论文标题
高准确性确定电肢偏移预测的Paul-trap稳定性参数
High-Accuracy Determination of Paul-Trap Stability Parameters for Electric-Quadrupole-Shift Prediction
论文作者
论文摘要
射频（RF）Paul陷阱中离子的运动用MATHIEU方程描述，以及与RF和DC电场梯度成正比的相关稳定性参数。在这里，提出了一种准确地从测量的世俗频率求解稳定参数的高阶，迭代方法。然后，它通过表明陷阱的径向不对称性以DC场梯度主导并测量应用电压与梯度之间的关系来表征端盖陷阱。结果证明该结果与陷阱的静电有限元元素模拟非常吻合。此外，提出了一种使用“滴答器”电压来确定径向陷阱轴方向的方法，并讨论了RF电压的温度依赖性。作为光离子时钟的应用，该方法用于使用施加的DC电压来预测和最小化电动四极移（EQS）。最后，在相互交织的低/高等式时钟测量中确定了Zeeman平等等式取消方法的取消因子的1070下限。这将我们的$^{88} $ sr $^+$光学时钟的等式不确定性降低到$ {\ sillssim} 1 \ times 10^{ - 19} $在分数频率单元中。
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 $^{88}$Sr$^+$ optical clock to ${\lesssim} 1\times 10^{-19}$ in fractional frequency units.
