  We demonstrate the simultaneous dressing of both vacuum-to-exciton and
exciton-to-biexciton transitions of a single semiconductor quantum dot in a
high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant
two-photon excitation of the biexciton is achieved by spectrally tuning the
quantum dot emission with respect to the cavity mode. The cavity couples to
both transitions and amplifies the Rabi-frequency of the likewise resonant cw
laser, driving the transitions. We observe strong-field splitting of the
emission lines, which depend on the driving Rabi field amplitude and the
cavity-laser detuning. A dressed state theory of a driven 4-level atom
correctly predicts the distinct spectral transitions observed in the emission
spectrum, and a detailed description of the emission spectra is further
provided through a polaron master equation approach which accounts for cavity
coupling and acoustic phonon interactions of the semiconductor medium.
