Quantum vacuum emission from a refractive index front

Abstract

A moving boundary separating two otherwise homogeneous regions of a dielectric is known to emit radiation from the quantum vacuum. An analytical framework based on the Hopfield model, describing a moving refractive index step in 1+1 dimensions for realistic dispersive media has been developed in [1]. We expand the use of this model to calculate explicitly spectra of all modes of positive and negative norm. Furthermore, for lower step heights we obtain a novel set of mode configurations. This leads to a realistic emission spectrum featuring black hole- and white hole emission for different frequencies. We also present spectra as measured in the laboratory frame that include all modes, in particular a dominant negative norm mode, which is the partner mode in any Hawking-type emission. We find that the emission spectrum is highly structured into intervals of emission with black hole-, white hole-, and no horizons. Finally we estimate the number of photons emitted as a function of the step height and find a power law of 2.5 for low step heights.