Polariton excitation rates from time dependent dielectrics

TL;DR

This paper develops a quantum mechanical model to calculate polariton excitation rates in time-dependent, lossy, dispersive dielectrics, with applications to phenomena like analogue Hawking radiation.

Contribution

It applies time dependent perturbation theory within macroscopic QED to derive excitation rates for polaritons in complex, dynamic dielectric environments, extending previous models.

Findings

Excitation rates increase near dispersion relation or material resonances.

Time dependent perturbation theory effectively models dynamic dielectric effects.

Results are relevant for experiments on analogue Hawking radiation.

Abstract

In recent years, a rigorous quantum mechanical model for the interaction between light and macroscopic dispersive, lossy dielectrics has emerged -macroscopic QED- allowing the application of the usual methods of quantum field theory. Here, we apply time dependent perturbation theory to a general class of problems involving time dependent lossy, dispersive dielectrics. The model is used to derive polariton excitation rates in three illustrative cases, including that of a travelling Gaussian perturbation to the susceptibility of an otherwise infinite homogeneous dielectric, motivated by recent experiments on analogue Hawking radiation. We find that the excitation rate is increased when the wave--vector and frequency of each polariton in the pair either satisfies (or nearly satisfies) the dispersion relation for electromagnetic waves, or is close to a material resonance.