Pauli principle in polaritonic chemistry

TL;DR

This paper explores how the Pauli principle influences the state space of molecular ensembles in cavity quantum electrodynamics, revealing that permutational symmetry constraints significantly reduce the number of allowed collective states as the system size grows.

Contribution

It introduces a group-theoretic approach to incorporate the Pauli principle into polaritonic chemistry, analyzing the impact on collective state spaces and their properties.

Findings

Number of Pauli-allowed states decreases rapidly with more molecules

Bosonic states are more prevalent than fermionic states

Brightness of allowed states varies with energy level structure

Abstract

The consequences of enforcing permutational symmetry, as required by the Pauli principle (spin-statistical theorem), on the state space of molecular ensembles interacting with the quantized radiation mode of a cavity are discussed. The Pauli-allowed collective states are obtained by means of group theory, i.e., by projecting the state space onto the appropriate irreducible representations of the permutation group of the indistinguishable molecules. It is shown that with increasing number of molecules the ratio of Pauli-allowed collective states decreases very rapidly. Bosonic states are more abundant than fermionic states, and the brightness of Pauli-allowed state space (the contribution from photon excited states) increases(decreases) with increasing fine structure in the energy levels of the material ground(excited) state manifold. Numerical results are shown for the realistic example of rovibrating H$_2$O molecules interacting with an infrared cavity mode.