Magic wavelengths in the alkaline-earth-metal ions

We present magic wavelengths for the n S_{1 /2}-n P_{1 /2 ,3 /2} , and n S_{1 /2}-m D_{3 /2 ,5 /2} transitions in Mg⁺, Ca⁺, Sr⁺, and Ba⁺ alkaline-earth-metal ions, for the principal quantum numbers n and m for the ground and first excited D states, respectively. These wavelengths are presented for linearly polarized light by plotting the dynamic polarizabilities of the n S ,n P_{1 /2 ,3 /2} , and m D_{3 /2 ,5 /2} states of the considered ions. Required dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with available high-precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca⁺ concur with the recent measurements reported by Liu et al. [Phys. Rev. Lett. 114, 223001 (2015), 10.1103/PhysRevLett.114.223001]. Knowledge of these magic wavelengths is propitious to carry out many proposed high-precision measurements trapping the above ions in electric fields with the corresponding frequencies.