# Theory for the stationary polariton response in the presence of vibrations

## TL;DR

This paper develops a quantum optical model for surface plasmon polaritons coupled with molecules, incorporating molecular vibrations to explain asymmetric emission and decoherence in hybrid systems, relevant for applications like coherent light harvesting.

## Contribution

It introduces a novel theoretical framework that includes molecular vibrations via $P(E)$ theory, enhancing understanding of polariton response and emission asymmetries in hybrid systems.

## Key findings

- Accounts for the effect of molecular vibrations on polariton response
- Explains asymmetric emission from upper and lower polariton modes
- Provides a link between hybrid mode response and molecular fluorescence

## Abstract

We construct a model describing the response of a hybrid system where the electromagnetic field - in particular, surface plasmon polaritons - couples strongly with electronic excitations of atoms or molecules. Our approach is based on the input-output theory of quantum optics, and in particular it takes into account the thermal and quantum vibrations of the molecules. The latter is described within the $P(E)$ theory analogous to that used in the theory of dynamical Coulomb blockade. As a result, we are able to include the effect of the molecular Stokes shift on the strongly coupled response of the system. Our model then accounts for the asymmetric emission from upper and lower polariton modes. It also allows for an accurate description of the partial decoherence of the light emission from the strongly coupled system. Our results can be readily used to connect the response of the hybrid modes to the emission and fluorescence properties of the individual molecules, and thus are relevant in understanding any utilization of such systems, like coherent light harvesting.