The Emission of Photons by Atoms: Electric Dipole Approximation

Miriam Kosik, O. Burlayenko, Carsten Rockstuhl +2 more

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.

Wolfgang Demtröder

Miriam Kosik, Oleksandr Burlayenko, Carsten Rockstuhl +2 more

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.

Wolfgang Demtröder

S. Swain

Difference equations are derived for the Laplace transforms of the time dependent probability amplitudes of a system consisting of a single photon interacting with a single two-level atom in the electric dipole approximation. Formally exact continued fraction solutions of these difference equations are obtained and applied to the problems of stimulated and spontaneous emission and absorption of radiation.