The Quantum Vacuum of Complex Media. A Unified Approach to the Dielectric Constant, the Spontaneous Emission and the Zero-Temperature Electromagnetic Pressure

TL;DR

This paper presents a comprehensive quantum-electrodynamic analysis of vacuum phenomena in complex media, emphasizing the role of dielectric self-energy and providing new insights into spontaneous emission, electromagnetic fluctuations, and Casimir pressure.

Contribution

It introduces a microscopic diagrammatic approach to unify the understanding of vacuum effects, clarifies the nature of local field factors, and derives exact expressions for electromagnetic fluctuations in dielectric media.

Findings

Vacuum effects are due to dielectric self-energy, not vacuum energy variations.

Derived exact spectrum of electromagnetic fluctuations in homogeneous dielectrics.

Provided analytical formulas for decay rates and Casimir pressure in complex media.

Abstract

We study from a critical perspective several quantum-electrodynamic phenomena commonly related to vacuum electromagnetic (EM) fluctuations in complex media. We compute the resonance-shift, the spontaneous emission rate, the local density of states and the van-der-Waals-Casimir pressure in a dielectric medium using a microscopic diagrammatic approach. We find, in agreement with some recent works, that these effects cannot be attributed to variations on the energy of the EM vacuum but to variations of the dielectric self-energy. This energy is the result of the interaction of the bare polarizability of the dielectric constituents with the EM fluctuations of an actually polarized vacuum. We have found an exact expression for the spectrum of these fluctuations in a statistically homogeneous dielectric. Those fluctuations turn out to be different to the ones of normal radiative modes. It is the latter that carry the zero-point-energy (ZPE). Concerning spontaneous emission, we clarify the nature of the radiation and the origin of the so-called local field factors. Essential discrepancies are found with respect to previous works. We perform a detailed analysis of the phenomenon of radiative and non-radiative energy transfer. Analytical formulae are given for the decay rate of an interstitial impurity in a Maxwell-Garnett dielectric and for the decay rate of a substantial impurity sited in a large cavity. The construction of the effective dielectric constant is found to be a self-consistency problem. The van-der-Waals pressure in a complex medium is computed in terms of variations of the dielectric self-energy at zero-temperature. An additional radiative pressure appears associated to variations of the EM vacuum energy.