  Vibrational ultrastrong coupling (USC), where the light-matter coupling
strength is comparable to the vibrational frequency of molecules, presents new
opportunities to probe the interactions of molecules with zero-point
fluctuations, harness cavity-enhanced chemical reactions, and develop novel
devices in the mid-infrared regime. Here we use epsilon-near-zero nanocavities
filled with a model polar medium (SiO$_2$) to demonstrate USC between phonons
and gap plasmons. We present classical and quantum mechanical models to
quantitatively describe the observed plasmon-phonon USC phenomena and
demonstrate a splitting of up to 50% of the resonant frequency. Our wafer-scale
nanocavity platform will enable a broad range of vibrational transitions to be
harnessed for USC applications.
