  Bilayer graphene is normally a semimetal with parabolic dispersion, but a
tunable bandgap up to few hundreds meV can be opened by breaking the symmetry
between the layers through an external potential. Ab-initio calculations show
that the optical response around the bandgap is strongly dominated by bound
excitons, whose characteristics and selection rules differ from the usual
excitons found in semiconductor quantum wells. In this work we study the
physics of those excitons resonantly coupled to a photonic microcavity,
assessing the possibility to reach the strong and the ultrastrong coupling
regimes of light-matter interaction. We discover that both regimes are
experimentally accessible, thus opening the way for a most promising
technological platform, combining mid-infrared quantum polaritonics with the
tunability and electronic features of graphene bilayers.
