Experimental Verification of Position-Dependent Angular-Momentum Selection Rules for Absorption of Twisted Light by a Bound Electron

TL;DR

This study experimentally verifies how the absorption of twisted light by a bound electron depends on position, confirming theoretical angular-momentum selection rules with high accuracy using a trapped ion.

Contribution

It provides the first experimental validation of position-dependent angular-momentum selection rules for twisted light absorption by a single trapped ion.

Findings

Experimental transition amplitudes agree with theoretical predictions within 3%.

Transition strengths vary with ion position relative to vortex center.

Proposes two-ion crystal schemes for improved vortex mode sensing.

Abstract

We analyze the multipole excitation of atoms with twisted light, i.e., by a vortex light field that carries orbital angular momentum. A single trapped $^{40}$Ca$^+$ ion serves as a localized and positioned probe of the exciting field. We drive the $S_{1/2} \to D_{5/2}$ transition and observe the relative strengths of different transitions, depending on the ion's transversal position with respect to the center of the vortex light field. On the other hand, transition amplitudes are calculated for a twisted light field in form of a Bessel beam, a Bessel-Gauss and a Gauss-Laguerre mode. Analyzing experimental obtained transition amplitudes we find agreement with the theoretical predictions at a level of better than 3\%. Finally, we propose measurement schemes with two-ion crystals to enhance the sensing accuracy of vortex modes in future experiments.