  The emission of light from an atom represents a fundamental process that
provides valuable insights into the atom-light interaction. The Jaynes-Cummings
model is one of the simplest fully quantized models to deal with these
interactions, allowing for an analytical solution, while exhibiting notable
non-trivial effects. We explore new features in the fluorescence emission
spectrum for initial "trapping states", which suppress the atomic population
inversion. Despite the seemingly dormant activity of the atom, the resulting
emission spectra exhibit rich features, and using a dressed-state coordinates
formalism, we are able to quantitatively explain the different profiles in the
spectrum. We generalize the trapping conditions for non-zero atom-field
detuning and also unveil two types of trapping states that lead to spectra with
three peaks, in contrast to previously known states: a center peak and one
secondary peak on each side. These are a trapping state formed by a
Schr\"odinger cat state with Poissonian statistics (Yurke-Stoler state) and
also a different type of "perfect trapping state".
