# Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics

## TL;DR

This paper demonstrates that multi-trajectory Ehrenfest dynamics can effectively simulate vacuum fluctuations and photon correlations in cavity QED systems, providing a promising semi-classical approach for quantum light-matter interactions.

## Contribution

It extends mixed quantum-classical Ehrenfest methods to model quantum vacuum effects and photon correlations in cavity QED, showing accurate results compared to exact quantum benchmarks.

## Key findings

- Accurately captures spontaneous emission dynamics.
- Reproduces quantum correlations and vacuum fluctuations.
- Offers a promising semi-classical simulation approach.

## Abstract

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field, through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum-classical (mean field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.