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The crossover from quantum to semiclassical behavior in the seminal Rabimodel of light-matter interaction still, surprisingly, lacks a complete andrigorous understanding. A formalism for deriving the semiclassical modeldirectly from the quantum Hamiltonian is developed here. Working in a displacedFock-state basis $\lvert \alpha, n \rangle$, the semiclassical limit isobtained by taking $\lvert \alpha \rvert \to \infty$ and the coupling to zero.This resolves the discrepancy between coherent-state dynamics and semiclassicalRabi oscillations in both standard and ultrastrong coupling/driving regimes.Furthermore, it provides a framework for studying the quantum-to-classicaltransition, with potential applications in quantum technologies.

Defining the semiclassical limit of the quantum Rabi Hamiltonian