The quantum Rabi model is a cornerstone of modern quantum optics, and has helped us understand some of the most important features of light-matter interaction. One of the key assumptions of the model is that the atom is a perfect two-level system.

In this talk, we will explore what happens when we drop this assumption and consider a multi-level system interacting with a single mode field. We will see how some order can be retrieved in the ensuing "chaos" by identifying some useful symmetries (exact or approximate), and by recognising some properties that are inherited from the simpler two-level case.