Multipolar polarizabilities and hyperpolarizabilities for alkaline-earth-metal ions

As measurement precision continues to advance, the accurate determination of multipolar polarizabilities and hyperpolarizabilities becomes increasingly crucial for precisely analyzing atomic light shifts in external fields, yet their investigation remains relatively limited. We employ the Dirac-Fock plus core polarization (DFCP) method to calculate the dynamic multipolar polarizabilities and hyperpolarizabilities for the lowest ${s}_{1/2}$ and ${d}_{5/2}$ states of alkaline-earth-metal ions. We take into account the contribution of negative-energy states to magnetic dipole polarizability, revealing its dominant impact at the $10{}^{\ensuremath{-}4}$ level. Furthermore, we conduct a comprehensive analysis of lattice light shift and find that ${\mathrm{Ca}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ ions exhibit promising candidates for developing all-optical-trapping ion clocks with a light shift uncertainty down to ${10}^{\ensuremath{-}18}$. Specifically, the ${\mathrm{Sr}}^{+}$ ion demonstrates potential for achieving an even lower uncertainty of ${10}^{\ensuremath{-}19}$ in light shift. Additionally, we predict the operational trap depths and laser detuning parameters necessary for conducting relevant experiments, thereby providing a solid theoretical framework to guide future endeavors in this promising research field.