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Physical Review A

Sympathetic-laser-cooling ion microwave frequency standard with accuracy and stability at 10 − 15 level

Y.Z. Zheng, S. N. Miao, Yiting Chen, Wenxin Shi, Jianwei Zhang, Lijun Wang

Published Mar 3, 2026• 0 citations
Publisher
DOI
10.1103/1fp9-738h

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Sympathetic cooling of 113^{113}113Cd+^++ by laser-cooled 40^{40}40Ca+^++ in a linear Paul trap for Microwave Ion Clocks
We report sympathetic cooling of 113^{113}113Cd+^++ by laser-cooled 40^{40}40Ca+^++ in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of 113^{113}113Cd+^++ ions was achieved. The temperature of these ions was measured at 90(10)90(10)90(10) mK, and the corresponding uncertainty arising from the second-order Doppler shifts was estimated to a level of 2×10−172\times10^{-17}2×10−17. Up to 4.2×1054.2\times10^54.2×105 Cd+^++ ions were confined in the trap, and the confinement time constant was measured to be 84 hours. After three hours of confinement, there were still 10510^5105 Cd+^++ ions present, indicating that this Ca+^++--Cd+^++ dual ion system is surprisingly stable. The ac Stark shift was induced by the Ca+^++ lasers and fluorescence, which was carefully estimated to an accuracy of 5.4(0.5)×10−175.4(0.5)\times10^{-17}5.4(0.5)×10−17 using a high-accuracy \textit{ab initio} approach. The Dick-effect-limited Allan deviation was also deduced because deadtimes were shorter. These results indicate that a microwave clock based on this sympathetic cooling scheme holds promise in providing ultra-high frequency accuracy and stability.
Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e gJ{g}_{J}gJ​ factors of 111,113Cd+^{111,113}\mathrm{Cd}^{+}111,113Cd+. The hyperfine splittings and Land\'e gJ{g}_{J}gJ​ factors of the 5s2S1/25s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}5s2S1/2​ and 5p2P1/2,3/25p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}5p2P1/2,3/2​ states of 111,113Cd+^{111,113}\mathrm{Cd}^{+}111,113Cd+ are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the 5p2P3/25p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}5p2P3/2​ state of 111,113Cd+^{111,113}\mathrm{Cd}^{+}111,113Cd+ are derived based on the laser-induced fluorescence spectroscopy. The Cd+{\mathrm{Cd}}^{+}Cd+ ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled Ca+{\mathrm{Ca}}^{+}Ca+ ions. The calculated values and the derived values are cross-checked, thereby guaranteeing the reliability of our results. The results provided in this paper can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, thus further improving the stability and accuracy of the microwave frequency standards based on trapped 111,113Cd+^{111,113}\mathrm{Cd}^{+}111,113Cd+ ions.