  We experimentally demonstrate that the Mollow triplet sidebands of a quantum
dot strongly coupled to a cavity exhibit anomalous power induced broadening and
enhanced emission when one sideband is tuned over the cavity frequency. We
observe a nonlinear increase of the sideband linewidth with excitation power
when the Rabi frequency exceeds the detuning between the quantum dot and the
cavity, consistent with a recent theoretical model that accounts for acoustic
phonon-induced processes between the exciton and the cavity. In addition, the
sideband tuned to the cavity shows strong resonant emission enhancement.
