Spectroscopic properties under vibrational strong coupling in disordered matter from path-integral Monte Carlo simulations

Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli-Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis-Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.