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High-Stability Single-Ion Clock with $5.5\times10^{-19}$ Systematic Uncertainty

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Pith's one-line read This paper reports that a single $^{27}\mathrm{Al}^+$ ion quantum logic clock reaches $5.5\times10^{-19}$ total systematic uncertainty and $3.5\times10^{-16}/\sqrt{\tau/\mathrm{s}}$ stability, the most accurate clock and most stable ion…

desk verdict Record-setting 27Al+ clock with a credible uncertainty budget; the secular-motion thermometry assumption is the soft spot, but the paper openly acknowledges it. read the letter →

arxiv 2504.13071 v2 pith:PVOQTW72 submitted 2025-04-17 physics.atom-ph quant-ph

Mason C. Marshall , Daniel A. Rodriguez Castillo , Willa J. Arthur-Dworschack , Alexander Aeppli , Kyungtae Kim , Dahyeon Lee , William Warfield , Joost Hinrichs
show 5 more authors
Nicholas V. Nardelli Tara M. Fortier Jun Ye David R. Leibrandt David B. Hume
This is my paper · ORCID
classification physics.atom-phquant-ph
keywords opticalatomicclock27Al+single-ionquantumlogicspectroscopyfractionalfrequencyuncertaintystabilitysidebandthermometrysystematicbudgetacZeemanshift
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports an optical clock built around a single $^{27}\mathrm{Al}^+$ ion, sympathetically cooled and read out through a co-trapped $^{25}\mathrm{Mg}^+$ logic ion. The authors claim the clock reaches a fractional frequency uncertainty of $5.5\times10^{-19}$—the lowest yet measured for any clock—and a stability of $3.5\times10^{-16}/\sqrt{\tau/\mathrm{s}}$, a threefold improvement over the previous aluminum-ion clock. The gains come from probing for a full second using laser stability transferred from a remote cryogenic silicon cavity through a 3.6 km fiber link, a redesigned Paul trap that reduces excess micromotion, a titanium vacuum system that cuts background-gas collisions by more than a factor of 150, and a three-axis measurement of the trap's ac magnetic field that removes a directional ambiguity. If the claims hold, no clock has been characterized more accurately, and the same engineering path points toward accuracy near $1\times10^{-19}$.

What carries the argument

The machinery is the two-ion Coulomb crystal in a Paul trap: a $^{27}\mathrm{Al}^+$ spectroscopy ion whose $^1\mathrm{S}_0\leftrightarrow{}^3\mathrm{P}_0$ clock transition is probed by Rabi spectroscopy, and a $^{25}\mathrm{Mg}^+$ logic ion that supplies sympathetic Doppler cooling during the probe and performs quantum logic readout of the aluminum state. This arrangement makes the clock transition accessible even though it cannot be directly laser-cooled or easily detected, and it provides the sideband thermometry, micromotion diagnostics, and ac-field measurements that anchor the uncertainty budget. A second load-bearing element is the laser-stability transfer chain: a cryogenic silicon cavity located 3.6 km away stabilizes a frequency comb, which steers the 267 nm clock laser through an acousto-optic modulator, extending the usable Rabi probe duration from 150 ms to 1 s and reducing the clock instability threefold.

What would settle it

Run the clock with the ion pair ground-state cooled through the same 1 s probe and compare its frequency with the Doppler-cooled operation. The frequency difference predicted from sideband thermometry must match the change in the secular-motion shift; if the observed difference deviates by more than the $3.8\times10^{-19}$ assigned uncertainty, the thermal-state assumption is falsified and the total uncertainty cannot stand. An independent check on the stability claim would be a direct comparison of two such clocks, since the reported $3.5\times10^{-16}/\sqrt{\tau/\mathrm{s}}$ was measured against a strontium lattice clock and attributed entirely to the aluminum clock.

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Extended reading notes

Core claim

The central claim is that a single $^{27}\mathrm{Al}^+$ ion, using quantum logic spectroscopy on a co-trapped $^{25}\mathrm{Mg}^+$ ion, now defines the most accurately characterized clock built to date. The total systematic uncertainty is $\Delta\nu/\nu = 5.5\times10^{-19}$, and the fractional instability is $3.5\times10^{-16}/\sqrt{\tau/\mathrm{s}}$. The uncertainty budget is dominated by the secular-motion (second-order Doppler) shift, evaluated at $-(114.6\pm3.8)\times10^{-19}$ from repeated sideband thermometry—using the ratio of red and blue motional-sideband strengths—of all six motional modes over several months, followed by the dc quadratic Zeeman shift, the cooling-laser ac Stark shift, and the blackbody radiation shift. The paper attributes the improvement to several concrete changes: a one-second Rabi probe enabled by transferring stability from a cryogenic silicon cavity over a 3.6 km stabilized fiber link, a redesigned Paul trap with balanced electrode capacitances that suppresses excess micromotion, a new all-titanium vacuum system with a measured pressure about 150 times lower than the previous clock, and a three-orientation measurement of the trap radio-frequency magnetic field so that the ac quadratic Zeeman shift no longer has a directional ambiguity.

Load-bearing premise

The load-bearing premise is that the two-ion crystal's motion is thermal, so the red/blue sideband contrast measured by sideband thermometry returns the true secular-mode occupation numbers; if the true motional distribution is not thermal, the secular-motion shift and the quoted $5.5\times10^{-19}$ total would be understated.

Editorial extensions

If this is right

  • If the $5.5\times10^{-19}$ total is correct, the aluminum-ion clock is the most accurate frequency reference ever characterized, suitable for testing other clocks and for searches of drifts in fundamental constants.
  • The threefold stability improvement means a comparison that previously required many hours of averaging reaches the same precision in roughly one ninth of the time, making dark-matter and relativistic-geodesy searches faster.
  • The demonstration that a 1 s probe can be sustained by remote cavity light transfer shows that clock stability need not be limited by the local clock laser, a route other optical-clock species can adopt.
  • The measured low micromotion and a vacuum pressure 150 times lower than the previous clock show that specific trap and vacuum engineering can push systematic uncertainties below the few-$10^{-19}$ level.
  • The direction-sensitive measurement of the trap rf magnetic field, repeated along three nearly orthogonal axes, removes a systematic that previously had to be bounded rather than measured.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that if the secular-motion uncertainty were reduced—for example by ground-state cooling the crystal during the probe—the next largest terms (dc quadratic Zeeman and cooling-laser Stark) would become the limit, and total accuracy near $1\times10^{-19}$ would require improving those as well.
  • The same three-axis ac-field measurement could be turned into a general-purpose, in-situ magnetometer for ion traps, since it reconstructs both magnitude and orientation of the trap rf magnetic field without needing to know the field direction in advance.
  • The remote-cavity stability transfer suggests a network architecture in which several independent ion clocks share one ultrastable cavity, allowing inter-clock comparisons without each clock carrying its own cryogenic reference.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This manuscript reports the NIST 27Al+ quantum-logic clock, claiming a total fractional frequency uncertainty of 5.5×10^-19 and a fractional frequency stability of 3.5×10^-16/√(τ/s). The clock uses a co-trapped 25Mg+ ion for sympathetic cooling and quantum-logic readout, a 1 s Rabi probe enabled by transferring stability from a remote cryogenic silicon cavity over a 3.6 km fiber link, and an improved Paul trap and all-titanium vacuum system. The systematic evaluation covers the secular-motion second-order Doppler shift, dc and ac quadratic Zeeman shifts, cooling-laser Stark shift, blackbody radiation, excess micromotion, background-gas collisions, clock-laser Stark shift, and first-order Doppler shift; the secular-motion term is the largest uncertainty. The paper claims the lowest fractional frequency uncertainty of any clock to date and the lowest instability of any ion clock reported to date.

Significance. If the quoted 5.5×10^-19 systematic uncertainty is correct, this is a landmark result in optical atomic clocks, directly relevant to the redefinition of the second and to searches for new physics. The manuscript has notable strengths: repeated sideband thermometry over several months; explicit parameter-dependence checks with an added 3% uncertainty on the secular-motion temperatures; direct calibration of the 280 nm Stark shift via Raman Rabi-rate measurements and depumping; a direction-sensitive ac-quadratic-Zeeman measurement with three quantization axes and parametric bootstrapping; and a 150× improvement in background pressure with a measured collision shift below 10^-19. These cross-checks make the central claim credible. The main weaknesses concern the consistency of the first-order Doppler entry in Table I, the absolute calibration of the secular-motion thermometry, and the quantitative support for the record claim in the abstract.

major comments (3)
  1. [First-order Doppler shift (main text) and Table I] The text reports a measured first-order Doppler shift of (0.1 ± 1.7)×10^-18 and states that, combined with the suppression from averaging opposite probe directions, the residual shift is negligible. Table I, however, lists a first-order Doppler shift of 0 with uncertainty <1×10^-19. The suppression factor that reconciles the 1.7×10^-18 statistical uncertainty with the <1×10^-19 table entry is not stated or derived anywhere in the main text or supplemental material. Because this entry contributes directly to the claimed total uncertainty of 5.5×10^-19, the reader cannot independently verify that the residual first-order Doppler shift is below 10^-19. Please provide the suppression factor, its measurement or derivation, and an explicit reconciliation of the text value with Table I.
  2. [Supplemental Section I (Secular motion)] The 3% uncertainty added to the secular-motion temperatures is justified by parameter-dependence checks (sideband pulse duration, mode-frequency pattern, cooling saturation, sideband order). These checks test reproducibility under changed conditions, but they do not provide an absolute calibration of nbar. A common-mode error in the two-ion Lamb-Dicke factor, in the assumed thermal occupation distribution, or in the Doppler-limit model would shift all six measured nbar values together; it would not appear in the weighted standard deviation or in the parameter-dependence comparisons. Since the secular-motion correction is -114.6×10^-19 and carries the largest uncertainty in Table I (3.8×10^-19), the total uncertainty claim depends on this point. Please provide an independent calibration of the nbar scale (for example, a different thermometry method) or an explicit quantitative argument that the 3% bound covers common-mode model errors.
  3. [Abstract and Conclusion] The claim that this clock achieves the lowest fractional frequency uncertainty of any clock to date is central to the paper, but no quantitative comparison with the best published uncertainties of other clocks is given. For a record claim, please provide a brief comparison with the relevant references (e.g., Refs. [3], [12], [14]), either as a table or as explicit numerical values, so that the reader can verify the stated record.
minor comments (4)
  1. [References] References [14] and [29] are identical (Aeppli et al., Physical Review Letters 133, 023401 (2024)); please consolidate to avoid duplicate citation.
  2. [Figure 1B caption] The red simulation points should state the assumed noise model and duty cycle; the current caption only says 'simulation incorporating experimental noise and duty cycle', which is insufficient to assess the comparison with the measured Allan deviation.
  3. [Table S2] The sign convention for the 'Frequency shift per quantum' column is not stated; since the secular-motion shift is negative, please define the convention explicitly.
  4. [Supplemental Section III, Eq. (5)] The Clebsch-Gordan coefficients g_B and g_rad are used in Eq. (5) without an explicit definition; please define all symbols in the equation and state which transitions they refer to.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 5.5e-19 uncertainty budget is assembled from independent measurements and externally published coefficients, not from the clock frequency being evaluated.

full rationale

Every load-bearing systematic shift in this uncertainty budget is derived from measurements or external coefficients that are independent of the claimed clock frequency. The secular-motion shift is computed from sideband thermometry values of n-bar listed in Table S2; the thermal-state relation n-bar = Pr/(Pb - Pr) is an assumption about the motional distribution, but the measured sideband contrasts are inputs to the shift, not outputs of it. The agreement with the calculated Doppler limit is explicitly presented only as a consistency check, and the assigned uncertainty is the scatter of repeated measurements, so no fitted parameter is renamed as a prediction. The cooling-laser Stark shift is calibrated by direct Stark-shift measurements at high power, with an absolute saturation parameter obtained from Raman Rabi rates (Supplement Eqs. 3-5), then scaled by the separately measured cooling-laser saturation parameter; no clock-frequency result is reused. The blackbody-radiation shift uses the externally measured polarizability from Wei et al. [40] together with local thermocouple temperatures. The ac quadratic Zeeman shift is extracted from a multi-axis hyperfine spectroscopy fit, the collision shift scales the previous theory of [27] using a measured reorder rate, and excess micromotion is bounded by resolved-sideband measurements. Self-citations such as [12], [17], and [36] supply methodology and prior characterizations, but they do not carry the central claim. The manuscript's own statement that accuracy is 'mainly limited by the measurement of the Doppler temperature' is an honest calibration limitation, not a circular step. No derivation in the paper reduces by construction to its own inputs.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on measured calibration parameters such as thermometry occupations, saturation parameters, magnetic fields, and vacuum pressure, plus externally supplied atomic-structure coefficients. None of the inputs are invented entities; the main epistemic risk is that calibration models, especially thermal-state sideband thermometry and collision-shift scaling, are inherited from prior work and are not independently validated here.

free parameters (6)
  • Secular mode phonon occupations nbar = 8.22 ± 0.48, 4.50 ± 0.19, 5.68 ± 0.49, 6.69 ± 0.51, 4.31 ± 0.14, 4.84 ± 0.24 for the six modes (Table S2)
    Measured by sideband thermometry; these set the secular motion time-dilation correction of -114.6×10^-19, the largest uncertainty in the budget.
  • Cooling laser saturation parameter S = Typical average 0.148 ± 0.004; day averages such as 0.1621 ± 0.0046
    Obtained from depumping fits during clock operation; governs the -37.2×10^-19 cooling laser Stark shift correction.
  • Quantization magnetic field B_DC = Operating field about 0.10 mT, day-dependent
    Derived from the real-time Zeeman splitting; determines the -6317.9×10^-19 dc quadratic Zeeman correction.
  • Trap ac magnetic field squared B_AC = 0.85 ± 0.09 µT^2
    Extracted from a simultaneous fit of 25Mg+ hyperfine shifts versus RF power in three field directions; gives the -0.54×10^-19 ac quadratic Zeeman correction.
  • Apparatus temperature for blackbody radiation = 24.0 ± 3.3 °C
    From six thermocouples; sets the -30.7×10^-19 blackbody radiation shift correction.
  • Ion crystal reorder period for vacuum pressure = 11,376 seconds (25 events in 79 hours)
    Used to infer a background pressure of (2.5 ± 1.3)×10^-10 Pa, which sets the collision shift correction.
assumptions (6)
  • domain assumption Atomic-structure coefficients for the 27Al+ clock transition are accurate.
    The quadratic Zeeman coefficient, blackbody radiation polarizability, and 280 nm polarizability are taken from cited measurements [36, 16, 40] and propagate directly into the quoted corrections.
  • domain assumption The sideband thermometry thermal-state model is valid.
    The relation nbar = Pr/(Pb-Pr) and the interpretation of the measured sideband ratios depend on the ion motion being thermal; the paper tests robustness but cannot independently prove it.
  • domain assumption The calculated Doppler limit model is correct for this trap.
    Supplemental Equation (1) with geometric factors of 1.7 for axial modes and 2.3 for radial modes is used to check measured temperatures; a wrong geometric factor or linewidth would bias the largest correction.
  • domain assumption The collision-shift scaling from prior work remains valid.
    The background-gas collision shift is scaled from reference [27] with a weakened Debye-Waller factor; this model is not independently verified in the new apparatus.
  • domain assumption The 25Mg+ hyperfine constants used to convert measured shifts to B_AC are correct.
    Converting the measured 25Mg+ hyperfine shifts into the ac magnetic field uses known magnetic constants; an error would affect the ac quadratic Zeeman correction, though this is a small term.
  • standard math Quadrature additivity of systematic uncertainties holds.
    The total 5.5×10^-19 is the quadrature sum of independently estimated terms; correlations between terms are assumed negligible.

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Pith. "Pith review of High-Stability Single-Ion Clock with $5.5\times10^{-19}$ Systematic Uncertainty." pith.science (2026). https://pith.science/paper/PVOQTW72

@misc{pith2026250413071,
  author       = {Pith},
  title        = {Pith review of: High-Stability Single-Ion Clock with $5.5\times10^-19$ Systematic Uncertainty},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVOQTW72}},
  note         = {Machine review of arXiv:2504.13071}
}
abstract

We report a single-ion optical atomic clock with fractional frequency uncertainty of $5.5\times10^{-19}$ and fractional frequency stability of $3.5 \times10^{-16}/\sqrt{\tau/\mathrm{s}}$, based on quantum logic spectroscopy of a single $^{27}$Al$^+$ ion. A co-trapped $^{25}$Mg$^+$ ion provides sympathetic cooling and quantum logic readout of the $^{27}$Al$^+$ $^1$S$_0\leftrightarrow^3$P$_0$ clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous $^{27}$Al$^+$ clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the RF ion trap, eliminating systematic uncertainty due to field orientation.

Figures

Figures reproduced from arXiv: 2504.13071 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Frequency shift on the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Stark shift due to cooling light. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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    4 µ s is the depumping time constant for S=1, cal- culated from 25Mg+ atomic structure coefficients and our Doppler cooling beam detuning. We integrate over the detection time td to account for continued depump- ing by the detection beam, giving the total counts Ctot = (b + d)td...

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.