Defining the semiclassical limit of the quantum Rabi Hamiltonian

The crossover from quantum to semiclassical behavior in the seminal Rabi model of light-matter interaction still, surprisingly, lacks a complete and rigorous understanding. A formalism for deriving the semiclassical model directly from the quantum Hamiltonian is developed here. Working in a displaced Fock-state basis \(\lvert \alpha, n \rangle\), the semiclassical limit is obtained by taking \(\lvert \alpha \rvert \to \infty\) and the coupling to zero. This resolves the discrepancy between coherent-state dynamics and semiclassical Rabi oscillations in both standard and ultrastrong coupling/driving regimes. Furthermore, it provides a framework for studying the quantum-to-classical transition, with potential applications in quantum technologies.