Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates

TL;DR

This paper investigates how the electromagnetic environment between two conducting plates affects the Lamb shift in non-degenerate energy systems, proposing a way to observe this quantum effect in quantum dots.

Contribution

It provides a new formula for the relative change in Lamb shift in the presence of conducting plates, resolving previous theoretical controversies and suggesting experimental applications.

Findings

Derived an explicit formula for the Lamb shift modification.

Resolved divergences in calculations using distribution theory.

Proposed experimental and theoretical methods to observe the Lamb shift in quantum dots.

Abstract

The issue of the observability of the Lamb shift in systems with non-degenerate energy levels is put to question. To this end, we compute the Lamb shift of such systems in the electromagnetic environment provided by two infinite parallel conducting plates, which is instrumental in demonstrating the existence of the so-called Casimir effect. A formula giving the relative change in the Lamb shift (as compared to the standard one in vacuum) is explicitly obtained for spherical semiconductor Quantum Dots (QD). It is the result of a careful mathematical treatment of divergences in the calculations involving distribution theory, which also settles a controversy on two different expressions in the existing literature. It suggests a possibility of QD non-degenerate energy spectrum fine-tuning for experimental purposes as well as a Gedankenexperiment to observe the Lamb shift in spherical semiconductor quantum dots.