Absolute Frequency Measurement of the ${}^{40}\mathrm{Ca}^{+}$ $4s{}^{2}S_{1/2}-3d{}^{2}D_{5/2}$ Clock Transition

We report on the first absolute transition frequency measurement at the ${10}^{-15}$ level with a single, laser-cooled ${}^{40}\mathrm{Ca}^{+}$ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the ${}^{40}\mathrm{Ca}^{+}$ $4s{}^{2}S_{1/2}-3d{}^{2}D_{5/2}$ electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency ${\nu }_{{\mathrm{Ca}}^{+}}=411042129776393.2(1.0)\mathrm{Hz}$ is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Landé $g$ factor of the $3d{}^{2}D_{5/2}$ level to be $g_{5/2}=1.2003340(3)$.

Figure 1

(a) Partial level scheme of ${}^{40}\mathrm{Ca}^{+}$ showing the $S_{1/2}-D_{5/2}$ clock transition as well as the transitions used for resetting, repumping, cooling, and detecting the ion. (b) Magnetic sublevels of the clock transition and the six transitions having the biggest coupling strength for the actual laser polarization, quantization axis, and $k$ vector of the laser at 729 nm. The numbers indicate the order in which the transitions were probed.

Figure 2

Experiment setup: The frequency of an ultrastable laser is locked to a single ${}^{40}\mathrm{Ca}^{+}$ stored in a linear ion trap and measured by a frequency comb referenced to a transportable Cs fountain atomic clock. The light of a second laser locked in a similar manner to another trap system in another lab is transported via a 500 m long optical fiber link. An optical beat note is detected on a fast photodiode (PD). The solid lines are optical signals, the dotted lines indicate electronic feedback, and the dash-dotted lines show rf signals.

Figure 3

(a) Example for a data set where the direct optical beat signal of both lasers was compared to the difference of the frequency comb readings. This information was used to detect cycle slips of the counters (gate time 1 s) mainly caused by low signal-to-noise ratio. An error shows up as a frequency difference larger than 1 Hz. (b) Frequency deviation during different days. The circles are mean values with statistical error bars ($1\sigma$) for normal trap drive power of 9 W. The solid line is the average of this data with the statistical uncertainty indicated by dashed lines. The squares show data obtained with the trap power reduced by a factor of 3.

Figure 4

Absolute frequency instability for the comparison of ${}^{40}\mathrm{Ca}^{+}$ against Cs. The data set consists of 2278 frequency measurement sets of all six transitions with an effective gate time of 22 s. The inset shows a histogram of the data which is consistent with a Gaussian fit of 23(1) Hz standard deviation.