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.
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