Comparison of Quantum and Classical Local-field Effects on Two-Level Atoms in a Dielectric

TL;DR

This paper compares quantum and classical approaches to local-field effects on two-level atoms in dielectrics, revealing contradictions and confirming classical results through microscopic quantum electrodynamics.

Contribution

It demonstrates that macroscopic quantum electrodynamics fails to match classical local-field predictions, emphasizing the validity of classical methods for certain atomic interactions in dielectrics.

Findings

Macroscopic quantum electrodynamics predicts an enhanced Lorentz redshift by the refractive index n.

Classical local-field theory yields an enhancement factor of (n*n+2)/3.

Microscopic quantum electrodynamics confirms classical local-field results.

Abstract

The macroscopic quantum theory of the electromagnetic field in a dielectric medium interacting with a dense collection of embedded two-level atoms fails to reproduce a result that is obtained from an application of the classical Lorentz local-field condition. Specifically, macroscopic quantum electrodynamics predicts that the Lorentz redshift of the resonance frequency of the atoms will be enhanced by a factor of the refractive index n of the host medium. However, an enhancement factor of (n*n+2)/3 is derived using the Bloembergen procedure in which the classical Lorentz local-field condition is applied to the optical Bloch equations. Both derivations are short and uncomplicated and are based on well-established physical theories, yet lead to contradictory results. Microscopic quantum electrodynamics confirms the classical local-field-based results. Then the application of macroscopic quantum electrodynamic theory to embedded atoms is proved false by a specific example in which both the correspondence principle and microscopic theory of quantum electrodynamics are violated.