# Analytical description of quantum emission in optical analogues to gravity

## TL;DR

This paper analytically studies quantum emission in optical analogues to gravity using a moving refractive index perturbation, revealing how dispersion and horizons influence spontaneous emission spectra and correlations.

## Contribution

It provides an analytical solution for scattering and emission spectra in dispersive optical analogues of gravity, incorporating the Hopfield model and curved spacetime field theory.

## Key findings

- Emission spectra depend on the presence of optical horizons.
- Spectral features are robust against parameter variations.
- The methods enable new experiments in analogue gravity systems.

## Abstract

We consider a moving refractive index perturbation in an optical medium as an optical analogue to waves under the influence of gravity. We describe the dielectric medium by the Lagrangian of the Hopfield model. We supplement the field theory in curved spacetime for this model to solve the scattering problem for all modes and frequencies analytically. Because of dispersion, the kinematic scenario of the field modes may contain optical event horizons for some frequencies. We calculate the spectra of spontaneous emission in the frame co-moving with the perturbation and in the laboratory frame. We also calculate the spectrally-resolved photon number correlations in either frame. The emitted multimode field comes in different types depending on the presence of horizons. We show that these types are robust against changes in the system parameters and thus are genuine features of optical and non-optical analogues. These methods and findings pave the way to new observations of analogue gravity in dispersive systems.