It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light–matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

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光腔中分子振动-极化子动力学的半经典截断维格纳近似理论

实验证明，分子振动与红外腔模强耦合形成的分子振动极化子可以显着改变各种分子系统的物理性质和化学反应性。然而，由于混合系统的复杂性，特别是包含许多分子的系统中极化子态的集体性质，对修饰的潜在机制的完整理论理解仍然难以捉摸。我们在此开发了基于截断维格纳近似（TWA）的分子振动极化子动力学的半经典理论，该近似在大型分子系统中易于处理，并同时捕获光学腔中光子的量子特征。然后将该理论应用于研究具有基态莫尔斯电势并在超强耦合状态下与红外腔模式强耦合的相同双原子分子系统的核量子动力学。通过将 TWA 与偶极子和库仑计中两种不同初始状态的单分子系统的完整量子动力学进行比较来检查 TWA 的有效性。对于偶极规范中的初始张量积基态（对应于库仑规范中的光物质纠缠态），在许多分子的系统中观察到分子振动极化子形成对核动力学的集体和共振效应。