An Optimized Ion Trap Geometry to Measure Quadrupole Shifts of $^{171}$Yb$^+$ Clocks

TL;DR

This paper introduces a new ion trap design that significantly reduces anharmonic effects, enabling more precise measurements of quadrupole shifts in $^{171}$Yb$^+$ ions to improve atomic clock accuracy and validate theoretical models.

Contribution

The paper presents a novel ion trap geometry that minimizes anharmonic potential components, facilitating highly accurate quadrupole shift measurements and validation of theoretical quadrupole moment calculations.

Findings

Trap reduces anharmonic components by four orders of magnitude.

Allows precise measurement of quadrupole moments of specific states.

Estimates quadrupole shifts using relativistic coupled-cluster calculations.

Abstract

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the $^{171}$Yb-ion. This trap will produce nearly ideal harmonic potential where the quadrupole shifts due to the anharmonic components can be reduced by four orders of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the $6s~{^2}S_{1/2} \rightarrow 4f^{13} 6s^2 ~{^2}F_{7/2}$ and $6s~{^2}S_{1/2} \rightarrow 5d ~{^2}D_{3/2}$ transitions, from which we can deduce precise values of the quadrupole moments ($\Theta$s) of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ and $5d ~{^2}D_{3/2}$ states. Moreover, it may be able to affirm validity of the measured $\Theta$ value of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ state where three independent theoretical studies defer almost by one order in magnitude from the measurement. We also perform calculations of $\Theta$s using the relativistic coupled-cluster (RCC) method. We use these $\Theta$ values to estimate quadrupole shift that can be measured in our proposed ion trap experiment.