# Quadrupole Shifts for the $^{171}$Yb$^+$ Ion Clocks: Experiments versus Theories

Source: [Quadrupole Shifts for the $^{171}$Yb$^+$ Ion Clocks: Experiments versus Theories](<https://www.sota2.com/research/paper/68fa31751e209131ce87eccd>)

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Data updated: 2025-10-24T18:51:02.379Z

Authors: D. K. Nandy, B. K. Sahoo

Published: 2014-08-20T14:50:53.000Z

## Abstract

Quadrupole shifts for three prominent clock transitions, $\[4f^{14} 6s\] ^2S\_{1/2} \\rightarrow \[4f^{14} 5d\] ^2D\_{3/2}$, $\[4f^{14} 6s\] ^2S\_{1/2} \\rightarrow \[4f^{14} 5d\] ^2D\_{5/2}$ and $\[4f^{14} 6s\] ^2S\_{1/2} \\rightarrow \[4f^{13} 6s^2\] ^2F\_{7/2}$, in the Yb$^+$ ion are investigated by calculating the quadrupole moments ($\\Theta$s) of the $5d\_{3/2,5/2}$ and $4f\_{7/2}$ states using the relativistic coupled-cluster (RCC) methods. We find an order difference in the $\\Theta$ value of the $4f\_{7/2}$ state between our calculation and the experimental result, but our result concur with the other calculations that are carried out using different many-body methods than ours. However, our $\\Theta$ value of the $5d\_{3/2}$ state is in good agreement with the available experimental result and becomes more precise till date to estimate the the quadrupole shift of the $\[4f^{14} 6s\] ^2S\_{1/2} \\rightarrow \[4f^{14} 5d\] ^2D\_{3/2}$ clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the $6s\_{1/2}$, $5d\_{3/2,5/2}$ and $4f\_{7/2,5/2}$ states of $^{171}$Yb$^+$ ion using the same RCC methods and compare the results with their experimental values. We also determine the lifetime of the $5d\_{3/2}$ state to eradicate the scepticism on the earlier measured value as claimed by a recent experiment.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1408.4683>)

[PDF](<https://arxiv.org/pdf/1408.4683.pdf>)