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arXiv:2609.02572 · Physical Review Letters

Magnetic-Field-Calibration-Free Determination of the Hyperfine Constant A in Ultracold Fermi Gases of K 40

Yajing Yang, Biao Shan, Yuhang Zhao, Jiahui Shen, Zhu-Xiong Ye, Liangchao Chen, Zengming Meng, Pengjun Wang, Wei Han, Jing Zhang, Lianghui Huang

Published Sep 1, 2026• 0 citations
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Abstract

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.

DOI
10.1103/7sjf-yj2z

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This paper presents an experimental study of microwave single-photon transitions that are magnetic-field-insensitive in degenerate Fermi gases of 40^{40}40K. 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|F∣F=9/2, mFm_{F}mF​=1/2⟩\rangle⟩ ⇔\Leftrightarrow⇔ $|7/2,−1/27/2, -1/27/2,−1/2\rangle$ and $|9/2,−1/29/2, -1/29/2,−1/2\rangle$ ⇔\Leftrightarrow⇔ $|7/2,1/27/2, 1/27/2,1/2\rangle$), 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^{40}40K Fermi gases offer promising applications in quantum information and precision measurements.
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rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.
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