Active compensation of the AC Stark shift in a two-photon rubidium optical frequency reference using power modulation

We implement a feedback protocol to suppress the AC Stark shift in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical power variations by a factor of 1000. This method alleviates the tradeoff between short-term and long-term stability imposed by the AC Stark shift, enabling us to simultaneously achieve instabilities of $3\times {10}^{-14}$ at 1 s and $2\times {10}^{-14}$ at ${10}^4$ s. We also quantitatively describe, and experimentally explore, a stability limit imposed on clocks using this method by frequency noise on the local oscillator.