Observation of the high-order Mollow triplet by quantum mode control with concatenated continuous driving

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 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.