Magnetic-Field-Calibration-Free Determination of the Hyperfine Constant $A$ in Ultracold Fermi gases of $^{40}$K

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 transition frequency between these two magnetically insensitive transitions with Hz-level resolution over a range of magnetic fields, and obtain the ground-state hyperfine constant $A = -h\times 285.730536(2)\,\mathrm{MHz}$, corresponding to an absolute uncertainty of about $2\,\mathrm{Hz}$. Our value reduces the uncertainty by nearly three orders of magnitude compared with previous determinations, providing a substantially improved reference for high-precision spectroscopy and metrology with $^{40}$K.