  The spontaneous emission spectrum for a three level cascade configuration
atom in a single mode high-Q cavity coupled to a zero temperature reservoir of
continuum external modes is determined from the atom-cavity mode master
equation using the quantum regression theorem. Initially the atom is in its
upper state and the cavity mode empty of photons. Following Glauber, the
spectrum is defined via the response of a detector atom. Spectra are calculated
for the detector located inside the cavity (case A), outside the cavity end
mirror (Case B-end emission), or placed for emission out the side of the cavity
(Case C). The spectra for case A and case B are found to be essentially the
same. In all the cases the predicted lineshapes are free of instrumental
effects and only due to cavity decay. Spectra are presented for intermediate
and strong coupling regime situations (where both atomic transitions are
resonant with the cavity frequency), for cases of non-zero cavity detuning, and
for cases where the two atomic transition frequencies differ. The spectral
features for Cases B(A) and C are qualitatively similar, with six spectral
peaks for resonance cases and eight for detuned cases. These general features
of the spectra can be understood via the dressed atom model. However, Case B
and C spectra differ in detail, with the latter exhibiting a deep spectral hole
at the cavity frequency due to quantum interference effects.
