Equivalence between the Hamiltonian and Langevin noise description of plasmon-polaritons in a dispersive and lossy inhomogeneous medium

TL;DR

This paper establishes a fundamental equivalence between two quantum electrodynamics descriptions in inhomogeneous, lossy, and dispersive media, linking the Hamiltonian and Langevin noise formalisms and exploring their implications for quantum observables.

Contribution

It demonstrates the practical equivalence of the Huttner-Barnett and Langevin noise approaches in describing plasmon-polaritons in complex media, introducing the concept of effective photon states.

Findings

The two formalisms are practically equivalent in describing quantum electromagnetic phenomena.

Effective photon states can be associated with specific noise current distributions.

The results impact the calculation and interpretation of quantum fluctuations, correlations, and Casimir forces.

Abstract

We demonstrate the fundamental links existing between two different descriptions of quantum electrodynamics in inhomogeneous, lossy and dispersive dielectric media which are based either on the Huttner-Barnett formalism for polaritons [B. Huttner and S. M. Barnett, Phys.Rev. A 46, 4306 (1992)] or the Langevin noise approach using fluctuating currents [T. Gruner and D.-G. Welsch, Phys.Rev.A 53, 1818 (1996)]. In this work we demonstrate the practical equivalence of the two descriptions by introducing the concept of effective photon state associated with some specific noise current distribution. We study the impact of these results on the calculation and interpretation of quantum observables such as fluctuations, correlations, and Casimir forces.