Annexing magic and tune-out wavelengths to the clock transitions of the alkaline-earth-metal ions

摘要

We present additional magic wavelengths (λ_(magic)) for the clock transitions in the alkaline-earth-metal ions, considering circular polarized light, aside from our previously reported values [Kaur et al., Phys. Rev. A 92, 031402(R) (2015)] for linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities [α_d (ω)] of the atomic states associated with the clock transitions play major roles in the evaluation of these λ_(magic), hence facilitating choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The λ_(magic) values in these hyperfine transitions are estimated and found to be different from λ_(magic) for the atomic transitions due to different contributions coming from the vector and tensor parts of α_d (ω). Importantly, we also present λ_(magic) values that depend only on the scalar component of α_d (ω) for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present α_d (ω) values explicitly at 1064 nm for the atomic states associated with the clock transitions, whichmay be useful for creating high-field-seeking traps for the above ions using the Nd:YAG laser. The tune-out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.