  The interplay between an open quantum system and its environment can lead to
both coherent and incoherent behaviour. We explore the extent to which strong
coupling to a single bosonic mode can alter the coherence properties of a
two-level system in a structured environment. This mode is treated exactly,
with the rest of the environment comprising a Markovian bath of bosonic modes.
The strength of the coupling between the two-level system and the single mode
is varied for a variety of different forms for the bath spectral density in
order to assess whether the coherent dynamics of the two-level system are
modified. We find a clear renormalisation of the site population oscillation
frequency that causes an altered interaction with the bath. This leads to
enhanced or reduced coherent behaviour of the two-level system depending on the
form of the spectral density function. We present an intuitive interpretation,
based on an analytical model, to explain the behaviour.
