  Nonlinear phononics holds the promise for controlling properties of quantum
materials on the ultrashort timescale. Using nonequilibrium dynamical
mean-field theory, we solve a model for the description of organic solids,
where correlated electrons couple nonlinearly to a quantum phonon mode. Unlike
previous works, we exactly diagonalize the local phonon mode within the
noncrossing approximation to include the full phononic fluctuations. By
exciting the local phonon in a broad range of frequencies near resonance with
an ultrashort pulse, we show it is possible to induce a Mott insulator-to-metal
phase transition. Conventional semiclassical and mean-field calculations, where
the electron-phonon interaction decouples, underestimate the onset of the
quasiparticle peak. This fact, together with the nonthermal character of the
photoinduced metal, suggests a leading role of the phononic fluctuations and of
the dynamic nature of the state in the vibrationally induced quasiparticle
coherence.
