Interference between multipolar two-photon transitions in quantum emitters near plasmonic nanostructures

In the vicinity of plasmonic nanostructures that support highly confined light fields, spontaneous emission processes, such as two-photon spontaneous emission (TPSE), exhibit higher-order multipolar emission pathways beyond the dipolar one. These multipolar emission channels occur simultaneously and can interfere with each other. We develop a novel framework that computes these interference effects for TPSE of a quantum emitter close to an arbitrary nanostructure. The model is based on the computation of Purcell factors that can be calculated with conventional electromagnetic simulations, which avoids complex analytic calculations for the environment. For a transition of a hydrogen-like emitter close to a graphene nanotriangle, we demonstrate a breakdown of the dipolar selection rule in the TPSE process. This breakdown is due to a huge enhancement of the two-electric dipole (2ED) and of the two-electric quadrupole (2EQ) transitions. We observe an important interference between these multipolar transitions, as it increases the total rate by 67%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$67 \, \%$$\end{document}. In the end, our framework is a complete tool to design emitters and nanostructures for TPSE, where the exploitation of previously ignored interference effects provides an additional degree of freedom, for example to boost desired transitions and to supress undesirable ones.