Numerical analysis of the optical pumping process coupled with Na-23 D-2 manifold modeled as a partially resolved hyperfine structure

All magnetometers using alkali atoms rely on the monochromatic light driving the optical pumping process in the D-1 or D-2 line to create spin-polarized atoms. In the study of a sodium (Na) magnetometer, we find that Na-23 exhibits the same hyperfine structure as exhibited by the Rb-87 atom but differs from Rb in terms of level splitting. The narrowly split hyperfine levels of the Na-23 3P(3/2) excited state are comparable to its natural broadening (9.8 MHz). We have modeled the nearly unresolved hyperfine structure as a partially resolved multilevel system in which the absorption at each photon detuning will induce adjacent allowed transition pathways simultaneously. Thus, the corresponding optical pumping processes of Na-23 and Rb-87 are governed by similar rate equations but result in different redistributed populations. By numerically solving the rate equations, we demonstrate that optically pumped Na-23 has a much smaller spin polarization than that of Rb-87 because the population imbalances between the ground state Zeeman levels of Na-23 are very small. The inefficient optical pumping can explain why Na magnetometers are not studied extensively. The investigation into the optical pumping process of Na-23 is helpful in preparing a highly spin-polarized atomic medium and optimizing the sensitivity of Na magnetometers.