  We theoretically investigate the real-time emission spectrum of a two-level
atom coupled to an optomechanical cavity (OMC). Using quantum trajectory
approach we obtain the single-photon time-dependent spectrum in this hybrid
system where the influence of a strong atom-cavity coupling and a strong
optomechanical interaction are studied. We find a dressed state picture can
explain the spectra by predicting the exact peak locations as well as the
relative peak heights. In our analysis we also include the effect of mechanical
losses (under weak mechanical damping limit) and single-photon loss through
spontaneous emission from the two-level emitter.
