Abstract
The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.
Highlights
The photonic environment can significantly influence emission properties and interactions among atomic systems
The resulting need to include corrections beyond the electric dipole approximation to properly quantify light-matter coupling was demonstrated for quantum dots near plasmonic nanoparticles[16]
After giving a statement of the problem, we offer expressions for spontaneous emission rate and Lamb shift of a single atomic system in such environment at first
Summary
The photonic environment can significantly influence emission properties and interactions among atomic systems In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. Besides emission enhancement on its own, photonic environment affects the interactions between multiple atomic systems In vacuum, examples such as dipole-dipole coupling[6], or collective phenomena like Dicke superradiance have been explored[7,8]. Corrections beyond the electric dipole approximation may be necessary if the electromagnetic field is focused into spots comparable in size to the atomic system The latter can be realized by nanoscopic environments and picocavities, capable to localize the electric field into nanometric spatial domains, providing high intensities and spatial modulations at the length scale of tens of nanometers. Transitions driven with several multipolar mechanisms have been considered[26] and observed[16,27] respectively in semiconductor quantum dots and transition-metal/lanthanide ions
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