  We propose a scheme to simulate the interaction between a two-level system
and a classical light field. Under the transversal driving of two microwave
tones, the system Hamiltonian is identical to that of the general
semi-classical Rabi model. We experimentally realize this Hamiltonian with a
superconducting transmon qubit. By tuning the strength, phase and frequency of
the two microwave driving fields, we simulate the quantum dynamics from weak to
extremely strong driving regime. The resulting evolutions gradually deviate
from the normal sinusoidal Rabi oscillations with increasing driving strength,
in accordance with the predictions of the general semi-classical Rabi model far
beyond the weak driving limit. Our scheme provides an effective approach to
investigate the extremely strong interaction between a two-level system and a
classical light field. Such strong interactions are usually inaccessible in
experiments.
