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arXiv:2601.14811

Precision measurement of the ground-state hyperfine constant for $^9Be^+$ in a linear Paul trap via magnetically insensitive hyperfine transitions

Ao Zhi-Yuan, Wenli Bai, Qian-yu Zhang, Wen-Cui Peng, Xin Tong

Published Jan 21, 2026• 0 citations
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Abstract

Direct measurements of the ground-state magnetically insensitive hyperfine transition |F=2,mF=0>->|F=1,mF=0> of $^9Be^+$ ions have been performed using microwave-driven state transfer. The $^9Be^+$ ions are confined and laser-cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic field range of $ \pm 0.5 mT $ centered at zero magnetic field, and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant A is determined to be -625.008840(35) MHz, achieving a relative precision of $ 5.6 \times 10^{-8}$.

DOI
10.48550/arxiv.2601.14811

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Precision measurement of the ground-state hyperfine constant for 9Be+^9Be^+9Be+ in a linear Paul trap via magnetically insensitive hyperfine transitions
Direct measurements of the ground-state magnetically insensitive hyperfine transition |F=2,mF=0>->|F=1,mF=0> of 9Be+^9Be^+9Be+ ions have been performed using microwave-driven state transfer. The 9Be+^9Be^+9Be+ ions are confined and laser-cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic field range of ±0.5mT\pm 0.5 mT±0.5mT centered at zero magnetic field, and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant A is determined to be -625.008840(35) MHz, achieving a relative precision of 5.6×10−8 5.6 \times 10^{-8}5.6×10−8.
Direct measurements of the ground-state magnetically insensitive hyperfine transition | F = 2 , m F = 0 〉 → | F = 1 , m F = 0 〉 of Be + 9 ions have been performed using microwave-driven state transfer. The Be + 9 ions are confined and laser cooled in a linear Paul trap, forming a Coulomb crystal. The transition frequencies have been measured over a magnetic-field range of ± 0.5 mT centered at zero magnetic field and the acquired data were fitted accounting for the high-order Zeeman effect. The hyperfine constant A is determined to be − 625.008 840 ( 35 ) MHz, achieving a relative precision of 5.6 × 10 − 8 .
We report an experimental determination of the ground-state hyperfine constant AAA of the 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.
The Ramsey fringes on the ground-state hyperfine transition of 199 Hg + (ΔF = 1, Δm F = 0) ions trapped in a hyperbolic Paul trap are firstly observed with the method of time-separated oscillatory fields. The full width at half maximum of central Ramsey fringes is about 25 mHz and the corresponding quality factor Q of the line is greater than 10 12 for the trapped 199 Hg + microwave frequency standard. The hyperfine transition frequency shifted by magnetic field is also measured by the high-resolution Ramsey fringes. The final result is Δν h f s = 40507347997.3(0.5) Hz, which is corrected to zero magnetic field.
We present and discuss results from a measurement of the hyperfine a constant of the 1s^(2)2s^(2)2p^(6)3p^(2)2P1/2 excited state in 25Mg+ and the linewidth of the same state in 24Mg+. We trapped a single ion in a linear Paul trap and laser-cooled it using the 2S1/2 -> 2P3/2 transition (in the case of 25Mg+) and the 2S1/2 -> 2P1/2 transition (in the case of 24Mg+). We optically pumped the ion into the (F=3, mp=±3) ground states and weakly probed it with a tunable fibre laser that was scanned to drive the ion from the ground state to the F'=3 and F'=2 manifolds of the 2P1/2 state. The final state of the ion was determined by counting fluorescence (or the reduction therein) from the 2S1/2 (F=3, mF=±3) -> 2P3/2 (F''=4, m''F=±4) cycling transition with a photomultiplier module. We determined that the hyperfine a constant is 102.16 ± 0.16 MHz and the natural linewidth is 42.4 ± 1.2 MHz.
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.