Perturbative photon production in a dispersive medium

Abstract

We investigate photon pair-creation in a dispersive dielectric medium induced by the presence of a spacetime varying dielectric constant. Our aim is to examine the possibility to observe new phenomena of pair creation induced by travelling dielectric perturbations e.g. created by laser pulses by means of the Kerr effect. In this perspective, we adopt a semi-phenomenological version of the Hopfield model in which a space-time dependent dielectric susceptibility appears. We focus our attention on perturbation theory, and provide general formulas for the photon production induced by a local but arbitrarily spacetime dependent refractive index perturbation. As an example, we further explore the case of an uniformly travelling perturbation, and provide examples of purely time-dependent perturbations.

Derivation of Hawking radiation in dispersive dielectric media

“…[37] and further developed in Refs. [43,[45][46][47]. This model is closely inspired by the Hopfield model [56,57].…”

Hopfield-Kerr model and analogue black hole radiation in dielectrics

“…In the current paper we base our analysis on a further refinement of the relativistically covariant Hopfield model, dubbed Hopfield-Kerr model, in which a self-interacting polarization term is added to the Lagrangian to describe the intrinsic non-linear effects of the dielectric medium. This work represents an improvement with respect to [23], in which a perturbative analysis of photon production was made through the quantization in the lab frame in a simple fixed gauge, and to [16], in which a non-perturbative deduction of thermality was accomplished in a simplified scalar model. See also [24,25] for an exact quantization of the covariant Hopfield model.…”

Quantum vacuum emission from a refractive-index front

“…Emission of light from the quantum vacuum has recently attracted attention [13,14,19,32] due to the high emission rates expected in the presence of an analog horizon and the hope to observe analog Hawking radiation. Using a fully analytical model introduced in [14], the spontaneous emission of light from a moving dielectric boundary, a refractive-index front, can be calculated.…”