Selection rules for atomic excitation by twisted light

A theoretical analysis of the selection rules for atomic excitation by twisted light is presented. To perform the analysis, we expand the vector potential of twisted light in terms of its multipole components. We find that its multipole composition locally depends on the radial position in the wavefront, and this position dependence is imprinted in the selection rules. Detailed calculations are performed for Bessel beams and the 4 s 2 S 1 2 → 3 d 2 D 5 2 transition of a Ca + ion. Our results indicate that the parameters of the twisted beams can be efficiently used to select the total angular momentum and its projection that can be transferred to an atom in the excitation process.