# Travelling to exotic places with cavity QED systems

## TL;DR

This paper reviews how cavity QED systems can simulate complex quantum phenomena like gauge potentials and relativistic effects, demonstrating their feasibility with current experimental setups.

## Contribution

It introduces a quadrature representation approach to derive various quantum models and verifies their predictions numerically with realistic parameters.

## Key findings

- Jahn-Teller models and gauge potentials can be realized in cavity QED systems.
- Numerical simulations confirm analytical predictions with realistic experimental parameters.
- Feasibility of implementing these quantum simulations with current technology is demonstrated.

## Abstract

Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials, transverse Hall currents, and relativistic effects naturally arise in these systems. Some of the analytical predictions are verified numerically using realistic experimental parameters taking into account for system losses. Thereby demonstrating their feasibility with current experimental setups.