Influence of phonons on solid-state cavity-QED investigated using nonequilibrium Green's functions

The influence of electron--phonon interactions on the dynamics of a quantum dot coupled to a photonic cavity mode is investigated using a nonequilibrium Green's function approach. Within a polaron frame, the self-consistent-Born approximation is used to treat the phonon-assisted scattering processes between the quantum dot polaron and the cavity. Two-time correlators of the quantum dot-cavity system are calculated by solving the Kadanoff-Baym equations, giving access to photon spectra and photon indistinguishability. The non-Markovian nature of the interaction with the phonon bath is shown to be very accurately described by our method in various regime of cavity-quantum electrodynamics (cavity-QED). The indistinguishability of the emitted photons emitted at zero temperature are found to be in very good agreement with a previously reported exact diagonalization approach [Phys.~Rev.~B~87,~081308~(2013)]. Besides, our method enables the calculations of photon indistinguishability at finite temperatures and for strong electron-phonon interactions. More generally, our method opens new avenues in the study of open quantum system dynamics coupled to non-Markovian environments.