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We present detailed numerical simulations of semiclassical and quantumspectra of a cavity quantum electrodynamics system consisting of a singlethree-level atom in $\Lambda$-configuration with one of its transitionsstrongly interacting with a quantized cavity mode while the other is driven bya coherent classical field. After deriving the equations of motion for theexpected values of the system operators from the master equation, we computenumerically the semiclassical and quantum spectra of the system under variouslevels of external driving field strengths. In the semiclassical approach weneglect the quantum correlations between cavity and atomic operators, while wemake no such assumption in the fully quantum approach. We show that, undersufficiently weak driving field conditions, the semiclassical and fully quantummechanical approaches result in identical spectra. However at higher drivingfield intensities, the two approaches yield starkly different results: Thefully quantum mechanical approach results in multiphoton spectrum withwell-defined structure while the semiclassical results in a bistable spectrum.Our results also reveal that the Raman transition mediated by the dark state ofthe system has a complex structure that depends on the manner in which thesystem is probed.

Semiclassical and quantum nonlinear spectra of a strongly coupled single $\Lambda$-type three-level atom-cavity QED system