  We observe a giant increase of the infrared intensity and a softening of the
in-plane antisymmetric phonon mode Eu (~0.2 eV) in bilayer graphene as a
function of the gate-induced doping. The phonon peak has a pronounced Fano-like
asymmetry. We suggest that the intensity growth and the softening originate
from the coupling of the phonon mode to the narrow electronic transition
between parallel bands of the same character, while the asymmetry is due to the
interaction with the continuum of transitions between the lowest hole and
electron bands. The growth of the peak is a manifestation of the
"charged-phonon" effect observed previously in organic chain conductors and
doped fullerenes, which can now be tuned with the gate voltage.
