Absorption of twisted light by hydrogenlike atoms

Theoretical analysis of the excitation of low-$Z$ hydrogenlike atoms by incident twisted light is presented. Emphasis is placed on the cross sections that describe transitions between particular atomic substates. Simple expressions for these partial cross sections are derived using the nonrelativistic first-order perturbation theory and the momentum representation of the photon wave functions. Based on the developed approach, calculations have been performed for the $1s\to 2p$ and $2p\to 3d$ transitions induced in the course of interaction of twisted (Bessel) light with a macroscopic hydrogen target. Results of these calculations, supported by an analytical analysis, clearly indicate that the sublevel population of residual atoms following absorption of twisted photons differs much from what is expected for the standard plane-wave case; this effect can be easily observed experimentally by measuring the linear polarization of the subsequent fluorescent emission.

Figure 1

Left panel: In the momentum space, the twisted light can be seen as a coherent superposition of plane waves with wave vectors $\mathit{k}$, lying on a cone with a polar opening angle ${\theta }_k=arctan\left(\right|{\mathit{k}}_{\perp }|/k_z)$, and with polarization vectors ${\mathit{e}}_{\mathit{k}\lambda }$, perpendicular to $\mathit{k}$. Right panel: Geometry of the atomic excitation by twisted Bessel light. The quantization $\left(z\right)$ axis is chosen along the propagation direction of the incident beam. The position of a target atom with respect to the zero-intensity line of the Bessel wave is characterized by the impact parameter $b$.

Figure 2

The relative total (26) and partial cross sections (27) for the $1s\to 2p$ excitation of neutral hydrogen atoms by the twisted photons. Results are presented as a function of the opening angle ${\theta }_k$ of the Bessel beam.

Figure 3

Same as Fig. 2, but for the $2p\to 3d$ transition in neutral hydrogen.

Figure 4

The Stokes parameter (32) of the Lyman-$\alpha$ radiation following the $1s\to 2p$ excitation of hydrogen atoms by twisted light with the opening angle ${\theta }_k$.