Measuring Spin Polarization of a Spin-Exchange Relaxation-Free Atomic Magnetometer at Extremely Large Optical Depths

This article presents a method for measuring the spin polarization of spin-exchange relaxation-free (SERF) atomic magnetometers at extremely large optical depths. Due to the slowing-down effect, spin polarization can be extracted by measuring the slowing-down factor extracted from the precession frequency. However, this technique is limited by a significant error in the regime of extremely large optical depths, where the pump beam intensity for achieving the optimal spin polarization of alkali atoms is significantly increased. We observed that the instantaneous precession frequency measured in the regime where the spin-exchange rate is not much larger than the Larmor frequency was no longer a constant but varied with the pump beam intensity. Thus, a method for measuring spin polarization based on the ratio of the precession frequency to the measured instantaneous precession frequency is proposed. Based on the proposed method, the spin polarization at a temperature of 473 K and an optical depth of 64 is measured. The measurement results were in accordance with theoretical analysis. The expanded uncertainties of the experimental results varied between 1.8% and 9.6%. The proposed method is also applicable to other atomic devices operated in the SERF regime with extremely large optical depths, such as co-magnetometers and atomic spin gyroscopes.