  We calculate the resonance fluorescence signal of a two-level system coupled
to a quantized phonon mode. By treating the phonons in the independent boson
model and not performing any approximations in their description, we also have
access to the state evolution of the phonons. We confirm the validity of our
model by simulating the limit of an initial quasi-classical coherent phonon
state, which can be compared to experimentally confirmed results in the
semiclassical limit. In addition we predict photon scattering spectra in the
limit of purely quantum mechanical phonon states by approaching the phononic
vacuum. Our method further allows us to simulate the impact of the light
scattering process on the phonon state by calculating Wigner functions. We show
that the phonon mode is brought into characteristic quantum states by the
optical excitation process.
