Spontaneous emission in dispersive media without point-dipole approximation

TL;DR

This paper extends the theory of light-matter interactions to include the spatial structure of quantum systems, overcoming divergence issues and clarifying the role of atomic asymmetry in spontaneous emission and Lamb shift calculations.

Contribution

It develops a framework that incorporates the spatial extension of quantum systems, moving beyond the point-dipole approximation to improve accuracy in emission rate and energy shift calculations.

Findings

Overcomes divergence problems in Green tensor propagator.

Reformulates spontaneous emission rate and Lamb shift expressions.

Highlights the impact of atomic state asymmetry on emission and shifts.

Abstract

We study a two-level quantum system embedded in a dispersive environment and coupled with the electromagnetic field. We expand the theory of light-matter interactions to include the spatial extension of the system, taken into account through its wavefunctions. This is a development beyond the point-dipole approximation. This ingredient enables us to overcome the divergence problem related to the Green tensor propagator. Hence, we can reformulate the expressions for the spontaneous emission rate and the Lamb shift. In particular, the inclusion of the spatial structure of the atomic system clarifies the role of the asymmetry of atomic states with respect to spatial inversion in these quantities.