Electric Quadrupole Shift Cancellation in Single-Ion Optical Frequency Standards

Abstract

The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for canceling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of $5\times {10}^{-18}$ for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the $5s{}^{2}S_{1/2}–4d{}^{2}D_{5/2}$ clock transition of ${}^{88}\mathrm{Sr}^{+}$.