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arXiv:2610.15609

Proposal for a multi-ion optical clock with hundreds of ions

Pavel Kamenskikh, Vasiliy Smirnov, Ilya Gerasin, Ilya Semerikov, Wei Zhang

physics.atom-phquant-phSubmitted Oct 11, 2026• Announced Oct 13, 2026• 0 citations
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Abstract

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 $^{40}\mathrm{Ca}^{+}$ 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 $10^{-18}$ level and an expected 20-fold improvement in frequency stability compared to single ion clocks.

AI Summary

Scaling ion clocks to hundreds of ions requires controlling spatially varying quadrupole shifts and micromotion. This paper proposes a segmented circular surface trap for a ring of 400 $^{40}\mathrm{Ca}^{+}$ ions, with radius approximately $600\,\mu\mathrm{m}$ and spacing approximately $10\,\mu\mathrm{m}$. With the quantization axis perpendicular to the ring, rotational symmetry makes the ideal space-charge quadrupole shift common to all ions rather than a source of inhomogeneous broadening. Electrostatic simulations, regularized electrode-voltage optimization, and numerical equilibrium-position calculations assess symmetry breaking and compensation. For the modeled uncompensated ring, the quadrupole-shift distribution has mean $2.07$ Hz and standard deviation $0.27$ Hz, compared with $24$ Hz and $11$ Hz for a reference 100-ion harmonic linear chain. Using 65 electrode pairs reduces the modeled tangential stray field by approximately 50%, leaving a standard deviation near $3.4$ V/m; the resulting residual quadrupole-shift inhomogeneity is estimated below $10^{-19}$ fractionally. The paper also specifies interrogation beams and a fluorescence-imaging objective. Combining compensation with established dynamical-decoupling, magic-RF, and cryogenic techniques gives a projected total fractional uncertainty below $0.7\times10^{-18}$. The ideal projection-noise stability gain is $\sqrt{400}=20$, assuming unchanged interrogation time and contrast. These are projections, not experimental results. The compensation study uses an interpolated, previously measured tangential-field profile and assumes zero radial and vertical stray fields. Several uncertainty contributions are adopted from single-ion literature. Preserving symmetry and compensating stray fields remain central experimental requirements; extension to thousands of ions would require additional electrode-control, interrogation, and readout engineering.

Little sign of AI-generated textStrong assumptionsMissing comparisonPossible errorOverclaims

Central claim may not hold: The reported ring-versus-linear space-charge shift spreads differ by about 41, not 100, and do not establish two-orders-of-magnitude suppression of quadrupole shifts generally. The compensation calculation tests only tangential stray fields, incorrectly calls its 1200-by-130 system underdetermined, and does not justify extending its achieved performance to arbitrary three-component fields. The quadrupole budget does not evaluate compensation-electrode and stray-field gradient contributions or establish how the calculated spatial spread translates into clock-frequency systematic uncertainty. The claimed post-compensation quadrupole uncertainty below 10^-19 lacks a reported post-compensation numerical distribution or sufficient supporting uncertainty analysis. The projected total uncertainty relies on transferring single-ion uncertainty estimates to the proposed architecture, while the valid 20-fold stability gain remains conditional on preserving interrogation time and contrast.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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10 pages, 6 figures

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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.
Scaling ion clocks to hundreds of ions requires controlling spatially varying quadrupole shifts and micromotion. This paper proposes a segmented circular surface trap for a ring of 400 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions, with radius approximately 600 μm600\,\mu\mathrm{m}600μm and spacing approximately 10 μm10\,\mu\mathrm{m}10μm. With the quantization axis perpendicular to the ring, rotational symmetry makes the ideal space-charge quadrupole shift common to all ions rather than a source of inhomogeneous broadening.
Electrostatic simulations, regularized electrode-voltage optimization, and numerical equilibrium-position calculations assess symmetry breaking and compensation. For the modeled uncompensated ring, the quadrupole-shift distribution has mean 2.072.072.07 Hz and standard deviation 0.270.270.27 Hz, compared with 242424 Hz and 111111 Hz for a reference 100-ion harmonic linear chain. Using 65 electrode pairs reduces the modeled tangential stray field by approximately 50%, leaving a standard deviation near 3.43.43.4 V/m; the resulting residual quadrupole-shift inhomogeneity is estimated below 10−1910^{-19}10−19 fractionally. The paper also specifies interrogation beams and a fluorescence-imaging objective.
Combining compensation with established dynamical-decoupling, magic-RF, and cryogenic techniques gives a projected total fractional uncertainty below 0.7×10−180.7\times10^{-18}0.7×10−18. The ideal projection-noise stability gain is 400=20\sqrt{400}=20400​=20, assuming unchanged interrogation time and contrast. These are projections, not experimental results. The compensation study uses an interpolated, previously measured tangential-field profile and assumes zero radial and vertical stray fields. Several uncertainty contributions are adopted from single-ion literature. Preserving symmetry and compensating stray fields remain central experimental requirements; extension to thousands of ions would require additional electrode-control, interrogation, and readout engineering.
Abstract We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic field shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions, such as 40 Ca + , 88 Sr + , 138 Ba + and 176 Lu + . Taking a spherically symmetric Coulomb crystal formed by 400 40 Ca + ions as an example, we show through numerical simulations that the inhomogeneous linewidth of tens of Hertz in such a crystal together with linear Zeeman shifts of order 10 MHz are reduced to form a linewidth of around 1 Hz. We estimate a two-order-of-magnitude reduction in averaging time compared to state-of-the art single ion frequency references, assuming a probe laser fractional instability of 10 − 15 . Furthermore, a statistical uncertainty reaching 2.9 × 10−16 in 1 s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an 27 Al + clock.
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.
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.
We study and characterize a quasicontinuous dynamical decoupling scheme that effectively suppresses dominant frequency shifts in a multi-ion optical clock. Addressing the challenge of inhomogeneous frequency shifts in such systems, our scheme mitigates primary contributors, namely, the electric quadrupole and the linear Zeeman shifts. Based on ^{88}Sr^{+} ions, we implement the scheme in linear chains of up to 7 ions and demonstrate a significant suppression of the shift by more than 3 orders of magnitude, leading to relative frequency inhomogeneity below 7×10^{-17}. Additionally, we evaluate the associated systematic shift arising from the radio-frequency drive used in the QCDD scheme, showing that, in the presented realization, its contribution to the systematic relative frequency uncertainty is below 10^{-17}, with the potential for further improvement. These results provide a promising avenue toward implementing multi-ion clocks exhibiting an order of magnitude or more improvement in stability while maintaining a similar high degree of accuracy to that of single-ion clocks.
The optical clock is a fundamental applications of the coherence of ultracold atoms. Most of the implementations with trapped ions are based on the single-ion optical clock by Dehmelt [1], and some of them have successfully achieved inaccuracies in the 10-18level [2]. The idea has been extended to systems consisting of many neutral atoms by Katori with proper engineering on light shift associated with the optical lattice [3]. The enhanced stability is the great advantage obtained by multiple atoms. Extension of the single-ion system to multi-ion systems requires considerations on the inhomogeneous electric quadrupole shift originating from non-uniform electric field gradient at the location of each ion. A straightforward approach is to use ion species with null quadrupole moment such as In+, Al+[4]. We present another approach using ions with non-zero quadrupole moment. In the approach we use a planar surface trap to arrange the ions in an equally-spaced manner to vanish the inhomogeneous shift. We show that a clock with multiple Ca+ions can be operated even without a reference cavity for the clock laser, and that superradiant clock is expected when the ions are coupled to a cavity.
We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals and impose one of the limitations forcing current optical ion clocks to work with a single probe ion. Canceling this shift, at each interrogation cycle of the ion frequency, reduces the complexity in using N>1 ions in clocks, thus allowing for a reduction of the instability in the clock frequency by sqrt[N] according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven ^{88}Sr^{+} ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to the ≈10 mHz level where other shifts, such as the relativistic second-order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of first-order Zeeman shifts.