Dynamics of Rabi model under second-order Born–Oppenheimer approximation

We apply the second-order Born–Oppenheimer (BO) approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approximation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.