Analytic Model Reveals Local Molecular Polarizability Changes Induced by Collective Strong Coupling in Optical Cavities

TL;DR

This paper presents an analytic model showing that collective strong coupling in optical cavities can induce local changes in molecular polarizability, challenging previous assumptions and impacting the understanding of polaritonic chemistry.

Contribution

It provides a non-perturbative analytic solution demonstrating local polarizability modifications due to collective strong coupling, even at small single-molecule couplings and in the large-N limit.

Findings

Electronic polarizabilities are modified even with very weak single-molecule coupling.

The non-perturbative mechanism persists in the large-N limit.

Perturbative calculations fail to capture the correct scaling behavior.

Abstract

Despite recent numerical evidence, one of the fundamental theoretical mysteries of polaritonic chemistry is how and if collective strong coupling can induce local changes of the electronic structure to modify chemical properties. Here we present non-perturbative analytic results for a model system consisting of an ensemble of $N$ harmonic molecules under vibrational strong coupling (VSC) that alters our present understanding of this fundamental question. By applying the cavity Born-Oppenheimer partitioning on the Pauli-Fierz Hamiltonian in dipole approximation, the dressed many-molecule problem can be solved self-consistently and analytically in the dilute limit. We discover that the electronic molecular polarizabilities are modified even in the case of vanishingly small single-molecule couplings. Consequently, this non-perturbative local polarization mechanism persists even in the large-$N$ limit. In contrast, a perturbative calculation of the polarizabilities leads to a qualitatively erroneous scaling behavior with vanishing effects in the large-$N$ limit. Nevertheless, the exact (self-consistent) polarizabilities can be determined from single-molecule strong coupling simulations instead. Our fundamental theoretical observations demonstrate that hitherto existing collective-scaling arguments are insufficient for polaritonic chemistry and they pave the way for refined single- (or few-) molecule strong-coupling ab-initio simulations of chemical systems under collective strong coupling.