  We investigate the emission properties of a single semiconductor quantum dot
deterministically coupled to a confined optical mode in the weak coupling
regime. A strong pulling, broadening and narrowing of the cavity mode emission
is evidenced when changing the spectral detuning between the emitter and the
cavity. These features are theoretically accounted for by considering the
phonon assisted emission of the quantum dot transition. These observations
highlight a new situation for cavity quantum electrodynamics involving
spectrally broad emitters.
