Quantum vacuum emission from a refractive index front

TL;DR

This paper develops an analytical model to calculate quantum vacuum emission spectra from a moving refractive index boundary in dispersive media, revealing structured emission patterns including black hole and white hole analogs.

Contribution

It extends the Hopfield model to explicitly compute all mode spectra, including negative norm modes, and introduces new mode configurations at lower step heights.

Findings

Emission spectrum features black hole and white hole analogs.

Dominant negative norm partner mode identified.

Photon emission follows a power law with step height, exponent 2.5.

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.