  We study experimentally and theoretically a coherently-driven
strongly-coupled quantum dot-microcavity system. Our focus is on physics of the
unexplored intermediate excitation regime where the resonant laser field
dresses a strongly-coupled single exciton-photon (polariton) system resulting
in a ladder of laser-dressed Jaynes-Cummings states. In that case both the
coupling of the emitter to the confined light field of the microcavity and to
the light field of the external laser are equally important, as proved by
observation of injection pulling of the polariton branches by an external
laser. This intermediate interaction regime is of particular interest since it
connects the purely quantum mechanical Jaynes-Cummings ladder and the
semi-classical Autler-Townes ladder. Exploring the driving strength-dependence
of the mutually coupled system we establish the maximum in the resonance
fluorescence signal to be a robust fingerprint of the intermediate regime and
observe signatures indicating the laser-dressed Jaynes-Cummings ladder. In
order to address the underlying physics we excite the coupled system via the
matter component of fermionic nature undergoing saturation - in contrast to
commonly used cavity-mediated excitation.
