We analyze the novel features of high-multipole excitation of quantum systems with twisted light, i.e, by the photons that carry extra orbital angular momentum (OAM) along the propagation direction. It was previously demonstrated experimentally  that OAM of the twisted light is passed to the internal degrees of freedom of an atom for electric quadrupole transitions. We extended these results to the analysis of individual S->D transition amplitudes by measuring Rabi frequencies for Ca40+ ions placed in a Paul trap. It is shown that relative strengths transitions into different Zeeman-split levels - most of them forbidden for plane-wave photons - depends on the target atom’s position with respect to the optical vortex center. The data compare favorably with the theoretical predictions. The selection rules also point to circular dichroism and birefringence of the twisted light interacting with non-chiral atomic matter.
Collaboration with Carl E. Carlson, Christian T. Schmiegelow, Ferdinand Schmidt-Kaler, and Maria Solyanik is gratefully acknowledged.
 C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, Nature communications, 7 (October 2016), DOI: 10.1038/ncomms12998.
Andrei Afanasev, "Quantum angular-momentum selection rules for absorption of twisted light by bound electrons
(Conference Presentation)," Proc. SPIE 10549, Complex Light and Optical Forces XII, 1054907 (Presented at SPIE OPTO: January 30, 2018; Published: 14 March 2018); https://doi.org/10.1117/12.2292647.5751547247001.
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