Probing the isolated vector magnetic field of structured laser beams by atoms

Abstract: Electric and magnetic fields are inherently coupled in an electromagnetic wave. However, structured light beams enable their spatial separation. In particular, azimuthally polarized laser beams exhibit a localized magnetic field on-axis without the electric counterpart. Recent study by Martin-Domene et al. [App. Phys. Lett. 124, 211101 (2024)] has shown that combining these beams enables the generation of locally isolated magnetic fields with a controllable direction and phase. In the present paper we propose a method to probe and characterize such magnetic fields by studying their interaction with a single trapped atom. In order to theoretically investigate magnetic sublevel populations and their dependence on the relative orientation and phase -- i.e. the polarization state -- of the isolated magnetic field, we use a time-dependent density-matrix method based on the Liouville-von Neumann equation. As illustrative cases, we consider the $2s^2 2p^2 \, {}^3P_0 \, - \, 2s^2 2p^2 \, {}^3P_1$, the $1s^2 2s^2 \, {}^1S_0 \, - \, 1s^2 2s 2p \, {}^3P_2$, and the $2 s^2 2p \, {}^2 P_{1/2} \, - \, 2 s^2 2p \, {}^2 P_{3/2}$ transitions in ${}^{40}$Ca$^{14+}$, ${}^{10}$Be, and ${}^{38}$Ar$^{13+}$, respectively. Our results indicate that monitoring atomic populations serves as an effective tool for probing isolated vector magnetic fields, which opens avenues for studying laser-induced processes in atomic systems where electric field suppression is critical.