  The Mollow triplet is a fundamental signature of quantum optics, and has been
observed in numerous quantum systems. Although it arises in the 'strong
driving' regime of the quantized field, where the atoms undergo coherent
oscillations, it can be typically analyzed within the rotating wave
approximation. Here we report the first observation of high-order effects in
the Mollow triplet structure due to strong driving. In experiments, we explore
the regime beyond the rotating wave approximation using concatenated continuous
driving that has less stringent requirements on the driving field power. We are
then able to reveal additional transition frequencies, shifts in energy levels,
and corrections to the transition amplitudes. In particular, we find that these
amplitudes are more sensitive to high-order effects than the frequency shifts,
and that they still require an accurate determination in order to achieve
high-fidelity quantum control. The experimental results are validated by the
Floquet theory, which enables the precise numerical simulation of the evolution
and further provides an analytical form for an effective Hamiltonian that
approximately predicts the spin dynamics beyond the rotating wave
approximation.
