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IEEE Transactions on Instrumentation and Measurement

Minimizing the time-dilation shift in Penning trap atomic clocks

Jun Tan, J. J. Bollinger, David J. Wineland

Published Apr 1, 1995• 19 citations
Publisher

Abstract

If environmental perturbations are made negligible, the time-dilation shift is expected to give one of the largest systematic uncertainties in a stored ion clock. In general, this shift increases with the number of trapped ions. Fluctuations in the time dilation shift therefore could limit the frequency stability of an ion clock. We show that in a Penning trap, relativistic time dilation can be minimized if the laser-cooled ions are prepared in a special spheroidal state. In addition, a modest stabilization of the spheroid near the minimum-shift configuration fan significantly reduce fluctuations in the time dilation. The results obtained for a single-species ion clock also provide a good approximation for a sympathetically cooled system.>

DOI
10.1109/19.377794

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Minimizing time dilation shift in Penning trap atomic clocks

J.N. Tan, J.J. Bollinger, D.J. Wineland

The time dilation shift is expected to give the largest systematic uncertainty in an ion clock. We show that, in a Penning trap, it can be minimized if the ions are prepared in a special spheroid. The results apply directly for one ion species and approximately for sympathetically cooled systems.>

Conference on Precision Electromagnetic Measurements•Dec 17, 2002•1 citation

High-stability optical clock based on a continuously ground-state cooled Al + ion without compromising its accuracy

Fabian Dawel, Lennart Pelzer, Kai Dietze +12 more

Single-ion optical clocks have shown systematic frequency uncertainties below 10 − 18 , but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an Al + clock ion via a cotrapped Ca + ion during clock interrogation suppresses the heating of the ions. Al + can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of ( − 1.69 ± 0.20 ) × 10 − 18 . The Ca + cooling light introduces an additional light shift on the Al + clock transition of ( − 9.3 ± 1.1 ) × 10 − 18 . We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with 10 − 19 motional and cooling laser-induced uncertainties for Al + and can be employed in other ion clocks as well.

arXiv:2509.22525•Physical Review Research•Apr 27, 2026•1 citation

Minimizing time-dilation in ion traps — Towards an optical clock with Coulomb crystals

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We present the status of our new experiment to lasercool linear chains of172Yb+and115In+ions for an optical clock based on the1S0-3P0transition in115In+. We successfully have trapped and laser-cooled Coulomb crystals of172Yb+ions in our new scalable ion trap that are used to characterize the trap and to sympathetically cool115In+ions. We could demonstrate an area of more than 65 μm, where the fractional frequency shifts due to time dilation are below 10-18for both ions.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2012•0 citations

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

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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.

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Laser Based, Single Trapped Ion Optical Atomic Clock with 1 × 10−17 Uncertainty Evaluated using the Time-Dilation Effect

Alan A. Madej, P. Dubé, Maria Tibbo +1 more

An atomic frequency reference using a single trapped ion has been evaluated to 1.2×10−17 uncertainty by exploiting the experimentally observed cancellation of micromotion induced Stark and time dilation shifts on the 88Sr+ 445-THz S-D transition.

Frontiers in Optics•Jan 1, 2014•0 citations

Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap

J. Keller, D. Kalincev, T. Burgermeister +5 more

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.

arXiv:1712.02335•Physical Review Applied•Jan 7, 2019•44 citations
If environmental perturbations are made negligible, the time-dilation shift is expected to give one of the largest systematic uncertainties in a stored ion clock. In general, this shift increases with the number of trapped ions. Fluctuations in the time dilation shift therefore could limit the frequency stability of an ion clock. We show that in a Penning trap, relativistic time dilation can be minimized if the laser-cooled ions are prepared in a special spheroidal state. In addition, a modest stabilization of the spheroid near the minimum-shift configuration fan significantly reduce fluctuations in the time dilation. The results obtained for a single-species ion clock also provide a good approximation for a sympathetically cooled system.>
Single-ion optical clocks have shown systematic frequency uncertainties below 10 − 18 , but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an Al + clock ion via a cotrapped Ca + ion during clock interrogation suppresses the heating of the ions. Al + can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of ( − 1.69 ± 0.20 ) × 10 − 18 . The Ca + cooling light introduces an additional light shift on the Al + clock transition of ( − 9.3 ± 1.1 ) × 10 − 18 . We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with 10 − 19 motional and cooling laser-induced uncertainties for Al + and can be employed in other ion clocks as well.
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.
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.