  The Rabi Hamiltonian, describing the interaction between a two-level atomic
system and a single cavity mode of the electromagnetic field, is one of the
fundamental models in quantum optics. The model becomes exactly solvable by
considering an atom without permanent dipole moments, whose excitation energy
is quasi-resonant with the cavity photon energy, and by neglecting the non
resonant (counter-rotating) terms. In this case, after including the decay of
either the atom or the cavity mode to a continuum, one is able to derive the
well-known phenomenology of quasi-resonant transitions, including the
fluorescence triplets. In this work we consider the most general Rabi model,
incorporating the effects of permanent atomic electric dipole moments, and,
based on a perturbative analysis, we compare the intensities of emission lines
induced by rotating terms, counter-rotating terms and parity-symmetry-breaking
terms. The analysis reveals that the emission strength related to the existence
of permanent dipoles may surpass the one due to the counter-rotating
interaction terms, but is usually much weaker than the emission due to the
main, resonant coupling. This ratio can be modified in systems with a reduced
dimensionality or by engineering the energy spectral density of the continuum.
