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It has been experimentally demonstrated that molecular-vibration polaritonsformed by strong coupling of a molecular vibration to an infrared cavity modecan significantly modify the physical properties and chemical reactivity ofvarious molecular systems. However, a complete theoretical understanding of theunderlying mechanisms of the modifications remains elusive due to thecomplexity of the hybrid system, especially the collective nature ofpolaritonic states in systems containing many molecules. We develop here thesemiclassical theory of molecular-vibration-polariton dynamics based on thetruncated Wigner approximation (TWA) that is tractable in large molecularsystems and simultaneously captures the quantum character of photons in theoptical cavity. The theory is then applied to investigate the nuclear quantumdynamics of a system of identical diatomic molecules having the ground-stateMorse potential and strongly coupled to an infrared cavity mode in theultrastrong coupling regime. The validity of TWA is examined by comparing itwith the fully quantum dynamics of a single-molecule system for two differentinitial states in the dipole and Coulomb gauges. For the initial tensor-productground state in the dipole gauge, which corresponds to a light-matter entangledstate in the Coulomb gauge, the collective and resonance effects ofmolecular-vibration-polariton formation on the nuclear dynamics are observed ina system of many molecules.

Semiclassical truncated-Wigner-approximation theory of molecular-vibration-polariton dynamics in optical cavities