Vacuum-field-induced state mixing

TL;DR

This paper develops a theoretical framework to analyze vacuum-field-induced state mixing in atoms near dielectric nanoparticles, revealing significant energy and decay rate modifications, and demonstrating potential for advanced quantum state control.

Contribution

The authors introduce a non-Hermitian Hamiltonian approach to study environment-induced atomic state mixing, extending previous models to complex geometries like dielectric nanoparticles.

Findings

Strong vacuum-field-induced state mixing observed near dielectric nanoparticles.

Decay rates can decrease contrary to Purcell enhancement expectations.

Significant mixing of unperturbed eigenstates due to non-diagonal perturbations.

Abstract

By engineering the electromagnetic vacuum field, the induced Casimir-Polder shift (also known as Lamb shift) and spontaneous emission rates of individual atomic levels can be controlled. When the strength of these effects becomes comparable to the energy difference between two previously uncoupled atomic states, an environment-induced interaction between these states appears after tracing over the environment. This interaction has been previously studied for degenerate levels and simple geometries involving infinite, perfectly conducting half-spaces or free space. Here, we generalize these studies by developing a convenient description that permits the analysis of these non-diagonal perturbations to the atomic Hamiltonian in terms of an accurate non-Hermitian Hamiltonian. Applying this theory to a hydrogen atom close to a dielectric nanoparticle, we show strong vacuum-field-induced state mixing that leads to drastic modifications in both the energies and decay rates compared to conventional diagonal perturbation theory. In particular, contrary to the expected Purcell enhancement, we find a surprising decrease of decay rates within a considerable range of atom-nanoparticle separations. Furthermore, we quantify the large degree of mixing of the unperturbed eigenstates due to the non-diagonal perturbation. Our work opens new quantum state manipulation possibilities in emitters with closely spaced energy levels.