Frequency shifts due to Stark effects on a rubidium two-photon transition

Abstract

The $5{S}_{1/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1-nm ac Stark shift $[2.30(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}]$ that is in good agreement with our measured value of $2.5(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}$. We include a calculation of the temperature-dependent blackbody radiation (BBR) shift, and we predict that the clock could be operated either with zero net BBR shift $[T=495.9(27)$ K] or with zero first-order sensitivity $[T=368.1(14)$ K]. Also described is the calculation of the dc Stark shift of $5.5(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}/(\mathrm{V}/{\mathrm{cm}}^{2}$) as well as clock sensitivities to optical alignment variations in both a cat's eye and a flat mirror retroreflector. Finally, we characterize these Stark effects, discussing mitigation techniques necessary to reduce final clock instabilities.