Interaction of atomic systems with quantum vacuum beyond electric dipole approximation

TL;DR

This paper develops an analytical framework to describe how nanostructured photonic environments influence atomic emission and interactions beyond the electric dipole approximation, explicitly including magnetic dipole and electric quadrupole effects.

Contribution

It introduces a new theoretical approach that accounts for higher-order multipole contributions in light-matter interactions in dispersive environments, extending beyond the electric dipole approximation.

Findings

Modified spontaneous emission rates in structured environments

Significant Lamb shift and superradiance alterations

Impact of multipole effects in nanophotonic structures

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.