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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>3</a:mn> <a:mo>×</a:mo> <a:msup> <a:mn>10</a:mn> <a:mrow> <a:mo>−</a:mo> <a:mn>14</a:mn> </a:mrow> </a:msup> </a:math> at 1 s and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>2</c:mn> <c:mo>×</c:mo> <c:msup> <c:mn>10</c:mn> <c:mrow> <c:mo>−</c:mo> <c:mn>14</c:mn> </c:mrow> </c:msup> </c:math> at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mn>10</e:mn> <e:mn>4</e:mn> </e:msup> </e:math> s. We also quantitatively describe, and experimentally explore, a stability limit imposed on clocks using this method by frequency noise on the local oscillator.