Mixed quantum-classical dynamics yields anharmonic Rabi oscillations

We apply a mixed quantum-classical (MQC) approach to the quantum Rabi model, involving a classical optical field coupled self-consistently to a quantum two-level system. Under the rotating wave approximation, we analytically show that this approach yields persistent yet anharmonic Rabi oscillations, governed by an undamped and unforced Duffing equation. We consider the single-quantum limit, where we find that such anharmonic Rabi oscillations closely follow full-quantum results once zero-point energy is approximately enforced when initializing the optical field coordinate. Our findings provide guidance in the application of MQC dynamics to classes of problems involving small quantum numbers and far away from decoherence.