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

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