Vibropolaritonic Reaction Rates in the Collective Strong Coupling Regime: Pollak-Grabert-H\"anggi Theory

TL;DR

This paper extends the Pollak-Grabert-H"anggi theory to large ensemble sizes in vibrational strong coupling, revealing that collective effects diminish cavity-induced modifications of reaction rates.

Contribution

It provides an analytical extension of the PGH model to realistic ensemble sizes, demonstrating the nullification of cavity-induced frictions in large N regimes.

Findings

Large N reduces the effective light-matter coupling per molecule

Cavity-induced frictions become negligible at realistic ensemble sizes

The model explains the absence of rate modifications in experiments

Abstract

Following experimental evidence that vibrational polaritons, formed from collective vibrational strong coupling (VSC) in optical microcavities, can modify ground-state reaction rates, a spate of theoretical explanations relying on cavity-induced frictions has been proposed through the Pollak-Grabert-H\"anggi (PGH) theory, which goes beyond transition state theory (TST). However, by considering only a single reacting molecule coupled to light, these works do not capture the ensemble effects present in experiments. Moreover, the relevant light-matter coupling should have been $\sqrt{N}$ times smaller than those used by preceding works, where $N\approx10^{6}-10^{12}$ is the ensemble size. In this work, we explain why this distinction is significant and can nullify effects from these cavity-induced frictions. By analytically extending the cavity PGH model to realistic values of $N$, we show how this model succumbs to the polariton "large $N$ problem", that is, the situation whereby the single reacting molecule feels only a tiny $1/N$ part of the collective light-matter interaction intensity, where $N$ is large.