Dipole polarizabilities and magic wavelengths for a Sr and Yb atomic optical lattice clock

The magic wavelength is a crucial parameter for the optical frequency standard field. In this paper, we have calculated the dipole polarizabilities of the ground state ns² and the metastable state nsnp for strontium and ytterbium by the method of the B-spline configuration interaction with a semiempirical core-polarization model potential, and finally obtained the values of the relevant magic wavelengths, which are 812 nm, 499 nm, and 752 nm, 550 nm, 458 nm for strontium and ytterbium atoms, respectively. The results of 812 nm and 752 nm are perfectly consistent with the corresponding experimental values. Here, we also predicted the new values of the magic wavelengths 499 nm, 550 nm and 458 nm. In addition, the relevant black-body radiation shifts, which are -1.96(37) Hz and -1.06(38) Hz for Sr and Yb, respectively, were obtained. It proves that the method we have developed is suitable to accurately calculate atomic structures of two-valence atoms, especially for their dipole polarizabilities and magic wavelengths.