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Optics Letters

Precision determination of the ground-state hyperfine splitting of trapped 113Cd+ ions

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

Published Nov 2, 2021• 21 citations
Publisher

Abstract

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.

DOI
10.1364/ol.444045

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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.

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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 present the determination of the ground-state hyperfine splitting (νHFS) in laser-cooled 171Yb+ ions using our microwave quantum frequency standard (QFS). Employing Ramsey spectroscopy in a closed-loop measurement configuration, we have achieved a νHFS value of 12 642 812 118 469.0(8) mHz with a fractional uncertainty of 6.6×10−14. This result aligns with previously reported values and represents the highest accuracy reported to date for such measurements conducted in a single-shot closed-loop configuration, without averaging over multiple dates. The development of this accurate 171Yb+ microwave QFS holds promise as a transportable time-frequency reference for satellite navigation systems.
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​.
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.
A stable and accurate frequency standard based on the 40.5 GHz ground-state hyperfine transition in 199Hg+{}^{199}{\mathrm{Hg}}^{+}199Hg+ ions is described. The ions are confined in a cryogenic linear Paul (rf) trap and laser cooled to form a linear crystal. With seven ions and a Ramsey interrogation time of 100 s, the fractional frequency stability is 3.3 $(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for measurement times $\ensuremath{\tau}<2\phantom{\rule{0ex}{0ex}}\mathrm{h}$. The ground-state hyperfine interval is measured to be 40 507 347 996.841 59 (14) (41) Hz, where the first number in the parentheses is the uncertainty due to statistical and systematic effects, and the second is the uncertainty in the frequency of the time scale to which our standard is compared.
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.