I will give an overview of a recently proposed mathematical procedure for taking the semiclassical limit of the quantum Rabi model, along with numerical results illustrating convergence towards the limit in both the full Rabi model and the RWA. Progress towards developing a theory that captures quantum fluctuations around the semiclassical dynamics will be presented, along with some very recent results on the analytical collapse envelope for displaced Fock states. Plans for future work in this area will be discussed, including studies of the polaron-transformed Hamiltonian and incorporating environmental interactions.

E.K. Twyeffort Irish and A.D. Armour, Defining the semiclassical limit of the Rabi Hamiltonian, Phys. Rev. Lett. 129, 183603 (2022).

H.F.A. Coleman and E.K. Twyeffort, Spectral and dynamical validity of the rotating-wave approximation in the quantum and semiclassical Rabi models [Invited], JOSA B 41, C188 (2024).