  We investigate the entanglement features in the interacting system of a
quantized optical field and a two-level system which is statically driven,
known as the asymmetric quantum Rabi model (AsymQRM). Intriguing entanglement
resonance valleys with the increase of the photon-atom coupling strength and
peaks with the increase of the driving amplitude are found. It is revealed that
both of these two kinds of entanglement resonance are caused by the avoided
level crossing of the associated eigenenergies. In sharp contrast to the
quantum Rabi model, the entanglement of the AsymQRM collapses to zero in the
strong coupling regime except when the driving amplitude equals to $m\omega/2$,
with $m$ being an integer and $\omega$ being the photon frequency. Our analysis
demonstrates that such entanglement reappearance is induced by the hidden
symmetry of the AsymQRM. Supplying an insightful understanding on the AsymQRM,
our results will be helpful in exploring the hidden symmetry and in preparing
photon-atom entanglement in light-matter coupled systems.
