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

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