Two independent 176Lu+^{176}\mathrm{Lu}^+ single-ion optical clocks have been evaluated with total systematic uncertainties of 1.2×10−191.2\times10^{-19} and 1.3×10−191.3\times10^{-19} and validated against each other by correlation spectroscopy with agreement verified at the 5.7×10−195.7\times10^{-19} statistical level (Arnold et al., arXiv:2512.07346, Dec 2025) — the highest validated clock accuracy reported to date. The remaining problem is to reduce the evaluated total systematic uncertainty of the 176Lu+^{176}\mathrm{Lu}^+ standard from ∼1×10−19\sim1\times10^{-19} to the mid-10−2010^{-20} regime, currently blocked by the dc differential polarizability entering the blackbody-radiation shift. The source further notes, as context for the same goal, that an absolute frequency realization at 10−1910^{-19} requires comb-referenced microwave synthesis and that accuracy claims at this level must ultimately be validated between independent institutes, as the roadmap for redefining the SI second requires.

Background

An optical atomic clock uses the sharply defined frequency of an atomic transition at optical frequencies as a reference for timekeeping; its accuracy is quantified by the fractional systematic uncertainty, the estimated residual error of the realized frequency after correcting all known shifts. The most accurate evaluated clocks now reach the 10−1810^{-18} range and below, and the international roadmap for redefining the SI second (Dimarcq et al., Metrologia 61, 012001 (2024)) sets mandatory criteria: comprehensively evaluated accuracy budgets with relative frequency uncertainty ≤2×10−18\leq2\times10^{-18}, and validation through frequency-ratio measurements between independent systems showing agreement ≤5×10−18\leq5\times10^{-18}.

One of the leading systems is the 176Lu+^{176}\mathrm{Lu}^+ single-ion clock operated at the National University of Singapore: a single lutetium ion is confined in a linear Paul trap (a radio-frequency quadrupole ion trap) and interrogated on the 1S0→3D1^1S_0\rightarrow{}^3D_1 transition at 848 nm. The 3D1^3D_1 excited state has a practically indefinite lifetime, so in principle very long coherent interrogation is possible. Because 176^{176}Lu has nuclear spin I=7I=7, the 3D1^3D_1 level splits into hyperfine levels F=6,7,8F=6,7,8; the clock frequency is realized as a hyperfine-averaged frequency, i.e., an average over Zeeman components that cancels the linear Zeeman shift and the electric-quadrupole shift, with a residual quadratic Zeeman shift calibrated by a measured coefficient. Microwave transitions between 3D1^3D_1 hyperfine levels (frequencies f1f_1 and f2f_2) enter the realization formula ν0=fL+13(2f1+f2)\nu_0=f_L+\frac{1}{3}(2f_1+f_2), where fLf_L is the optical clock-laser frequency.

In December 2025, Arnold et al. (arXiv:2512.07346) reported a full systematic assessment of two such systems (Lu-1 and Lu-2), with total systematic uncertainties of 1.2×10−191.2\times10^{-19} and 1.3×10−191.3\times10^{-19} — the highest accuracy reported to date — and compared them by correlation spectroscopy: both ions are interrogated by the same laser and the two-ion parity (product of the measured spin states) is read out, which permits comparison beyond the laser's own coherence time. With Ramsey interrogation times (free evolution between two interrogation pulses) up to 10 s and an instability of 4.8×10−16(τ/s)−1/24.8\times10^{-16}(\tau/\mathrm{s})^{-1/2}, they demonstrated a frequency difference of [−0.1±(5.7)stat±(1.0)sys]×10−19[-0.1\pm(5.7)_{\mathrm{stat}}\pm(1.0)_{\mathrm{sys}}]\times10^{-19} after about 200 hours — the first comparison of optical references with total uncertainty below 10−1810^{-18}.

The dominant single systematic for the individual clocks is the blackbody-radiation (BBR) shift: the ac Stark shift of the clock transition induced by thermal radiation from the room-temperature apparatus. For 176Lu+^{176}\mathrm{Lu}^+ it is δνBBR/ν0=−4.90×10−19 Tˉ4(1+1.77 Tˉ2)\delta\nu_{\mathrm{BBR}}/\nu_0=-4.90\times10^{-19}\,\bar{T}^{4}(1+1.77\,\bar{T}^{2}) with Tˉ=T/(300 K)\bar{T}=T/(300\,\mathrm{K}), and over the practical range 270–330 K its uncertainty is approximately 9.8×10−20 Tˉ49.8\times10^{-20}\,\bar{T}^{4} — limited not by temperature measurement but by the uncertainty of the differential scalar polarizability Δα(ω)\Delta\alpha(\omega) (the difference between the two clock states' electric-dipole responses, the quantity that sets the Stark sensitivity) extrapolated from measurements at optical wavelengths down to dc (zero frequency). Δα(ω)\Delta\alpha(\omega) of the 848-nm transition was measured at several wavelengths (Arnold et al., Nat. Commun. 9, 1650 (2018); Phys. Rev. A 99, 012510 (2019)). Barrett and Arnold (New J. Phys. 27, 013005 (2025)) introduced a 'projection method' for such dc extrapolations: it expands Δα(ω)\Delta\alpha(\omega) in basis functions tied to the allowed atomic transitions and progressively eliminates reliance on atomic-structure theory as wavelength coverage grows. Applied to the existing Lu+^+ data it yields mutually consistent estimates, and the clock paper states that an improved dc-polarizability evaluation along these lines 'would immediately reduce the total uncertainty of these existing systems to the level of mid 10−2010^{-20}', although the measurement precision must advance to take advantage of that reduction (roughly 33–5×10−205\times10^{-20}).

Several further experimental factors bound both the accuracy and the stability needed to resolve 10−2010^{-20}-level shifts. Ambient magnetic-field flicker (about 7 nT on 1–100 s timescales) washes out the Ramsey fringe at long interrogation; ion heating (slow warming of the trapped ion's motion driven by electric-field noise from the trap electrodes) increases the second-order Doppler shift (SODS) — the relativistic time dilation due to the ion's thermal motion — which at the demonstrated 5 s interrogation contributes only at the low-10−2010^{-20} level but would become the largest uncertainty at substantially longer times; collisions with background gas (bounded through the classical Langevin collision rate times a factor characterizing decoupling of the ion from the clock laser) also grow with interrogation time. The trap's own radio-frequency heating degrades knowledge of the BBR environment temperature: one batch of Al2_2O3_3 ceramic electrode spacers showed an anomalously high dielectric loss (a 6.6 K/W temperature rise per watt of rf power versus 2.3 K/W for Macor spacers), with strong supplier-to-supplier variability and suspicion of a mislabeled or bad batch. Operating at a reduced dc magnetic field (25 µT instead of the present 0.1 mT) would reduce magnetic sensitivity and is assessed to allow interrogation times up to 30 s, at the cost of small Zeeman splittings and reconfigured laser and microwave addressing; magnetic shielding and cryogenics could extend coherence further at the cost of apparatus complexity. Finally, an absolute frequency realization at 10−1910^{-19} requires the microwave frequencies f1f_1 and f2f_2 in the realization formula to be known to δf/f≲3×10−15\delta f/f\lesssim3\times10^{-15}, which the authors anticipate achieving by referencing the microwave synthesizers to the optical frequency via a frequency comb (a pulsed-laser interferometer that phase-coherently links optical and microwave frequencies); and accuracy claims at this level must ultimately be validated between independent institutes, as the redefinition roadmap requires.

Problem Statement

Advance the 176Lu+^{176}\mathrm{Lu}^+ single-ion optical frequency standard from its demonstrated ∼1×10−19\sim1\times10^{-19} total systematic uncertainty to the mid-10−2010^{-20} regime (roughly 33–5×10−205\times10^{-20}). The source identifies as the immediate remaining step an improved determination of the dc differential polarizability of the 848-nm clock transition of 176Lu+^{176}\mathrm{Lu}^+ — by new polarizability or matrix-element measurements at suitable wavelengths, or by an equivalent re-evaluation of the existing data such as the projection-method extrapolation — with an uncertainty small enough that the blackbody-radiation shift no longer limits the total budget above the mid-10−2010^{-20} level (it currently contributes about 1×10−191\times10^{-19}, the largest single systematic). Per the source, an improved evaluation of the dc polarizability 'would immediately reduce the total uncertainty of these existing systems to the level of mid 10−2010^{-20}', although the source notes that its measurement precision must advance to take advantage of that reduction.

The source discusses the following as supporting context and outlook for the same goal, not as mandatory completion requirements:

  • (Supporting control and evaluation) Keeping the remaining systematics below a mid-10−2010^{-20} total budget: the BBR environment temperature (including trap rf heating and the supplier-dependent dielectric loss of ceramic trap spacers), the quadratic Zeeman shift and magnetic-field flicker (about 7 nT on 1–100 s), the second-order Doppler shift from ion heating at extended interrogation, background-gas collision shifts, and the quadrupole shift. Conceivable upgrades discussed by the source — operation at a reduced dc magnetic field near 25 µT (assessed to permit Ramsey times up to about 30 s), magnetic shielding, cryogenics, improved vacuum, or trap engineering — are optional, and each newly introduced systematic would require fresh characterization; the source also notes that at significantly longer interrogation times the second-order Doppler shift would become the largest source of uncertainty.
  • (Realization and validation context) An absolute frequency realization at 10−1910^{-19} requires the microwave references f1f_1 and f2f_2 in the realization formula ν0=fL+13(2f1+f2)\nu_0=f_L+\frac{1}{3}(2f_1+f_2) to be known to δf/f≲3×10−15\delta f/f\lesssim3\times10^{-15}, e.g., via comb-referenced synthesis; and the roadmap for redefining the SI second requires validation of the accuracy budget through same-species, or multiple inter-species, frequency-ratio measurements between independent institutes showing agreement ≤5×10−18\leq5\times10^{-18}.

References

  1. K. J. Arnold, M. D. K. Lee, Qi Zhao, Qin Qichen, Zhang Zhao, N. Jayjong, M. D. Barrett, "Lu+^+ optical frequency references with accuracy verified at the 19th digit", arXiv:2512.07346 (2025). https://arxiv.org/abs/2512.07346
  2. M. D. Barrett, K. J. Arnold, "An extrapolation method for polarisability assessments of ion-based optical clocks", New Journal of Physics 27, 013005 (2025), DOI 10.1088/1367-2630/ada4d1 (preprint arXiv:2409.01476). https://arxiv.org/abs/2409.01476
  3. K. J. Arnold, R. Kaewuam, A. Roy, T. R. Tan, M. D. Barrett, "Blackbody radiation shift assessment for a lutetium ion clock", Nature Communications 9, 1650 (2018), DOI 10.1038/s41467-018-04079-x (preprint arXiv:1712.00240). https://arxiv.org/abs/1712.00240
  4. K. J. Arnold, R. Kaewuam, T. R. Tan, S. G. Porsev, M. S. Safronova, M. D. Barrett, "Dynamic polarizability measurements with 176^{176}Lu+^+", Physical Review A 99, 012510 (2019), DOI 10.1103/PhysRevA.99.012510 (preprint arXiv:1810.11168). https://arxiv.org/abs/1810.11168
  5. N. Dimarcq et al., "Roadmap towards the redefinition of the second", Metrologia 61, 012001 (2024), DOI 10.1088/1681-7575/ad17d2. https://doi.org/10.1088/1681-7575/ad17d2
  6. K. J. Arnold, Scott Bustabad, Qin Qichen, Zhang Zhao, Qi Zhao, Murray D. Barrett, "Validating a lutetium frequency reference", arXiv:2404.16414 (2024). https://arxiv.org/abs/2404.16414
  7. M. D. K. Lee, Qi Zhao, Qin Qichen, Zhang Zhao, N. Jayjong, K. J. Arnold, M. D. Barrett, "Precision measurement of the 176^{176}Lu+^+ 3D1^3D_1 microwave clock transitions", arXiv:2510.06814 (2025). https://arxiv.org/abs/2510.06814
  8. Qin Qichen, Qi Zhao, M. D. K. Lee, Zhang Zhao, N. Jayjong, K. J. Arnold, M. D. Barrett, "Zeeman degenerate sideband cooling in 176^{176}Lu+^+", Physical Review A 113, 013109 (2026), DOI 10.1103/tjwn-bq6b (preprint arXiv:2508.02026). https://arxiv.org/abs/2508.02026
  9. M. D. Barrett, K. J. Arnold, "Analysis of collision-shift assessments in ion-based clocks", Physical Review A 114, 013104 (2026), DOI 10.1103/hdl1-nwrn (preprint arXiv:2512.05474). https://arxiv.org/abs/2512.05474
  10. N. Jayjong, M. D. K. Lee, K. J. Arnold, M. D. Barrett, "Zero crossings of the differential scalar polarizability of Ba+^+ clock transition", Physical Review A 114, 012804 (2026), DOI 10.1103/wdgl-2vhf (preprint arXiv:2603.10740). https://arxiv.org/abs/2603.10740
  11. N. Jayjong, M. D. K. Lee, K. J. Arnold, M. D. Barrett, "Measurement of the reduced dipole matrix element in Ba+^+", arXiv:2607.20920 (2026). https://arxiv.org/abs/2607.20920
  12. K. J. Arnold, Bin Jian, Zhang Zhao, Qi Zhao, Qin Qichen, N. Jayjong, M. D. K. Lee, Scott Beattie, M. D. Barrett, "Absolute frequency measurement of the 176^{176}Lu+^+(3^3D1_1) standard against the NRC-FCs2 fountain with 2.6×10−162.6\times10^{-16} uncertainty", arXiv:2607.07044 (2026). https://arxiv.org/abs/2607.07044
  13. Marco Pizzocaro et al., "International Optical Clock Comparison Using the European Optical Fiber Network", arXiv:2604.27963 (2026). https://arxiv.org/abs/2604.27963
  14. Alexander Aeppli et al., "Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18\leq3.2\times10^{-18}", arXiv:2512.21428 (2025). https://arxiv.org/abs/2512.21428
  15. Melina Filzinger, Martin R. Steinel, Jian Jiang, Daniel Bennett, Tanja E. Mehlstäubler, Ekkehard Peik, Nils Huntemann, "A multi-ion optical clock with 5×10−195\times10^{-19} uncertainty", arXiv:2603.23446 (2026). https://arxiv.org/abs/2603.23446
  16. Fabian Dawel et al., "An Al+^+ clock with 1.6×10−181.6\times10^{-18} systematic uncertainty and its frequency ratios", arXiv:2606.23151 (2026). https://arxiv.org/abs/2606.23151