  We investigate the degree of entanglement between an atom and a driven cavity
mode, in the presence of dissipation. Previous work has shown that in the limit
of weak driving fields, the steady state entanglement is proportional to the
square of the driving intensity. This quadratic dependence is due to the
generation of entanglement by the creation of pairs of photons/excitations. In
this work we investigate the entanglement between an atom and a cavity in the
presence of multiple photons. Nonlinearity of the atomic response is needed to
generate entanglement, but as that nonlinearity saturates the entanglement
vanishes. We posit that this is due to spontaneous emission, which puts the
atom in the ground state and the atom-field state into a direct product state.
An intermediate value of the driving field, near the field that saturates the
atomic response, optimizes the atom-field entanglement. In a parameter regime
for which multiphoton resonances occur, we find that entanglement recurs at
those resonances. \cite{Shamailov-10} In this regime, we find that the
entanglement decreases with increaing photon number. We also investigate, in
the bimodal regime of Alsing et. al.\cite{Alsing-91-DressedState}
\cite{Alsing-92-DSS}\cite{Carm-15-X}, the entanglement as a function of atom
and/or cavity detuning. Here we find that there is evidence of a phase
transition in the entanglement, which occurs at $2\epsilon/g \geq 1$.
