The shape of the electric dipole function determines the sub-picosecond dynamics of anharmonic vibrational polaritons

Vibrational strong coupling has emerged as a promising route for manipulating the reactivity of molecules inside infrared cavities. We develop a full-quantum methodology to study the unitary dynamics of a single anharmonic vibrational mode interacting with a quantized infrared cavity field. By comparing multi-configurational time-dependent Hartree simulations for an intracavity Morse oscillator with an equivalent formulation of the problem in Hilbert space, we describe for the first time the essential role of permanent dipole moments in the femtosecond dynamics of vibrational polariton wavepackets. We classify molecules into three general families according to the shape of their electric dipole function d_e(q) along the vibrational mode coordinate q. For polar species with a positive slope of the dipole function at equilibrium, an initial diabatic light-matter product state without vibrational or cavity excitations evolves into a polariton wavepacket with a large number of intracavity photons for interaction strengths at the conventional onset of ultrastrong coupling. This buildup of the cavity photon amplitude is accompanied by an effective lengthening of the vibrational mode that is comparable with a laser-induced vibrational excitation in free space. In contrast, polar molecules with a negative slope of the dipole function experience an effective mode shortening, under equivalent coupling conditions. We validate our predictions using realistic ab initio ground state potentials and dipole functions for HF and CO₂ molecules. We also propose a non-adiabatic state preparation scheme to generate vibrational polaritons with molecules near infrared nanoantennas for the spontaneous radiation of infrared quantum light.