  A quantitative and predictive theory of quantum light-matter interactions in
ultra thin materials involves several fundamental challenges. Any realistic
model must simultaneously account for the ultra-confined plasmonic modes and
their quantization in the presence of losses, while describing the electronic
states from first principles. Herein we develop such a framework by combining
density functional theory (DFT) with macroscopic quantum electrodynamics, which
we use to show Purcell enhancements reaching $10^7$ for intersubband
transitions in few-layer transition metal dichalcogenides sandwiched between
graphene and a perfect conductor. The general validity of our methodology
allows us to put several common approximation paradigms to quantitative test,
namely the dipole-approximation, the use of 1D quantum well model wave
functions, and the Fermi's Golden rule. The analysis shows that the choice of
wave functions is of particular importance. Our work lays the foundation for
practical ab initio-based quantum treatments of light matter interactions in
realistic nanostructured materials.
