The first optical atomic clock based on a highly charged ion (B-like Ar13+^{13+}, a 441 nm magnetic-dipole fine-structure transition) achieved in 2022 a total evaluated fractional systematic uncertainty of 2.2×10−172.2\times10^{-17}, dominated by an uncompensated axial excess-micromotion (time-dilation) shift, and its isotope-shift measurement between 40^{40}Ar13+^{13+} and 36^{36}Ar13+^{13+} provided the first experimental test of the quantum-electrodynamic (QED) nuclear-recoil contribution in a many-electron system, at the 31% level. The open problem is to advance the highly-charged-ion (HCI) clock platform from this proof of principle to clock operation with a comprehensively evaluated total systematic uncertainty below 1×10−181\times10^{-18}, controlling the micromotion shift through improved trapping so that every itemized systematic term — including the clock-laser-induced ac Zeeman shift, which contributed 2×10−182\times10^{-18} in the 2022 budget — falls within the sub-10−1810^{-18} quadrature total. Longer-lived HCI clock species (e.g. Ni12+^{12+}, Pd12+^{12+}, Pr9+^{9+}) and extension of HCI isotope shifts to several charge states of one element for fifth-force and ultralight dark-matter searches are explicitly linked extensions of the same program named in the source, and more stringent tests of the many-electron QED nuclear recoil enabled by the improved accuracy are a further linked extension; none of these is an acceptance requirement. No HCI clock below the 10−1810^{-18} total systematic level has yet been reported; the problem is open and actively pursued.

Background

An optical atomic clock steers a laser to a narrow (sub-hertz to millihertz) atomic transition and realizes time/frequency with fractional systematic uncertainties at the 10−1810^{-18} level in the best systems; the 'total systematic uncertainty' is the quadrature sum of all known frequency shifts of the reference transition (with their uncertainties), determined by measurement, bounded, or calculated. Highly charged ions (HCIs) — atoms stripped of many electrons — were proposed decades ago as clock references because their remaining electrons are so tightly bound that electric-dipole-allowed transitions move out of the optical range, suppressing sensitivity to external electric and magnetic fields (blackbody radiation, quadrupole and Stark shifts) by orders of magnitude, while simultaneously magnifying sensitivity to relativistic, nuclear-size, and possible new-physics effects, including variation of the fine-structure constant α\alpha. Three techniques unlocked HCI clocks: sympathetic cooling of hot HCIs by Be+^{+} ions in a Paul trap, quantum-logic spectroscopy (QLS — mapping the HCI's internal state onto a co-trapped, laser-coolable 'logic' ion whose fluorescence is detected), and quantum control of the HCI's motion. Excess micromotion is the driven oscillation of a trapped ion at the radio-frequency of the Paul trap's confining field; any residual (uncompensated) component adds second-order Doppler (time-dilation) shift that has historically limited trapped-ion clock accuracy. In November 2022, King, Spieß, Micke, Wilzewski, Leopold, Benkler, Lange, Huntemann, Surzhykov, Yerokhin, Crespo López-Urrutia and Schmidt demonstrated the first HCI clock, based on the boron-like Ar13+^{13+} ground-configuration fine-structure magnetic-dipole (M1) transition 2P1/2→2P3/22P_{1/2}\rightarrow2P_{3/2} at 441 nm (natural linewidth 17 Hz), read out by QLS and compared against a 171^{171}Yb+^{+} E3 optical clock. Its total systematic uncertainty was 2.2×10−172.2\times10^{-17}, by far the largest contributor being time dilation from an unexpectedly axial, uncompensated excess-micromotion component; the next-largest systematic was the ac Zeeman shift (a shift of Zeeman sublevels by oscillating magnetic fields) induced by the clock laser, at the low-10−1810^{-18} level, while the quadratic Zeeman shift from the trap's rf magnetic fields was only bounded (assumed below 10−2110^{-21}) because its magnitude was difficult to determine. The authors state that an improved ion trap will reduce the micromotion uncertainty 'to well below the 10−1810^{-18} level'. Beyond clock operation, comparing the two argon isotopes 40^{40}Ar13+^{13+} and 36^{36}Ar13+^{13+} measured the isotope shift (the frequency difference between isotopes) with nine-orders-of-magnitude improvement. The isotope shift decomposes into the mass shift — the normal and specific (electron-correlation) mass shifts arising from nuclear recoil, including a purely radiative QED recoil contribution of order αm/M\alpha m/M — and the field shift from the different nuclear charge radii. The measurement, compared with the authors' improved configuration-interaction-plus-QED calculations (CI: a many-electron variational method combining a finite set of electronic configurations; QED corrections for radiative and recoil effects), tested the QED mass shift at the 31% level — the first experimental verification of the QED nuclear-recoil effect in a many-electron system, since all prior QED tests probed the static external-field regime. The paper's outlook names several forward goals: total systematic uncertainty demonstrably below 10−1810^{-18} via trap and micromotion-compensation improvements; HCI species with longer excited-state lifetimes (Ni12+^{12+}, Pd12+^{12+}, Pr9+^{9+}) to overcome the 17 Hz-linewidth stability penalty; and isotope shifts extended to very different charge states of the same element, enabling King-plot searches (plots of mass-scaled isotope shifts of two transitions against each other, whose nonlinearities can reveal a hypothetical fifth force mediated by a new boson, possibly associated with dark matter) — a context in which HCI transitions offer the largest known sensitivity to α\alpha variation and ultralight scalar dark matter. More stringent many-electron QED recoil tests are enabled by further improvements in measurement precision and reduced CI+QED theory uncertainty — the source calculates the QED recoil within the independent-electron approximation, with an ascribed 20% uncertainty representing residual electron-correlation effects (Methods 6.6, Supplementary Sec. 12.2). The 2022 apparatus also carried residual rf-magnetic-field and interrogation-field effects that were bounded, not eliminated: the rf-field magnitude was 'difficult to determine in our system' (its quadratic Zeeman shift bounded at the 10−2110^{-21} level, Supplementary Sec. 2.2, with the bounded g-factor-ratio effect ∣Δr/r∣<7×10−7|\Delta r/r|<7\times10^{-7} taken fully as uncertainty, Methods 6.4), a bound already negligible for a sub-10−1810^{-18} quadrature total, and the clock-laser ac Zeeman shift was pre-calibrated by zero-power extrapolation although it 'can be removed in real-time using more advanced interrogation schemes' (Supplementary Sec. 1.2).

Problem Statement

Advance the highly-charged-ion optical-clock platform from its 2022 proof of principle (total evaluated fractional systematic uncertainty 2.2×10−172.2\times10^{-17} for the Ar13+^{13+} 441 nm magnetic-dipole clock transition) to clock operation with a comprehensively evaluated total fractional systematic uncertainty below 1×10−181\times10^{-18}, in which the excess-micromotion (second-order Doppler) shift, including the previously uncompensated axial component, is measured, compensated, and bounded at or below that level through trap-design and micromotion-compensation improvements, and every other itemized systematic term — including the clock-laser-induced ac Zeeman shift, which contributed 2×10−182\times10^{-18} in the 2022 budget — is controlled at or below that level by whatever experimental means are used. The completion boundary of the problem is an operating HCI clock with a published, itemized systematic uncertainty budget whose quadrature total is below 1×10−181\times10^{-18}. Realizing longer-lived HCI clock species (e.g. Ni12+^{12+}, Pd12+^{12+}, Pr9+^{9+}) to improve short-term stability, extending isotope-shift measurements to multiple charge states of the same element for King-plot searches for hypothetical fifth forces or ultralight scalar dark matter, and using the resulting accuracy — in combination with refined configuration-interaction-plus-QED isotope-shift calculations — to test the many-electron QED nuclear recoil in HCI optical clock transitions between isotopes (as demonstrated for 40^{40}Ar13+^{13+} versus 36^{36}Ar13+^{13+}) more stringently than the 31% level of 2022 are explicitly linked extensions of this program (the first two named in the source, the recoil-test extension enabled by the platform's demonstrated isotope-shift capability); answers may pursue them, but acceptance of the core problem does not require them.

References

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