# Light-Matter Interactions via the Exact Factorization Approach

## TL;DR

This paper extends the exact factorization approach to light-matter interactions, providing a new framework for accurately modeling photon-matter coupling effects, especially in strong-coupling regimes, with potential for improved simulation methods.

## Contribution

The paper introduces an exact factorization formalism for light-matter interactions, enabling a Schrödinger equation for the photonic wavefunction that captures coupling effects exactly.

## Key findings

- Significant differences from conventional potentials in strong-coupling regimes
- Potential for developing semiclassical trajectory methods
- Formalism applicable to systems with multiple photon modes

## Abstract

The exact factorization approach, originally developed for electron-nuclear dynamics, is extended to light-matter interactions within the dipole approximation. This allows for a Schrodinger equation for the photonic wavefunction, in which the potential contains exactly the effects on the photon field of its coupling to matter. We illustrate the formalism and potential for a two-level system representing the matter, coupled to an infinite number of photon modes in the Wigner-Weisskopf approximation, as well as a single mode with various coupling strengths. Significant differences are found with the potential used in conventional approaches, especially for strong-couplings. We discuss how our exact factorization approach for light-matter interactions can be used as a guideline to develop semiclassical trajectory methods for efficient simulations of light-matter dynamics.