We present an open-system master equation study of the coherent and incoherent resonance fluorescence spectrum from a two-level quantum system under coherent pulsed excitation. Several pronounced features which differ from the fluorescence under a constant drive are highlighted, including a multi-peak structure and a pronounced off-resonant spectral asymmetry, in stark contrast to the conventional symmetrical Mollow triplet. We also study semiconductor quantum dot systems using a polaron master equation, and show how the key features of dynamic resonance fluorescence change with electron--acoustic-phonon coupling.
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