Precise many-body calculations and hyperfine interaction effect on dynamic polarizabilities at the low-lying energy levels of Y$^{2+}$

Abstract

The present work determines the precise values of magic wavelengths corresponding to the clock transitions 5 2 S-4 2 D of Y 2+ ion both at the levels of fine-and hyperfine-structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a state-insensitive and blue-detuned trapping scheme. We also present the tune-out wavelengths which are useful in state-insensitive trapping and cooling. Noticeable contributions to the total polarizabilities were observed from the vector part due to the circularly polarized light beams which provide additional magic wavelengths compared to linearly polarized light beams. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine structure splitting.