Dual-Platform Precision Measurement of the $3^2D_{5/2}$ to $4^2S_{1/2}$ $g$-Factor Ratio in $^{40}\text{Ca}^+$

Abstract

We report precision measurements of the ratio of Landé $g$ factors between the $3^2D_{5/2}$ and $4^2S_{1/2}$ states of a single trapped $^{40}\text{Ca}^+$ ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements yield a ratio of $0.599~488~813~3(2)$, which represents a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurement yields a concurring value of $0.599~488~813(6)$. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.