Correlation between the magic wavelengths and the polarization direction of the linearly polarized laser in the Ca+ optical clock

The magic wavelengths for different Zeeman components are measured based on the Ca-40(+) optical clock. The dynamic dipole polarizability of a non-zero angular moment level has correlation with the polarization direction of the linearly polarized laser beam, and we show that the four hyperfine structure levels of 4s(1/2,m=+/-1/2) and 3d(5/2,m=+/-1/2) for Ca-40(+) have the same dynamic dipole polarizability at the magic wavelength and a certain polarization direction. In addition, the existence of a specific direction of polarization may provide a new idea for improving the precision of magic wavelength measurement in experiment.