Precision measurement of the ground-state hyperfine constant for $^9Be^+$ 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 $^9Be^+$ 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 $5.6 \times 10^{-8}$.