One- and multiphoton resonances in the light-atom interaction

The interaction between atomic systems and electromagnetic fields is central to modern physics and emerging quantum technologies. The Rabi models, in their semiclassical and quantum versions, provide the simplest and most fundamental description of this interaction. In this work, we present a concise derivation of both models and show how one- and multiphoton resonances arise in the semiclassical regime. We then analyze how these resonances manifest in the quantum Rabi model, discussing similarities and differences in relation to the classical description. Special attention is given to the three-photon resonance, a phenomenon usually neglected in textbooks due to its relative weakness, but which is intrinsic to the radiation-matter interaction. Our goal is to offer an accessible pedagogical reference for students and researchers interested in Quantum Optics and Quantum Information, with an emphasis on the fundamentals of the Rabi models.