In Situ Spin Polarization Measurement Method and Identification of Optimal Spin Polarization Range in Atomic Magnetometer

In this study, an in situ measurement method of spin polarization in single-beam atomic magnetometer is presented. Modeling magnetic linewidth by incorporating nonlinear attenuation along the propagation direction of light and employing the output response equation of magnetometers at zero-field resonance. Utilizing the model for fitting to extract relaxation rate information, the photon absorption cross-sections at three temperatures are estimated to be 2.12x10-13$2.12\times 10<^>{-13}$, 1.85x10-13$1.85\times 10<^>{-13}$, and 1.64x10-13$1.64\times 10<^>{-13}$ cm2$\mathrm{{c m}<^>2}$, respectively. Further, the spin polarization curves are obtained by introducing the spin polarization equations. Given the diminishing marginal utility resulting from the enhancement of performance through increased spin polarization, long-term sensitivity is employed to determine optimal spin polarization range. The optimal long-term sensitivity for four displayed states is 15.3 +/- 5.5$15.3 \pm 5.5$ fTHz-1/2$\text{fTHz}<^>{-1/2}$ (@31.5Hz), while the ultimate minimum sensitivity is 10.7 fTHz-1/2$\text{fTHz}<^>{-1/2}$ (@31.5Hz). The optimal spin polarization ranges at three temperatures are 78.9%-87.1%, 82.3%-88.5%, and 84.5%-88.4%, respectively. The measurement method applied to single-beam magnetometer can be easily extended to multi-axis vector magnetometer. The determination of optimal spin polarization range is of great significance for the performance and stability of the magnetometer system, improving the sensitivity of magnetic field measurement, and ensuring its widespread application in bio-magnetic measurement. The total relaxation rate of the magnetometer is obtained by the magnetic linewidth of the dispersion curve. The relationship between the magnetic linewidth and the incident light power is established and fitted, and the information of the other relaxation rates and photon absorption cross-sections of the magnetometer are obtained respectively. image