  From the high vibrational dipolar strength offered by molecular liquids, we
demonstrate that a molecular vibration can be ultra-strongly coupled to
multiple IR cavity modes, with Rabi splittings reaching $24\%$ of the vibration
frequencies. As a proof of the ultra-strong coupling regime, our experimental
data unambiguously reveal the contributions to the polaritonic dynamics coming
from the anti-resonant terms in the interaction energy and from the dipolar
self-energy of the molecular vibrations themselves. In particular, we measure
the opening of a genuine vibrational polaritonic bandgap of ca. $60$ meV. We
also demonstrate that the multimode splitting effect defines a whole
vibrational ladder of heavy polaritonic states perfectly resolved. These
findings reveal the broad possibilities in the vibrational ultra-strong
coupling regime which impact both the optical and the molecular properties of
such coupled systems, in particular in the context of mode-selective chemistry.
