  We investigate the influence of exciton-phonon coupling on the dynamics of a
strongly coupled quantum dot-photonic crystal cavity system and explore the
effects of this interaction on different schemes for non-classical light
generation. By performing time-resolved measurements, we map out the
detuning-dependent polariton lifetime and extract the spectrum of the
polariton-to-phonon coupling with unprecedented precision. Photon-blockade
experiments for different pulse-length and detuning conditions (supported by
quantum optical simulations) reveal that achieving high-fidelity photon
blockade requires an intricate understanding of the phonons' influence on the
system dynamics. Finally, we achieve direct coherent control of the polariton
states of a strongly coupled system and demonstrate that their efficient
coupling to phonons can be exploited for novel concepts in high-fidelity single
photon generation.
