Signatures of non-Markovianity in cavity QED with color centers in two-dimensional materials

Light-matter interactions of defects in two-dimensional materials are expected to be profoundly impacted by strong coupling to phonons. In this work, we combine ab initio calculations of a defect in hBN with a fully quantum mechanical and numerically exact description of a cavity-defect system to elucidate this impact. We show that, even at weak light-matter coupling, the dynamical evolution of the cavity-defect system has clear signatures of non-Markovian phonon effects, and that linear absorption spectra show the emergence of hybridized light-matter-phonon states in regimes of strong light-matter coupling. We emphasise that our methodology is general, and can be applied to a wide variety of material-defect systems.