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Typical optical clock transitions have ~Hz linewidths, not MHz.

The intrinsic frequency stability of almost all lasers is by far not good enough to be able to probe such transitions. Therefore, ultra-stable optical cavities are used as a frequency reference, and the laser is constantly steered to stay on the cavity resonance by a fast electronic feedback system. In this way, laser linewidths in the sub-Hz range can be achieved. Then an acousto-optic modulator is used to scan the laser frequency across the clock transition.