractional uncertainties of 5.9, 8.0 and 6.8×10^-18, then the most accurate inter-species ratios, using a Bayesian hierarchical model that combines per-day measurements with evaluated systematic uncertainties and an extra between-day variance parameter ξ (a 'dark uncertainty' in the sense of interlaboratory meta-analysis, since day-to-day frequency fluctuations exceeded known effects). The campaign also verified internal closure — the product of the three ratios agrees with unity to 6×10^-19. The scientific stakes of a globally consistent ratio dataset are high: the Consultative Committee for Time and Frequency has targeted a redefinition of the SI second based on optical transitions around 2030, and the roadmap identifies validation of optical frequency-standard uncertainty budgets through comparisons as the least-advanced mandatory criterion. Consistent ratios also underpin secondary representations of the second in international time scales, chronometric (relativistic) geodesy, and searches for ultralight dark matter and variation of fundamental constants, which use long ratio time series as data. One specific systematic entering the Yb lattice clock budget deserves definition: beyond the electric-dipole (E1) light shift, magnetic-dipole (M1) and electric-quadrupole (E2) 'multipolar' polarizabilities of the clock states produce residual lattice shifts that couple to the atoms' motional state, and in 2021 the only experimental determination of the Yb multipolarizability (Nemitz et al. 2019) disagreed with the theoretical values used in the systematic evaluation.

Problem Statement

The overarching objective, as posed by the 2021 BACON campaign and its successors, is to establish the worldwide ensemble of optical-clock frequency-ratio measurements as self-consistent at the few-10^-18 accuracy level that the individual clocks claim — that is, to demonstrate that independently evaluated clocks, compared across institutions and link technologies, agree within their stated uncertainties. The concrete open questions are: (1) identify the physical source(s) of the discrepancies between independently measured inter-species frequency ratios — originally the up-to-~3σ differences between the 2021 direct optical Al+-based ratios and ratios derived from absolute-frequency chains traceable to caesium and Hg+, now sharpened to the ~14σ (Sr-involving ratios) and 2.4σ (Al+/Yb) differences between the 2021 and 2026 BACON campaigns, the 8.6σ difference between the 2021 BACON and 2026 PTB Al+/Sr values, and the 2–4σ disagreements among historical few-10^-16-level measurements across laboratories — and determine which measurements' systematic uncertainty budgets are incomplete; (2) identify the physical origin of the residual between-day variability ('dark uncertainty') in multi-day ratio campaigns — reduced but not eliminated (Yb/Sr χ²_red = 6.4 in the 2026 campaign, with uncharacterized shifts, where χ²_red is the reduced chi-squared, i.e. the chi-squared per degree of freedom of the daily ratio means, so 6.4 indicates scatter well beyond the stated per-day error bars) — and constrain it well enough that it no longer dominates ratio uncertainties; (3) develop consensus/meta-analysis methods that correctly propagate correlations (shared clocks, shared links, shared systematic evaluations) when combining the rapidly growing multi-laboratory ratio dataset, including for the CIPM (International Committee for Weights and Measures) recommended frequency values and a possible multi-transition definition of the second; and (4) extend validated 10^-18-accurate comparisons to intercontinental, mobile and satellite scales by combining free-space and fibre links, where current satellite-based comparison remains limited near 2×10^-16. The Yb multipolar-polarizability question is treated as settled (Refs. 4, 6, 7) and is outside the present scope. The four components (1)–(4) jointly constitute the single scientific objective of a validated, globally consistent 10^-18 ratio dataset: (1) identification of the physical source(s) of the inter-campaign and historical discrepancies, together with the systematic uncertainty budgets thereby shown to be incomplete; (2) identification of the physical origin of the residual between-day variability, plus a constraint on it tight enough that it no longer dominates the ratio uncertainties; (3) a consensus/meta-analysis method that correctly propagates the correlations among measurements and yields agreed combined values; and (4) demonstrated 10^-18-accurate comparisons across intercontinental, mobile and satellite scales. This objective is the least-advanced mandatory criterion on the 2024 redefinition roadmap for redefining the SI second.

References

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