Magic wavelengths in the alkaline-earth-metal ions

Abstract

We present magic wavelengths for the $n{S}_{1/2}\text{\ensuremath{-}}n{P}_{1/2,3/2},$ and $n{S}_{1/2}\text{\ensuremath{-}}m{D}_{3/2,5/2}$ transitions in ${\mathrm{Mg}}^{+},$ ${\mathrm{Ca}}^{+},$ ${\mathrm{Sr}}^{+},$ and ${\mathrm{Ba}}^{+}$ 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 $nS,n{P}_{1/2,3/2},$ 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 ${\mathrm{Ca}}^{+}$ concur with the recent measurements reported by Liu et al. [Phys. Rev. Lett. 114, 223001 (2015)]. 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.