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arXiv:2601.12800 · Physical Review A

Experimental study of magnetically insensitive transitions in an ultracold Fermi gas of K 40

Biao Shan, Lianghui Huang, Yajing Yang, Yuhang Zhao, J. Shen, Zhuxiong Ye, Liangchao Chen, Zengming Meng, Pengjun Wang, Wei Han, Jing Zhang

Published Jan 13, 2026• 1 citation
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Abstract

This paper presents an experimental study of microwave single-photon transitions that are magnetic-field-insensitive in degenerate Fermi gases of $^{40}$K. This contrasts with microwave single-photon clock transitions for 0-0 magnetic-field-insensitive states and two-photon clock transitions for non 0-0 magnetic-field-insensitive states in bosonic alkali metal atoms. We show that there are two sets of special transitions between two different hyperfine ground states ($|F$=9/2, $m_{F}$=1/2$\rangle$ $\Leftrightarrow$ $|$7/2, -1/2$\rangle$ and $|$9/2, -1/2$\rangle$ $\Leftrightarrow$ $|$7/2, 1/2$\rangle$), whose microwave single-photon transition frequency is insensitive to low magnetic fields, as the first-order Zeeman shift is almost completely canceled. By using the microwave spectrum and Ramsey interference fringes, we demonstrate the long-time stability of the coherent transition under magnetic field fluctuations. These magnetic-field-insensitive microwave hyperfine transitions in ultracold $^{40}$K Fermi gases offer promising applications in quantum information and precision measurements.

DOI
10.1103/jk8m-snjw

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Hyperfine constant A is a key parameter of the hyperfine structure and underpins precision spectroscopy and metrology. In this Letter, we develop a magnetic-field-calibration-free method for determining the ground-state hyperfine constant A in an ultracold ^{40}K Fermi gas by utilizing a pair of magnetically insensitive ("clock") transitions. This overcomes the stringent magnetic-field calibration requirements of conventional methods. We measure the frequencies of these two magnetically insensitive transitions with Hz-level resolution over a range of magnetic fields and obtain the ground-state hyperfine constant A=-h×285.730536(2) MHz, corresponding to an absolute uncertainty of about 2 Hz. Our value reduces the uncertainty by nearly 3 orders of magnitude compared with previous determinations, providing a substantially improved reference for high-precision spectroscopy and metrology with ^{40}K.
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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 $ \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}$.
We demonstrate control of the differential Zeeman shift between clock states of ultracold rubidium atoms by means of nonresonant microwave dressing. Using the dc field dependence of the microwave detuning, we suppress the first- and second-order differential Zeeman shift in magnetically trapped 87Rb^{87}\mathrm{Rb}87Rb atoms. By dressing the state pair 5S1/25{S}_{1/2}5S1/2​ F=1F=1F=1, ${m}_{F}=\ensuremath{-}1$ and F=2F=2F=2, mF=1{m}_{F}=1mF​=1, a residual frequency spread of <0.1<0.1<0.1 Hz in a range of 100 mG around a chosen magnetic offset field can be achieved. This is one order of magnitude smaller than the shift of the bare states at the magic field of the Breit-Rabi parabola. We further identify double magic points, around which the clock frequency is insensitive to fluctuations both in the magnetic field and in the dressing Rabi frequency. The technique is compatible with chip-based cold-atom systems and allows the creation of clock and qubit states with reduced sensitivity to magnetic-field noise.