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

We demonstrate the fundamental links existing between two different descriptions of quantum electrodynamics in inhomogeneous, lossy, and dispersive dielectricmedia which are based either on the Huttner-Barnett formalism for polaritons [Huttner and Barnett, Phys. Rev. A 46, 4306 (1992)] or the Langevin noise approach using fluctuating currents [Gruner andWelsch, Phys. Rev. A 53, 1818 (1996)]. In this work we demonstrate the practical equivalence of the two descriptions by introducing the concept of the 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.