  Employing a recently developed method that is numerically accurate within a
model space simulating the real-time dynamics of few-body systems interacting
with macroscopic environmental quantum fields, we analyze the full dynamics of
an atomic system coupled to a continuum light-field with a gapped spectral
density. This is a situation encountered, for example, in the radiation field
in a photonic crystal, whose analysis has been so far been confined to limiting
cases due to the lack of suitable numerical techniques. We show that both
atomic population and coherence dynamics can drastically deviate from the
results predicted when using the rotating wave approximation, particularly in
the strong coupling regime. Experimental conditions required to observe these
corrections are also discussed.
