Suppression of Clock Shifts at Magnetic-Field-Insensitive Transitions

We show that it is possible to significantly reduce rank 2 tensor shifts of a clock transition by operating at a judiciously chosen magnetic-field-insensitive point. In some cases shifts are almost completely eliminated making the transition an effective $J=0$ to $J=0$ candidate. This significantly improves the feasibility of a recent proposal for clock operation with large ion crystals. For such multi-ion clocks, geometric constraints and selection rules naturally divide clock operation into two categories based on the orientation of the magnetic field. We discuss the limitations imposed on each type and how calibrations might be carried out for clock operation.

Figure 1

The magnetic field dependence of the $|S_{1/2},4,-3⟩$ to $|D_{3/2},5,-3⟩$ transition in ${{}^{43}\mathrm{Ca}}^{+}$. The solid curve shows the frequency dependence of the transition relative to the zero-field value with the vertical line marking the field-insensitive point of approximately 1.28 mT. The dashed curve shows the field dependence of the corresponding shift coefficient with the horizontal line marking the intercept at the field-insensitive point giving a shift coefficient $C_2\approx -5.8\times {10}^{-5}$.