  Interference between different possible paths lies at the heart of quantum
physics. Such interference between coupled discrete and continuum states of a
system can profoundly change its interaction with light as seen in Fano
resonance. Here we present a unique many-body Fano system composed of a
discrete phonon vibration and continuous electron-hole pair transitions in
bilayer graphene. Mediated by the electron-phonon interactions, the excited
state is described by new quanta of elementary excitations of hybrid
phonon-exciton nature. Infrared absorption of the hybrid states exhibit
characteristic Fano lineshapes with parameters renormalized by many-body
interactions. Remarkably, the Fano resonance in bilayer graphene is
continuously tunable through electrical gating. Further control of the
phonon-exciton coupling may be achieved with an optical field exploiting the
excited state infrared activity. This tunable phonon-exciton system also offers
the intriguing possibility of a 'phonon laser' with stimulated phonon
amplification generated by population inversion of band-edge electrons.
