Analysis on the effect of electron spin polarization on a hybrid optically pumped K-Rb-²¹Ne co-magnetometer

In this paper, the effect of longitudinal electron spin polarization under the combined action of alkali metal density ratio and pump laser power density on the hybrid optically pumped co-magnetometer operated in the spin-exchange relaxation-free (SERF) regime is studied. The AC response model of rotation velocity and magnetic noise of the SERF co-magnetometer system is proposed, and the factors of frequency and system bandwidth are considered. Based on the proposed response model, the error equation of the system is obtained, and the relationship between alkali metal density ratio and pump laser power density and the system noise response is theoretically analyzed and experimentally tested. The results show that when the product of pumping rate and alkali metal density ratio is greater than the electron spin relaxation rate, there is a longitudinal electron spin polarization point that minimizes the system error. In addition, the range of minimum error calculated results obtained by changing the pumping rate for the cells with different alkali metal density ratios is within 5% of the average value, that is, their minimum error potential is roughly the same within a certain range. Under the experimental conditions in this paper, due to the limitation of the electron spin relaxation rate and the operating capacity of the pump laser, the optimal alkali metal density ratio range is about 1/100-1/300.