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arXiv:2501.09615 · Journal of Physics Conference Series

High-accuracy multi-ion spectroscopy with mixed-species Coulomb crystals

Jonas Keller, H. N. Hausser, Ingo Richter, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, Erik Benkler, B. Lipphardt, Sören Dörscher, K. Stahl, J. Klose, Christian Lisdat, Melina Filzinger, Nils Huntemann, E. Peik, T. E. Mehlstäubler

Published Nov 1, 2024• 1 citation
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Abstract

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.

DOI
10.1088/1742-6596/2889/1/012050

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In + 115 − Yb + 172 Coulomb Crystal Clock with 2.5 × 10 − 18 Systematic Uncertainty

H. N. Hausser, J. Keller, T. Nordmann +17 more

We present a scalable mixed-species Coulomb crystal clock based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{115}In^{+}. ^{172}Yb^{+} ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In^{+}-3Yb^{+} crystal, achieving a relative systematic uncertainty of 2.5×10^{-18} and a relative frequency instability of 1.6×10^{-15}/sqrt[τ/1 s]. We report on absolute frequency measurements with an uncertainty of 1.3×10^{-16} and optical frequency comparisons with clocks based on ^{171}Yb^{+} (E3) and ^{87}Sr. With a fractional uncertainty of 4.4×10^{-18}, the former is-to our knowledge-the most accurate frequency ratio value reported to date. For the ^{115}In^{+}/^{87}Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four ^{115}In^{+} clock ions, which reduces the instability to 9.2×10^{-16}/sqrt[τ/1 s].

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Optical clocks based on linear ion chains with high stability and accuracy

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Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of $10^{-18}$ 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 $10^{-19}$. 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 $10^{-19}$ level. Using this method, we demonstrate regions of $400$ $\mu$m and $2$ mm length in our trap array with time dilation shifts due to micromotion close to $1\times10^{-19}$ and below $10^{-18}$, 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 $1\times10^{-19}$. 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.

•Dec 6, 2017•5 citations

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

Melina Filzinger, Martin R. Steinel, Jian Jiang +4 more

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.

physics.atom-phCross-listedarXiv:2603.23446•Mar 25, 2026•0 citations

In+ 115 - Yb+ 172 Coulomb Crystal Clock with 2.5×10-18 Systematic Uncertainty

H. N. Hausser, Jonas Keller, T. Nordmann +12 more

We present a scalable mixed-species Coulomb crystal clock based on the S01↔P30 transition in In+115. Yb+172 ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In+-3Yb+ crystal, achieving a relative systematic uncertainty of 2.5×10-18 and a relative frequency instability of 1.6×10-15/τ/1 s. We report on absolute frequency measurements with an uncertainty of 1.3×10-16 and optical frequency comparisons with clocks based on Yb+171 (E3) and Sr87. With a fractional uncertainty of 4.4×10-18, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the In+115/Sr87 ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four In+115 clock ions, which reduces the instability to 9.2×10-16/τ/1 s.

•Jan 1, 2025•0 citations

Evaluation of an In+ Coulomb crystal clock with relative uncertainties in the low 10−18 range

H. N. Hausser

Clocks have been among the most accurate man-made devices for centuries. Atomic clocks, which have been defining time by means of a microwave transition in the 133Cs atom since 1967, represent a major step in this development. A redefinition of the SI unit of time based on optical atomic clocks is currently under discussion. This forthcoming redefinition requires, among other criteria, the repeated demonstration of the consistency of different optical frequency standards in the low 10−18 range. In this work, the first evaluation of the systematic shifts and their uncertainties in a 115In+–172Yb+ Coulomb crystal clock is presented. This clock utilizes the 1S0 ↔ 3P0 transition in 115In+. 172Yb+ ions are co-trapped with the 115In+ ions in a segmented Paul trap and used for sympathetic cooling. With a systematic uncertainty of 2.5×10−18 when operating with a 1In+–3Yb+ crystal and 2.6×10−18 when operating with a 2In+–4Yb+ crystal, this clock is one of the most accurate clocks in the world. In addition, the operation of the clock with multiple clock ions is the first of its kind at this level of uncertainty. Measurements with up to four clock ions show a reduction in instability from 1.6×10−15/√ τ for a single indium ion to 9.2(4)×10−16/√τ when operating with four indium ions. By using an additional quench laser, the instability in another series of measurements was reduced from a single-ion instability of 1.5×10−15/√ τ to a four-ion instability of 7.1(15)×10−16/√τ , which is consistent with the expected scaling of 1/√N with the number of clock ions N. In this work, the hyperfine structure of the 3P0 ↔ 1P1 transition used for quenching was also resolved for the first time and the hyperfine constants were determined to be AHFS = 265.42(75)MHz and BHFS = 291.4(135) MHz. In frequency comparisons with other clocks, the optical frequency ratios 115In+/171Yb+(E3) and 115In+/87Sr were determined. With a relative total uncertainty of 4.2 × 10−18, the former ratio is the most accurate frequency ratio of different species published to date. It is also the first to meet one of the requirements defined on the roadmap for redefining the SI unit of the second: Measurements of frequency ratios with relative total measurement uncertainties below 5 × 10−18. The determination of the absolute frequency results in an uncertainty of 1.3 × 10−16 for the 1S0 ↔ 3P0 transition in 115In+, which is limited by that of the cesium fountains. The results obtained summarized: ν115In+ ν171Yb+(E3) =1.973 773 591 557 215 788(8) ν115In+ ν87Sr =2.952 748 749 874 860 781(27) ν115In+ =1 267 402 452 901 038.87(16) Hz

•Jan 1, 2025•0 citations

Controlling systematic frequency uncertainties at the 10−19 level in linear Coulomb crystals

Jonas Keller, T. Burgermeister, Dimitri Kalincev +5 more

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 ${\mathrm{In}}^{+}$ clock, sympathetically cooled with ${\mathrm{Yb}}^{+}$ 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.

arXiv:1803.08248•Physical Review A•Jan 7, 2019•68 citations
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.
We present a scalable mixed-species Coulomb crystal clock based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{115}In^{+}. ^{172}Yb^{+} ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In^{+}-3Yb^{+} crystal, achieving a relative systematic uncertainty of 2.5×10^{-18} and a relative frequency instability of 1.6×10^{-15}/sqrt[τ/1 s]. We report on absolute frequency measurements with an uncertainty of 1.3×10^{-16} and optical frequency comparisons with clocks based on ^{171}Yb^{+} (E3) and ^{87}Sr. With a fractional uncertainty of 4.4×10^{-18}, the former is-to our knowledge-the most accurate frequency ratio value reported to date. For the ^{115}In^{+}/^{87}Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four ^{115}In^{+} clock ions, which reduces the instability to 9.2×10^{-16}/sqrt[τ/1 s].
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 present a scalable mixed-species Coulomb crystal clock based on the S01↔P30 transition in In+115. Yb+172 ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In+-3Yb+ crystal, achieving a relative systematic uncertainty of 2.5×10-18 and a relative frequency instability of 1.6×10-15/τ/1 s. We report on absolute frequency measurements with an uncertainty of 1.3×10-16 and optical frequency comparisons with clocks based on Yb+171 (E3) and Sr87. With a fractional uncertainty of 4.4×10-18, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the In+115/Sr87 ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four In+115 clock ions, which reduces the instability to 9.2×10-16/τ/1 s.
Clocks have been among the most accurate man-made devices for centuries. Atomic clocks, which have been defining time by means of a microwave transition in the 133Cs atom since 1967, represent a major step in this development. A redefinition of the SI unit of time based on optical atomic clocks is currently under discussion. This forthcoming redefinition requires, among other criteria, the repeated demonstration of the consistency of different optical frequency standards in the low 10−18 range. In this work, the first evaluation of the systematic shifts and their uncertainties in a 115In+–172Yb+ Coulomb crystal clock is presented. This clock utilizes the 1S0 ↔ 3P0 transition in 115In+. 172Yb+ ions are co-trapped with the 115In+ ions in a segmented Paul trap and used for sympathetic cooling. With a systematic uncertainty of 2.5×10−18 when operating with a 1In+–3Yb+ crystal and 2.6×10−18 when operating with a 2In+–4Yb+ crystal, this clock is one of the most accurate clocks in the world. In addition, the operation of the clock with multiple clock ions is the first of its kind at this level of uncertainty. Measurements with up to four clock ions show a reduction in instability from 1.6×10−15/√ τ for a single indium ion to 9.2(4)×10−16/√τ when operating with four indium ions. By using an additional quench laser, the instability in another series of measurements was reduced from a single-ion instability of 1.5×10−15/√ τ to a four-ion instability of 7.1(15)×10−16/√τ , which is consistent with the expected scaling of 1/√N with the number of clock ions N. In this work, the hyperfine structure of the 3P0 ↔ 1P1 transition used for quenching was also resolved for the first time and the hyperfine constants were determined to be AHFS = 265.42(75)MHz and BHFS = 291.4(135) MHz. In frequency comparisons with other clocks, the optical frequency ratios 115In+/171Yb+(E3) and 115In+/87Sr were determined. With a relative total uncertainty of 4.2 × 10−18, the former ratio is the most accurate frequency ratio of different species published to date. It is also the first to meet one of the requirements defined on the roadmap for redefining the SI unit of the second: Measurements of frequency ratios with relative total measurement uncertainties below 5 × 10−18. The determination of the absolute frequency results in an uncertainty of 1.3 × 10−16 for the 1S0 ↔ 3P0 transition in 115In+, which is limited by that of the cesium fountains. The results obtained summarized: ν115In+ ν171Yb+(E3) =1.973 773 591 557 215 788(8) ν115In+ ν87Sr =2.952 748 749 874 860 781(27) ν115In+ =1 267 402 452 901 038.87(16) Hz
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.