  We present detailed numerical simulations of semiclassical and quantum
spectra of a cavity quantum electrodynamics system consisting of a single
three-level atom in $\Lambda$-configuration with one of its transitions
strongly interacting with a quantized cavity mode while the other is driven by
a coherent classical field. After deriving the equations of motion for the
expected values of the system operators from the master equation, we compute
numerically the semiclassical and quantum spectra of the system under various
levels of external driving field strengths. In the semiclassical approach we
neglect the quantum correlations between cavity and atomic operators, while we
make no such assumption in the fully quantum approach. We show that, under
sufficiently weak driving field conditions, the semiclassical and fully quantum
mechanical approaches result in identical spectra. However at higher driving
field intensities, the two approaches yield starkly different results: The
fully quantum mechanical approach results in multiphoton spectrum with
well-defined structure while the semiclassical results in a bistable spectrum.
Our results also reveal that the Raman transition mediated by the dark state of
the system has a complex structure that depends on the manner in which the
system is probed.
