The most accurate optical clock to date, a fermionic strontium optical lattice clock with a total systematic uncertainty of 8.1×10−198.1\times10^{-19} in fractional frequency units (Aeppli et al., Phys. Rev. Lett. 133, 023401 (2024)), is limited by the blackbody-radiation (BBR) Stark shift: the few-mK-drift in-vacuum radiant-temperature environment and the model-dependent dynamic BBR correction extracted from fitted Einstein AA coefficients. The paper's Summary identifies the BBR shift as the most significant source of uncertainty and states that future cryogenic operation should reduce the uncertainty to the low-10−1910^{-19} level; the paper also acknowledges as open methodological limitations the model dependence of the dynamic correction (its fitted Einstein-AA-coefficient analysis yet to include theoretically calculated high-lying-state values), collective radiative phenomena (radiation trapping, superradiance, dipole-dipole interactions) that bias lifetime extraction at non-negligible optical depth, and direct measurement and control of tunneling shifts for coherent off-site superpositions at the shallow lattice depths used to suppress light shifts. As of late 2025–2026 no optical lattice clock has reported a total systematic uncertainty below 10−1910^{-19}: the most recent room-temperature strontium budget (Jia et al. 2026) stands at 9.2×10−199.2\times10^{-19} with BBR uncertainty of 6.3×10−196.3\times10^{-19}, a cryogenic ytterbium lattice clock has reduced only its BBR term (to 1.7×10−201.7\times10^{-20}), and the only systematics evaluated below the 10−1910^{-19} level are those of a lutetium single-ion clock pair (9.6×10−209.6\times10^{-20} for the difference of two clocks with 1.1×10−191.1\times10^{-19} and 1.4×10−191.4\times10^{-19} individual totals) — a trapped single-ion platform, not a neutral-atom lattice. The problem of realizing a strontium lattice clock — the platform of the source — with total systematic uncertainty below 10−1910^{-19}, with the dominant BBR shift uncertainty correspondingly reduced, remains open.

Background

An optical lattice clock interrogates an ultra-narrow atomic transition in neutral atoms trapped in a standing-wave laser field (the 'lattice') tuned to a magic wavelength at which the lattice light shift on the two clock states cancels; the best such clocks use the 1S0→3P0^1S_0\to{}^3P_0 transition of fermionic 87^{87}Sr near 698 nm. The clock's accuracy is quantified by its total systematic uncertainty, the quadrature sum of all frequency-shift corrections and their uncertainties in fractional frequency units. Aeppli, Kim, Warfield, Safronova, and Ye (Phys. Rev. Lett. 133, 023401 (2024)) reported a vertically oriented, shallow, one-dimensional strontium lattice clock with total systematic uncertainty 8.1×10−198.1\times10^{-19} — at the time the lowest of any clock — with every systematic other than the blackbody-radiation (BBR) shift already below 1×10−191\times10^{-19}. The BBR shift is the AC Stark shift of the clock transition induced by ambient thermal radiation. Its 'static' part is fixed by the differential static polarizability of the clock states and the fourth power of the effective radiant temperature of the atoms' environment; the 'dynamic' correction accounts for the frequency dependence of the polarizability across the blackbody spectrum and is constrained by Einstein AA coefficients (spontaneous decay rates) of the atom's excited states. Aeppli et al. revised the Sr dynamic correction by measuring the lifetime of the 5s4d 3D15s4d\,{}^3D_1 state, which required characterizing many-body effects in the cascaded multi-level 3D13D_1 decay. That measurement sits at the heart of the remaining open issues. First, at non-negligible optical depth (a measure of how opaque the atomic cloud is to its own resonance fluorescence), collective radiative phenomena bias lifetime extraction: radiation trapping (resonant reabsorption and re-emission of photons lengthening the observed decay), superradiance (collective emission faster than the single-atom rate), and resonant dipole-dipole interactions between atoms; a first-principles or validated effective model of these effects across atomic densities, and the reconciliation of high-optical-depth lifetime measurements with low-density extrapolations, were left open. Second, the dynamic correction still depended on a finite fit over measured AA coefficients with methodological choices (leave-one-out validation, number of free coefficients), and the paper flagged extending the fit with theoretically calculated high-lying-state AA coefficients — with theory uncertainties and correlations treated — as an open task. Third, although the in-vacuum radiant temperature was measured to the mK level, residual few-mK drifts coupled to room temperature and building chilled water left the BBR environment as the dominant uncertainty, motivating further isolation or cryogenic operation. Fourth, operating at shallow lattice depth suppresses the lattice light shift but brings the atoms closer to tunneling between lattice sites, which would delocalize the coherent off-site superpositions used in spectroscopy; the clock suppressed tunneling by timing and depth choices rather than direct measurement, and model-independent tunneling-shift measurements or control strategies were left open. Among these threads, the paper singles out the BBR shift as the dominant uncertainty and points to future cryogenic operation as the route to the low-10−1910^{-19} level; progress toward the field's stated goal — clocks with systematic uncertainties in the low 10−1910^{-19} regime and below, needed for the planned redefinition of the SI second, relativistic geodesy, and new-physics searches — runs through closing the BBR gap, with the collective-effect and tunneling threads as acknowledged methodological limitations relevant wherever they contribute to the budget. Earlier milestones anchor the lineage: Middelmann et al. (Phys. Rev. Lett. 109, 263004 (2012)) directly measured the Sr BBR shift at the 10−1710^{-17} level a decade earlier.

Problem Statement

Realize an optical lattice clock — on the strontium platform of Aeppli et al. (Phys. Rev. Lett. 133, 023401 (2024)) — whose total systematic uncertainty is below 10−1910^{-19} in fractional frequency units, closing the dominant gap that the 8.1×10−198.1\times10^{-19} evaluation identified — the blackbody-radiation shift, whose environment part (controlling the in-vacuum radiant temperature and its few-mK drifts through improved isolation or cryogenic operation, as demonstrated for the BBR term alone in ytterbium) and dynamic part (determining the Sr dynamic BBR correction with reduced model dependence — extending the fitted Einstein-AA-coefficient analysis with theoretically calculated high-lying-state values whose theory uncertainties and correlations are treated, and/or by direct verification of the leading correction coefficient, as done for ytterbium in Hassan et al. 2025) are the source's principal routes to a quadrature total below 10−1910^{-19}, though not the only admissible ones. Insofar as they contribute to the budget of such a clock, the source's other acknowledged limitations — collective radiative phenomena (radiation trapping, superradiance, and resonant dipole-dipole interactions) biasing lifetime and AA-coefficient extraction in cascaded multi-level decays such as the 5s4d 3D15s4d\,{}^3D_1 decay, and tunneling shifts of coherent off-site superpositions at the shallow lattice depths used to suppress lattice light shifts — are to be evaluated and their resulting contribution to the budget shown — by model, measurement, or explicit bound — to lie below the 10−1910^{-19} target. The completion boundary is a complete, self-consistent systematic-uncertainty budget for such a clock whose quadrature total is below 10−1910^{-19}, with the BBR contributions correspondingly reduced, every contribution evaluated with an uncertainty below the 10−1910^{-19} target, each supported by admissible evidence — a measurement, an ab-initio calculation with a stated uncertainty, or an explicit bound — and checked against at least one independent source or method.

References

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