Spin Polarization Measurement in SERF Comagnetometer Based on Phase-Frequency Response of Magnetic Field

This work presents an innovative approach for measuring the spin polarizations of coupled atomic ensembles in spin-exchange relaxation-free (SERF) comagnetometers, using the phase-frequency response of the magnetic field. The zero-phase point in the phase-frequency response of the magnetic field along the $y$-axis is examined to determine the deceleration factor and electronic magnetic field. Ultimately, the spin polarizations of electrons and noble-gas atoms are calculated. The method is applied to test vapor cells with different parameters under various temperatures and pumping light intensities. The measurement errors caused by transverse electron relaxation of electronic spin polarization and nuclear spin polarization are $\approx$5.59% and 1.95% under high polarization, and 8.06% and 2.62% under low polarization. The measurement method features minimal impact on nuclear spin polarization and wide applicability compared to other methods, making it more applicable and suitable for SERF comagnetometers. This method has great significance in better understanding the system state of the SERF comagnetometer and improving its sensitivity.