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arXiv:2204.05040 · Physical Review Applied

High-Performance Microwave Frequency Standard Based on Sympathetically Cooled Ions

H. R. Qin, S. N. Miao, J. Z. Han, N. C. Xin, Y. T. Chen, Jianwei Zhang, L.J. Wang

Published Aug 8, 2022• 15 citations
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Abstract

The ion microwave frequency standard is a candidate for the next generation of microwave frequency standard with the potential for very wide applications. The Dick effect and second-order Doppler frequency shift (SODFS) limit the performance of ion microwave frequency standards. The introduction of sympathetic cooling technology can suppress the Dick effect and SODFS and improve the stability and accuracy of the frequency standard. However, the sympathetically cooled ion microwave frequency standard has seldom been studied before. This paper reports a high-performance sympathetically cooled ion microwave frequency standard in a Paul trap. Using laser-cooled ${}^{40}{\mathrm{Ca}}^{+}$ as coolant ions, ${}^{113}{\mathrm{Cd}}^{+}$ ion crystal is cooled to below 100 mK and has a coherence lifetime of over 40 s. The short-term frequency stability reached $3.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/{\ensuremath{\tau}}^{1/2}$, which is comparable to that of the mercury ion frequency standard. Its uncertainty is $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$, which is better than that of directly laser-cooled cadmium ion frequency standard.

DOI
10.1103/physrevapplied.18.024023

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The ion microwave frequency standard is a candidate for the next generation of microwave frequency standard with the potential for very wide applications. The Dick effect and second-order Doppler frequency shift (SODFS) limit the performance of ion microwave frequency standards. The introduction of sympathetic cooling technology can suppress the Dick effect and SODFS and improve the stability and accuracy of the frequency standard. However, the sympathetically cooled ion microwave frequency standard has seldom been studied before. This paper reports a high-performance sympathetically cooled ion microwave frequency standard in a Paul trap. Using laser-cooled 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ as coolant ions, 113Cd+{}^{113}{\mathrm{Cd}}^{+}113Cd+ ion crystal is cooled to below 100 mK and has a coherence lifetime of over 40 s. The short-term frequency stability reached 3.48\ifmmode×\else\texttimes\fi10\ensuremath−13/\ensuremathτ1/23.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/{\ensuremath{\tau}}^{1/2}3.48\ifmmode×\else\texttimes\fi10\ensuremath−13/\ensuremathτ1/2, which is comparable to that of the mercury ion frequency standard. Its uncertainty is 1.5\ifmmode×\else\texttimes\fi10\ensuremath−141.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}1.5\ifmmode×\else\texttimes\fi10\ensuremath−14, which is better than that of directly laser-cooled cadmium ion frequency standard.
A microwave frequency standard based on113Cd+ions at Tsinghua University has been carried out for twelve years. To overcome the limitations of the Dick effect and the second-order Doppler frequency shift (SODFS), we propose to use heavy174Yb+as the coolant ions to sympathetically cool the large113Cd+cloud, which is expected to further improve the performance of the cadmium-ion microwave frequency standard. This paper reports our recent experimental and simulation progress towards the cadmium-ion microwave frequency standard.
We report a high-performance transportable microwave frequency standard scheme based on sympathetically cooled 113Cd+ ions using 40Ca+ as coolant ions. A transportable physical package (1.4 m3) with high-performance magnetic shielding (radial shielding coefficient 460 000) has been built. In experiments, more than 105 113Cd+ ions were sympathetically cooled to 90 mK in a Paul trap and the ion-loss time constant extends to 84 hours. Without direct cooling procedures, the Dick effect-limited Allan deviation due to the deadtimes is reduced to 1.8×10−14/τ. Under our scheme, the uncertainties in the main frequency shifts such as those from second-order Zeeman and second-order Doppler terms were reduced below the order of 10−15. The relevant ac Stark shifts uncertainties were estimated to be below 5×10−18. Minor shifts further reflect the superiority of coolant ions 40Ca+ for 113Cd+. These results indicate that a microwave clock based on this sympathetic cooling scheme shows potential in establishing a vehicle transportable ground-based time-frequency reference for navigation systems.
Abstract As a candidate for the next generation microwave clock, microwave atomic clocks based on trapped ions are currently studied worldwide. Since 2010, our team at Tsinghua University has been committed to developing a high-performance 113Cd+ microwave ion clock. In 2021, the laser-cooled cadmium-ion microwave clock constructed in our laboratory demonstrated remarkable performance, with a short-term instability of 4.2 × 10 − 13 / τ and a relative frequency uncertainty of 1.8 × 10−14, improving nearly three orders of magnitude compared to the result from JPL. The 0-0 ground-state hyperfine splitting frequency of 113Cd+ was determined to be 15199862855.02799(27) Hz, currently the most accurate measurement result for this transition frequency. Apart from that, we introduced the sympathetic cooling technology into the experiment of cadmium-ion microwave clock. Using 40Ca+ as the coolant ion, we obtained Ramsey patterns with a free evolution time of up to 100 seconds, ultimately improving the short-term instability of the system to 3.48 × 10 − 13 / τ . Moreover, a microwave frequency standard based on laser-cooled 171Yb+ ions has also been developed in our laboratory since 2021. The short-term frequency instability was measured to be 8.5 × 10 − 13 / τ . The ground-state hyperfine splitting frequency of 171Yb+ was determined to be 12642812118.4674(8) Hz with a fractional frequency uncertainty of 6.33 × 10−14.
174Yb+^{174}\mathrm{Yb}^+174Yb+-113Cd+^{113}\mathrm{Cd}^+113Cd+ sympathetic-cooling bi-species Coulomb crystal applied to microwave frequency standard
We reported the realization of a 174Yb+^{174}\mathrm{Yb}^+174Yb+-113Cd+^{113}\mathrm{Cd}^+113Cd+ bi-species Coulomb crystal comprising 174Yb+^{174}\mathrm{Yb}^+174Yb+ ions as coolant and verified its potential for application as a 113Cd+^{113}\mathrm{Cd}^+113Cd+ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+^{113}\mathrm{Cd}^+113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the 113Cd+^{113}\mathrm{Cd}^+113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−165\times10^{-16}5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+^{40}\mathrm{Ca}^+40Ca+-113Cd+^{113}\mathrm{Cd}^+113Cd+ crystal. The uncertainty from the second-order Zeeman effect, which contributes the largest uncertainty to the microwave-ion frequency standard, is reduced to 4×10−164\times10^{-16}4×10−16. The relevant AC Stark shift uncertainty is estimated to be 4×10−194\times10^{-19}4×10−19. These results indicate using 174Yb+^{174}\mathrm{Yb}^+174Yb+ as coolant ions for 113Cd+^{113}\mathrm{Cd}^+113Cd+ is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+^{174}\mathrm{Yb}^+174Yb+-113Cd+^{113}\mathrm{Cd}^+113Cd+ two-component crystal.
We reported the realization of a 174Yb+–113Cd+ bi-species Coulomb crystal comprising 174Yb+, a heavier ion, as coolant and verified the potential of applying a coolant ion with a greater mass than the clock ion to sympathetically cooled microwave frequency standard. The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micro-motion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+–113Cd+ crystal. The second-order Zeeman frequency shift, which contributes the largest term of the systematic frequency shifts to the microwave ion frequency standard, is estimated to be as low as 7.133×10−13 corresponding to the low value of the operating magnetic field. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results demonstrate that using a heavier coolant ion is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+–113Cd+ bicrystal.
SummaryThe ion microwave frequency standard is a candidate for the next generation of practical microwave frequency standards, which has a very wide application potential. Tsinghua University has continuously been working on the research and development of ion microwave frequency standards. A demonstration experiment of two laser-cooled cadmium ion microwave clocks with zero dead time shows a short-term stability of τ-0.95averaging. Besides, a microwave frequency standard based on cadmium ions sympathetically cooled by ytterbium ions has been realized, and the clock signal has been obtained. In addition, two new laser-cooled ytterbium ion microwave clocks are also being built.