Macroscopic QED and noise currents in time-varying media

Macroscopic QED (MQED) is the field theory for computing quantum electromagnetic effects in dispersive media. Here we extend MQD to treat time-varying, dispersive media. For a time dependent Drude model, we find that the expected replacement $\epsilon (\omega )\to \epsilon (t,\omega )$ within standard MQED leads to nonphysical polarization currents, becoming singular in the limit of a step change in the carrier density. We show this singular behaviour can be removed through modifying the reservoir dynamics, quantizing the resulting theory and finding the non-equilibrium, time-varying noise currents, which exhibit extra correlations due to temporal reflections within the material dynamics.