When a two-level quantum system is driven periodically with a Rabi frequency $\mathrm{\Omega }$ comparable to the driving frequency ${\nu }_s$, the resonant transition frequency deviates from the bare energy gap—an effect known as the Bloch-Siegert shift. Observing sub-Hertz Bloch-Siegert shift is challenging due to its small energy scale and its mixing with other systematic shifts. Using a Floquet-engineered optical lattice clock, we directly observe this sub-hertz shift in ultracold atoms. We tune driving parameters to suppress micromotion and apply a self-comparison stroboscopic method to remove unwanted frequency shifts. Assisted by closed-loop feedback, we achieve high-precision results after one hour of averaging and longer integration will further improve the measurement accuracy.

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• Atomic, optical & lattice clocks
• Coherent control