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

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.