Determination of hyperfine splittings and Land\'{e} $g_J$ factors of $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ states of $^{111,113}$Cd$^+$ for a microwave frequency standard

TL;DR

This paper measures hyperfine splittings and Landé g-factors of specific cadmium ion states to enhance the precision and stability of microwave frequency standards using trapped ions.

Contribution

It provides new experimental measurements and theoretical calculations of hyperfine structures and g-factors for $^{111,113}$Cd$^+$ ions, improving accuracy for atomic clock applications.

Findings

Hyperfine splittings of $5p~^2P_{3/2}$ state measured with laser-induced fluorescence.

Calculated hyperfine splittings and g-factors using multiconfiguration Dirac--Hartree--Fock method.

Results enhance the signal-to-noise ratio and accuracy of cadmium ion-based microwave clocks.

Abstract

Regarding trapped-ion microwave-frequency standards, we report on the determination of hyperfine splittings and Land\'{e} $g_J$ factors of $^{111,113}$Cd$^+$. The hyperfine splittings of the $5p~^2P_{3/2}$ state of $^{111,113}$Cd$^+$ ions were measured using laser-induced fluorescence spectroscopy. The Cd$^+$ ions were confined in a linear Paul trap and sympathetically cooled by Ca$^+$ ions. Furthermore, the hyperfine splittings and Land\'{e} $g_J$ factors of the $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ levels of $^{111,113}$Cd$^+$ were calculated with greater accuracy using the multiconfiguration Dirac--Hartree--Fock scheme. The measured hyperfine splittings and the Dirac--Hartree--Fock calculation values were cross-checked, thereby further guaranteeing the reliability of our results. The results provided in this work can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, and subsequently the stability and accuracy of the microwave frequency standard based on trapped Cd$^+$ ions.