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arXiv:2603.23446

A multi-ion optical clock with $\mathbf{5 \times 10^{-19}}$ uncertainty

Melina Filzinger, Martin R. Steinel, Jian Jiang, Daniel Bennett, Tanja E. Mehlstäubler, Ekkehard Peik, Nils Huntemann

physics.atom-phquant-phSubmitted Mar 24, 2026• Announced Mar 25, 2026• 0 citations
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Abstract

Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below $1\times10^{-18}$. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of $5.3\times10^{-19}$ and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the $10^{-20}$-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of $0.6926711632159660405(20)$, with a statistical uncertainty of $0.9\times10^{-18}$ and a combined uncertainty of $2.9\times 10^{-18}$. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.

Comments
11 pages, 4 figures

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A multi-ion optical clock with 5×10−19\mathbf{5 \times 10^{-19}}5×10−19 uncertainty
Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below 1×10−181\times10^{-18}1×10−18. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of 5.3×10−195.3\times10^{-19}5.3×10−19 and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the 10−2010^{-20}10−20-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of 0.6926711632159660405(20)0.6926711632159660405(20)0.6926711632159660405(20), with a statistical uncertainty of 0.9×10−180.9\times10^{-18}0.9×10−18 and a combined uncertainty of 2.9×10−182.9\times 10^{-18}2.9×10−18. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.
Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of 10−1810^{-18}10−18 and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, versatile platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as 10−1910^{-19}10−19. The concept is applicable to all clock transitions with low differential electric quadrupole moments. We observe 3D excess micromotion amplitudes of all individual ions inside a Coulomb crystal with nm resolution and prove that the related frequency shifts can be controlled simultaneously at the 10−1910^{-19}10−19 level. Using this method, we demonstrate regions of 400400400 μ\muμm and 222 mm length in our trap array with time dilation shifts due to micromotion close to 1×10−191\times10^{-19}1×10−19 and below 10−1810^{-18}10−18, respectively. Further measurements of the trapping environment and cooling dynamics calculations for mixed In+{}^++ / Yb+{}^++ crystals show that achievable clock uncertainties due to multi-ion operation in our setup are below 1×10−191\times10^{-19}1×10−19. This work will enable clock operation with multiple ions and open up the possibility of new interrogation schemes which allow optical clock stabilities beyond classical limits.
Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertainties related to spectroscopy with ion chains in an rf trap array designed for precision spectroscopy on simultaneously trapped ion ensembles. For the example of an In+{\mathrm{In}}^{+}In+ clock, sympathetically cooled with Yb+{\mathrm{Yb}}^{+}Yb+ ions, we show in our system that the expected systematic frequency uncertainties related to multi-ion operation can be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$. Our results pave the way to advanced spectroscopy schemes such as entangled clock spectroscopy and cascaded clock operation.
Abstract Multi-ion optical clocks offer the possibility of overcoming the low signal-to-noise ratio of single-ion clocks, while still providing low systematic uncertainties. We present simultaneous spectroscopy of up to four 115 In + clock ions in a linear Coulomb crystal, sympathetically cooled with 172 Yb + ions. In first clock comparisons, we see agreement below 1 × 10 −17 with results obtained using a single In + ion, for which we have evaluated the systematic uncertainty to be 2.5 × 10 −18 . Operation with four clock ions reduces the instability from 1.6 × 10 − 15 / t / ( 1 s ) to 9.2 × 10 − 16 / t / ( 1 s ) . We derive a model for decay-related dead time during state preparation, which matches the observed scaling of instability with clock ion number N , and indicates that 1 / N scaling can be achieved with the addition of a repump laser.
Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the 10−1810^{-18}10−18 level and an expected 20-fold improvement in frequency stability compared to single ion clocks.
We report a single-ion optical atomic clock with a fractional frequency uncertainty of 5.5×10^{-19} and fractional frequency stability of 3.5×10^{-16}/sqrt[τ/s], based on quantum logic spectroscopy of a single ^{27}Al^{+} ion. A cotrapped ^{25}Mg^{+} ion provides sympathetic cooling and quantum logic readout of the ^{27}Al^{+}^{1}S_{0}↔^{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.
Optical clocks based on trapped ions can achieve systematic frequency uncertainties below 10${}^{\ensuremath{-}18}$, enabling relativistic geodesy and precise tests of fundamental physics. However, today's single-ion clocks require averaging times of over a week to resolve frequencies at this level, and no multi-ion clock has been implemented, due to difficulties in controlling ion motion. The authors present an ion-trap array that confines up to 100 clock ions with time-dilation shifts in the low-10${}^{\ensuremath{-}19}$ range, and measure the driven motion of individual ions within an ion crystal. These results point to the next generation of ion clocks, and the realization of clock schemes that have languished.