# Environmental non-additivity and Franck-Condon physics in non-equilibrium quantum systems

## TL;DR

This paper demonstrates that non-additive interactions between vibrational and electromagnetic environments are crucial for accurately modeling non-equilibrium quantum systems, revealing effects like Franck-Condon physics and population inversion.

## Contribution

It introduces a non-additive master equation using a collective coordinate approach to better capture vibrational effects in quantum emitters.

## Key findings

- Photon emission rates decrease with vibrational coupling, aligning with Franck-Condon physics.
- Additive models fail to predict vibrational influence on emission.
- Non-additivity enables population inversion under incoherent excitation.

## Abstract

We show that for a quantum system coupled to both vibrational and electromagnetic environments, enforcing additivity of their combined influences results in non-equilibrium dynamics that does not respect the Franck-Condon principle. We overcome this shortcoming by employing a collective coordinate representation of the vibrational environment, which permits the derivation of a non-additive master equation. When applied to a two-level emitter our treatment predicts decreasing photon emission rates with increasing vibrational coupling, consistent with Franck-Condon physics. In contrast, the additive approximation predicts the emission rate to be completely insensitive to vibrations. We find that non-additivity also plays a key role in the stationary non-equilibrium model behaviour, enabling two-level population inversion under incoherent electromagnetic excitation.