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Optics Express

High-accuracy measurement of the ^113Cd^+ ground-state hyperfine splitting at the milli-Hertz level

Shiguang Wang, Jianwei Zhang, K. Miao, Z. B. Wang, Ling Wang

Published May 14, 2013• 19 citations
Publisher

Abstract

We have developed a microwave frequency standard based on the 15.2 GHz ground-stated hyperfine transition of (113)C(+) ions. Using a laser-cooled ion cloud trapped in a linear quadrupole Paul trap, the clock transition frequency is measured to be 15 199 862 855.0125(87) Hz, with an accuracy at the 10(-13) level. The main errors are from the microwave frequency reference used in the experiment. The precision is improved by nearly two orders of magnitude than that reported before.

DOI
10.1364/oe.21.012434

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Microwave frequency standards based on ions are promising as the next generation atomic clocks. This paper reports the recent progresses of the microwave frequency standard based on laser-cooled113Cd+ions developed at Tsinghua University. Based on the current experimental setup, the ground-state hyperfine splitting of113Cd+is measured with higher precision and a better short-term frequency stability is obtained than before. To improve the performance of the Cd+clock further, a new experimental setup with dual-traps is designed, and bi-ions operation is proposed.

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Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e ${g}_{J}$ factors of $^{111,113}\mathrm{Cd}^{+}$. The hyperfine splittings and Land\'e ${g}_{J}$ factors of the $5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}$ states of $^{111,113}\mathrm{Cd}^{+}$ are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{111,113}\mathrm{Cd}^{+}$ are derived based on the laser-induced fluorescence spectroscopy. The ${\mathrm{Cd}}^{+}$ ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled ${\mathrm{Ca}}^{+}$ 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 $^{111,113}\mathrm{Cd}^{+}$ ions.

arXiv:2201.06719•Physical Review A•Jul 27, 2022•6 citations
We have developed a microwave frequency standard based on the 15.2 GHz ground-stated hyperfine transition of (113)C(+) ions. Using a laser-cooled ion cloud trapped in a linear quadrupole Paul trap, the clock transition frequency is measured to be 15 199 862 855.0125(87) Hz, with an accuracy at the 10(-13) level. The main errors are from the microwave frequency reference used in the experiment. The precision is improved by nearly two orders of magnitude than that reported before.
We measured the ground-state hyperfine splitting of trapped 113 C d + ions to be 15199862855.02799(27) Hz with a fractional uncertainty of 1.8 × 10 − 14 . The ions were trapped and laser-cooled in a linear quadrupole Paul trap. The fractional frequency stability was measured to be 4.2 × 10 − 13 / τ , obtained from Ramsey fringes of high signal-to-noise ratios and taken over a measurement time of nearly 5 h, which is close to the short-term stability limit estimated from the Dick effect. Our result is consistent with previously reported values, but the measurement precision is four times better than the best result obtained to date.
We discuss frequency standards based on laser-cooled 199Hg+ ions confined in cryogenic rf traps. In one experiment, the frequency of a microwave source is served to the ions' ground-state hyperfine transition at 40.5 GHz. For seven ions and a Ramsey free precession time of 100 s, the fractional frequency stability is 3.3 (2) X 10-13 (tau) -1/2 for measurement times (tau) < 2 h. The ground-state hyperfine interval is measured to be 40 507 347 996.841 59 (14) (41) Hz, where the first number in parentheses is the uncertainty due to statistics and systematic errors, and the second is the uncertainty in the frequency of the time scale to which the standard is compared. In a second experiment under development, a strong-binding cryogenic trap will confine a single ion used for an optical frequency standard based on a narrow electric quadrupole transition at 282 nm. The bandwidth of the laser used to drive this transition is less than 10 Hz at 563 nm.
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-performance113Cd+^{113}\text{Cd}^{+}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 of4.2×10−13/τ4.2\times 10^{-13}/\sqrt{\tau}4.2×10−13/τ​and a relative frequency uncertainty of1.8×10−141.8\times 10^{-14}1.8×10−14, improving nearly three orders of magnitude compared to the result from JPL. The ground-state hyperfine splitting of113Cd+^{113}\text{Cd}^{+}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. Using40Ca+^{40}\text{Ca}^{+}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 to3.48×10−13/τ3.48\times 10^{-13}/\sqrt{\tau}3.48×10−13/τ​.
Microwave frequency standards based on ions are promising as the next generation atomic clocks. This paper reports the recent progresses of the microwave frequency standard based on laser-cooled113Cd+ions developed at Tsinghua University. Based on the current experimental setup, the ground-state hyperfine splitting of113Cd+is measured with higher precision and a better short-term frequency stability is obtained than before. To improve the performance of the Cd+clock further, a new experimental setup with dual-traps is designed, and bi-ions operation is proposed.
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.