Superradiance of Quantum Antennas in a Solid-State Environment: Phonon-Modified Electromagnetics

We consider sub- and superradiance of quantum emitters in a solid-state environment. This collective emission depends on the electromagnetic interaction between the emitters that can be engineered via the environment and described by the classical electromagnetic Green function. But also phonons may affect the collective emission. Phonons produce dephasing, both non-exponential fast initial dephasing and slower exponential dephasing. We compared several ways to account for both types of phonon interactions into the more standard optical master equation for an arbitrary number of quantum emitters that mutually interact via the electromagnetic field. In particular we present a concatenation method that incorporates phonon effects without adding computational complexity, suitable for arrays of emitters. Here we use it to study the effects of detunings on two-emitter spectra and on the corresponding population and entanglement dynamics.