Electric Quadrupole Shift Cancellation in Single-Ion Optical Frequency Standards

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 ${}^{88}\mathrm{Sr}^{+}$.

Figure 1

Clock transition frequency of ${}^{88}\mathrm{Sr}^{+}$ as a function of the square of the magnetic quantum number in the ${}^{2}D_{5/2}$ state for three orientations of the magnetic field. The legend gives the frequency intercepts at $m_{F^{\prime }}^2=35/12$, and their standard deviations.

Figure 2

Measured clock transition frequencies of ${}^{88}\mathrm{Sr}^{+}$ after cancellation of the electric quadrupole shift and of the tensor terms of the Stark shifts as a function of time ($\mathrm{\text{MJD}}=\mathrm{\text{modified julian day}}$). The dashed line represents the mean frequency; its value and standard deviation are given on the figure. These data were taken between 2004-02-05 ($\mathrm{MJD}=53040$) and 2004-05-12 ($\mathrm{MJD}=53137$).

Figure 3

Slope of the ion frequency dependence on $m_{F^{\prime }}^2$ as a function of the angle $\beta$ between the quantization axis and the perturbing field.