Magic wavelengths in the alkaline earth ions

Abstract

We present magic wavelengths for the $nS$ - $n{P}_{1/2,3/2}$ and $nS$ - $m{D}_{3/2,5/2}$ 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 $nS$, $n{P}_{1/2,3/2}$ and $m{D}_{3/2,5/2}$ 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.

5 pages, four tables, four figures

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• Static and dynamic polarizabilities of Yb-ion]{Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the $6{\mathrm{S}}_{1/2}\to 5{\mathrm{D}}_{3/2}$ clock transition in Yb${}^{+}$
• Precision Measurement of the Quadrupole Transition Matrix Element in a Single Trapped ${}^{40}$Ca${}^{+}$
• Annexing magic and tune-out wavelengths to the clock transitions of the alkaline-earth metal ions
• Comparing magic wavelengths for the $6s{}^2{S}_{1/2}-6p{}^2{P}_{1/2,3/2}$ transitions of Cs using circularly and linearly polarized light
• Magnetic sublevel independent magic wavelengths: Application in the Rb and Cs atoms
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• Angle-dependent magic wavelengths for the $4s_{1/2}\to 3d_{5/2,3/2}$ transitions of Ca${}^{+}$ ions
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• Precise many-body calculations and hyperfine interaction effect on dynamic polarizabilities at the low-lying energy levels of Y${}^{2+}$
• Magic wavelengths of Ca${}^{+}$ ion for linearly and circularly polarized light
• State-insensitive wavelengths for light shifts and photon scattering from Zeeman states