Magic wavelengths in the alkaline earth ions

TL;DR

This paper calculates magic wavelengths for specific transitions in alkaline earth ions using relativistic methods, aiding high-precision experiments by identifying wavelengths where light shifts are canceled.

Contribution

It provides new theoretical predictions of magic wavelengths for Mg+, Ca+, Sr+, and Ba+ ions, validated against experimental data, facilitating precision measurements.

Findings

Identified multiple magic wavelengths for alkaline earth ions.

Validated polarizability calculations with experimental data.

Some predicted wavelengths match recent experimental measurements.

Abstract

We present magic wavelengths for the $nS$ - $nP_{1/2,3/2}$ and $nS$ - $mD_{3/2,5/2}$ transitions, with the respective ground and first excited $D$ states principal quantum numbers $n$ and $m$, in the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth ions for linearly polarized lights by plotting dynamic polarizatbilities of the $nS$, $nP_{1/2,3/2}$ and $mD_{3/2,5/2}$ states of the ions. These dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with the available high precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca$^+$ concurs with the recent measurements reported in [{\bf Phys. Rev. Lett. 114, 223001 (2015)}]. Knowledge of these magic wavelengths are propitious to carry out many proposed high precision measurements trapping the above ions in the electric fields with the corresponding frequencies.