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

Abstract

Quadrupole shifts for three prominent clock transitions, $[4f^{14}6s{]}^2{S}_{1/2}\to [4f^{14}5d{]}^2{D}_{3/2}$, $[4f^{14}6s{]}^2{S}_{1/2}\to [4f^{14}5d{]}^2{D}_{5/2}$ and $[4f^{14}6s{]}^2{S}_{1/2}\to [4f^{13}6s^2{]}^2{F}_{7/2}$, 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 $[4f^{14}6s{]}^2{S}_{1/2}\to [4f^{14}5d{]}^2{D}_{3/2}$ 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.

5 pages and 2 figures. Minor changes are incorporated

References in corpus (2)

• Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit
• Electric quadrupole moment of the $5d^2{D}_{3/2}$ state in ${}^{171}Y{b}^{+}$ : A relativistic coupled-cluster analysis

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