Analytic model reveals local molecular polarizability changes induced by collective strong coupling in optical cavities

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 nonperturbative analytic results for a model system consisting of an ensemble of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math> 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 nonperturbatively and analytically in the dilute limit, i.e., a self-consistent solution with the mean-field Hartree-product wave function becomes exact. We discover that the electronic molecular polarizabilities are modified even in the case of vanishingly small single-molecule couplings. Consequently, this nonperturbative local polarization mechanism persists even in the large-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>N</b:mi></b:math> limit. In contrast, a perturbative calculation of the polarizabilities based on the uncoupled ensemble wave function leads to a qualitatively erroneous scaling behavior with vanishing effects in the large-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>N</c:mi></c:math> 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 simulations of chemical systems under collective strong coupling.