Magic wavelengths for 6s _1/2 → 5d _3/2,5/2 transitions of Yb ⁺ ions

The wave functions, energy levels and matrix elements of Yb ⁺ ions are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined. Then, the magic wavelengths of the magnetic sublevel 6s _{1/2, m = 1/2} → 5d _{3/2, m = ±3/2,±1/2} and 6s _{1/2, m = 1/2} → 5d _{5/2, m = ±5/2,±3/2,±1/2} transitions in the linearly, right-handed, and left-handed polarized light are further determined. The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.