Theoretical study of the alignment-to-orientation conversion in magneto-optical rotation based on atomic multipole moments

We theoretically investigate the magneto-optical rotation (MOR) effect in cesium atoms in the Voigt geometry, in which an off-resonance linearly polarized laser beam serves as both pump and probe. By calculating the detailed evolution of atomic multipole moments truncated to second-rank, alignment-to-orientation conversion (AOC) effects are observed in two hyperfine ground states. The mechanisms responsible for this effect are demonstrated. The tensor AC-Stark shift produced by the optical pumping generates a nonlinear effect, resulting in atomic alignment directly coupled to orientation, which enables spin orientation to be obtained. Simultaneously, spin-exchange collisions lead to atomic alignment and orientation transfer between two ground-state manifolds. Additionally, we present the analytical expression of atomic spin polarization described by atomic multipole moments, and the contributions of the AOC effect to the optical-rotation signals are discussed in different light power regimes. Our results can be helpful for guiding MOR experiments by refining and optimizing the parameters.