Evaluation of systematic shifts of the88Sr+single-ion optical frequency standard at the10−17level

Abstract

An ion trap of the end-cap design was built recently at the National Research Council of Canada for improved control of the ${}^{88}$Sr${}^{+}$ single-ion optical frequency standard systematic shifts. The uncertainty on the micromotion-induced shifts is smaller by more than four orders of magnitude when compared to our previous trap system and reaches a fractional frequency uncertainty of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. To obtain this low uncertainty level, the micromotion is minimized with trim electrodes and the trap is operated at a special frequency at which there is anticorrelation between the second-order Doppler and Stark shifts. This choice of operating frequency, determined by the differential scalar polarizability of the clock transition, yields a suppression by a factor of $\ensuremath{\approx}$28 in the combined micromotion shifts. Like many optical frequency standards, the dominant source of uncertainty in the new trap is the blackbody radiation shift. Its uncertainty has been reduced by an order of magnitude with a recent theoretical evaluation of the differential scalar polarizability of the clock transition. The fractional blackbody shift uncertainty, estimated using a model of the blackbody field at the ion, is $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The otherwise dominant electric quadrupole shift is reduced to below the $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ level with a cancellation method based on the average frequency of several pairs of Zeeman components. This method also cancels the tensor Stark shift and simplifies the description of the frequency shifts that are quantization-axis dependent. This paper provides a detailed description of the ${}^{88}$Sr${}^{+}$ optical frequency standard uncertainty evaluation and the methods used to make the standard robust against changes in the trap environment. The total fractional frequency uncertainty of the ${}^{88}$Sr${}^{+}$ ion for our current system is estimated at $2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. We also discuss the uncertainty evaluation of a recently reported measurement of the ${}^{88}$Sr${}^{+}$ $S$-$D$ clock transition made over a 2-month period by comparison with a maser referenced to the SI second. The frequency measured is $444\phantom{\rule{0.16em}{0ex}}779\phantom{\rule{0.16em}{0ex}}044\phantom{\rule{0.16em}{0ex}}095\phantom{\rule{0.16em}{0ex}}485.5(9)$ Hz, with an uncertainty limited by the evaluation of the maser frequency.