  We analyze the dynamics of a two-level quantum system (TLS) under the
influence of a strong sinusoidal driving signal whose origin is the interaction
of the two-level system with a quantum field. In this approach the driving
field is replaced by a harmonic oscillator that is either strongly coupled to
the TLS or populated with a large number of photons. Starting from the Rabi
model, we derive expressions for the TLS's oscillation frequencies and compare
the results with those obtained from the model where the driving signal is
treated classically. We show that in the limits of weak coupling and large
photon number, the well-known expression for the Rabi frequency in the strong
driving regime is recovered. In the opposite limit of strong coupling and small
photon number, we find differences between the predictions of the semiclassical
and quantum models. The results of the quantum picture can therefore be
understood as Landau-Zener-Stueckelberg interferometry in the fully quantum
regime.
