High-accuracy determination of Paul-trap stability parameters for electric-quadrupole-shift prediction

The motion of an ion in a radiofrequency (rf) Paul trap is described by the Mathieu equation and the associated stability parameters that are proportional to the rf and dc electric field gradients. Here, a higher-order, iterative method to accurately solve the stability parameters from measured secular frequencies is presented. It is then used to characterize an endcap trap by showing that the trap's radial asymmetry is dominated by the dc field gradients and by measuring the relation between the applied voltages and the gradients. The results are shown to be in good agreement with an electrostatic finite-element-method simulation of the trap. Furthermore, a method to determine the direction of the radial trap axes using a tickler voltage is presented, and the temperature dependence of the rf voltage is discussed. As an application for optical ion clocks, the method is used to predict and minimize the electric quadrupole shift (EQS) using the applied dc voltages. Finally, a lower limit of 1070 for the cancellation factor of the Zeeman-averaging EQS cancellation method is determined in an interleaved low-/high-EQS clock measurement. This reduces the EQS uncertainty of our Sr-88 (+) optical clock to <= 1 x 10 (- 19) in fractional frequency units. Published under an exclusive license by AIP Publishing.

Automated summary

This article presents a method to solve the stability parameters and characterizes an endcap trap using this method. It also introduces a method to determine the direction of the radial trap axes and discusses the temperature dependence of the rf voltage. The application of this method in optical ion clocks predicts and minimizes the electric quadrupole shift.