Magnetic Sublevel Independent Magic and Tune-out Wavelengths of the Alkaline-earth Ions

TL;DR

This paper identifies M-independent magic and tune-out wavelengths in alkaline-earth ions, enabling more accurate determination of electric dipole matrix elements by reducing angular momentum dependence.

Contribution

It reports M-independent magic and tune-out wavelengths for specific states in Mg+, Ca+, Sr+, and Ba+ ions, facilitating precise E1 matrix element measurements.

Findings

Identified M-independent $ ext{λ}_T$ and $ ext{λ}_{magic}$ wavelengths for multiple states.

Proposed a measurement setup to accurately infer E1 matrix elements.

Enhanced understanding of angular momentum effects on light shifts.

Abstract

Lightshift of a state due to the applied laser in an atomic system vanishes at the tune-out wavelengths ($\lambda_T$s). Similarly, differential light shift of a transition vanishes at the magic wavelengths ($\lambda_{magic}$s). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements of $\lambda_{magic}$ with the calculated their values. Similarly, the $\lambda_T$ values of an atomic state can be used to infer the E1 matrix element as it involves dynamic electric dipole ($\alpha$) values of only one state whereas the $\lambda_{magic}$ values are dealt with $\alpha$ values of two states. However, both the $\lambda_T$ and $\lambda_{magic}$ values depend on angular momenta and their magnetic components ($M$) of states. Here, we report the $\lambda_T$ and $\lambda_{magic}$ values of many $S_{1/2}$ and $D_{3/2,5/2}$ states, and transitions among these states of the Mg$^{+}$, Ca$^{+}$, Sr$^{+}$ and Ba$^{+}$ ions that are independent of $M$- values. Measuring these wavelengths in a special set-up as discussed in the paper, it could be possible to infer a large number of E1 matrix elements of the above ions accurately.