# Langevin Approach to Quantum Optics with Molecules

## TL;DR

This paper develops a quantum Langevin equations framework to analytically study light-molecule interactions, revealing effects on emission, cavity transmission, and energy transfer in quantum optical systems with vibrational modes.

## Contribution

It introduces an analytical approach to model molecular quantum optics, including emission profiles, cavity effects, and energy transfer, advancing understanding of light-molecule interactions.

## Key findings

- Analytical expressions for emission branching ratios in the Purcell regime.
- Characterization of cavity transmission asymmetries in strong coupling.
- Insights into F"{o}rster energy transfer mediated by vacuum or cavity modes.

## Abstract

We investigate the interaction between light and molecular systems modeled as quantum emitters coupled to a multitude of vibrational modes via a Holstein-type interaction. We follow a quantum Langevin equations approach that allows for analytical derivations of absorption and fluorescence profiles of molecules driven by classical fields or coupled to quantized optical modes. We retrieve analytical expressions for the modification of the radiative emission branching ratio in the Purcell regime and for the asymmetric cavity transmission associated with dissipative cross-talk between upper and lower polaritons in the strong coupling regime. We also characterize the F\"{o}rster resonance energy transfer process between donor-acceptor molecules mediated by the vacuum or by a cavity mode.