CUT-E as a $1/N$ expansion for multiscale molecular polariton dynamics

TL;DR

This paper introduces a new derivation of the CUT-E formalism for molecular polariton dynamics, connecting it with $1/N$ expansions and extending its applicability through bosonization techniques and higher excitation manifolds.

Contribution

The paper provides a novel derivation of the CUT-E formalism using bosonization, linking it to $1/N$ expansions and exploring new approximations and extensions.

Findings

Connections between CUT-E and $1/N$ expansion methods established.

New approximations and extensions to high excitation manifolds developed.

Enhanced understanding of multiscale molecular polariton dynamics achieved.

Abstract

Molecular polaritons arise when the collective coupling between an ensemble of $N$ molecules and an optical mode exceeds individual photon and molecular linewidths. The complexity of their description stems from their multiscale nature, where the local dynamics on each molecule can, in principle, be influenced by the collective behavior of the entire ensemble. To address this, we previously introduced a formalism called collective dynamics using truncated equations (CUT-E). CUT-E approaches the problem in two stages. First, it exploits permutational symmetries to obtain a substantial simplification of the problem. However, this is often insufficient for parameter regimes relevant to most experiments. Second, it takes the exact solution of the problem in the $N\to\infty$ limit as a reference and derives systematic $\mathcal{O}(1/N)$ corrections. Here we provide a novel derivation of CUT-E based on recently developed bosonization techniques. We lay down its connections with $1/N$ expansions that are ubiquitous in other fields of physics, and present previously unexplored key aspects of this formalism, including various types of approximations and extensions to high excitation manifolds.