Theory of double-resonance alignment magnetometers based on atomic high-order multipole moments using effective master equations

We present a theoretical study of double-resonance alignment magnetometers using linearly polarized light, in which the effect of atomic high-order multipole moments is considered. Starting from the effective master equation of our system obtained by eliminating the excited state adiabatically, we derive the full evolution equations of the atomic multipole moments. The analytic solutions of resonance signals involving the four-order multipole moments effect are obtained by using the perturbation approach. We present that the four-order multipole moments effect is negligible in the weak laser field, and the results reduce to that obtained by a three-step approach. However, the role of four-order multipole moments coupled by two-order tensor moments is more significant with the increasing Rabi frequency of light, which cannot be ignored. Meanwhile, the analytic expressions of relaxation processes are also studied, which are a linear combination of the laser-induced equivalent relaxation rate ΓL and the spin-exchange collision rate Γg. The expected domain of validity of the three-step approach on light power is roughly given by ΓL<12Γg. In addition, the steady-state results of resonance signals are presented in a strong radio-frequency magnetic field; in that case, the physical mechanism of the splitting of resonance signals is discussed. These results are valid for arbitrary light power and for an arbitrarily oriented static magnetic field.