Nuclear Spin Isomers and the Pauli Principle in Polaritonic Chemistry

Abstract

The Pauli principle has far-reaching consequences in quantum physics. Here, we investigate, for the first time, its implications, together with nuclear spin isomerism, in polaritonic chemistry. The theory is developed for a single and a few molecules as well as for an ensemble of molecules. As an explicit and detailed example we first present an accurate numerical description of a realistic situation involving two $^{14}$NH$_3$ molecules, existing as ortho and para spin isomers, in an infrared plasmonic cavity. Then, we generalize the approach for molecular ensembles using analytical considerations based on the Tavis-Cummings model and simulate the transmission spectrum of a Fabry-P\'erot cavity filled with $^{14}$NH$_3$ gas using quantum mechanics. These results are directly relevant for recent gas-phase experiments studying rovibrational polaritons in molecules. Our findings undoubtedly demonstrate that the Pauli principle and nuclear spin isomerism significantly reshape collective light-matter coupling involving molecules with identical nuclei.