The magic wavelengths for different Zeeman components are measured based on the ^40Ca^＋ 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 4S1/2,m=±1/2 and 3d5/2,m=±1/2 for ^40Ca^＋ 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.
Precision measurement of the 4s2 S1/2-3d2 D5/2 clock transition based on 40Ca＋ ion at 729 nm is reported. A single 40Ca＋ ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly. The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5 ×10^-16. The absolute frequency of the clock transition is measured at the 10^-15 level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system （GPS）, The frequency value is 411 042 129 776 393.0（1.6） Hz with the correction of the systematic shifts. In order to carry out the comparison of two 40Ca＋ optical frequency standards, another similar 40Ca＋ optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1 × 10^-14 T-1/2 with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped 40Ca＋ ion are carried out. One is the 3d2Ds/2 state lifetime measurement, and our result of 1174（10） ms agrees well with the results reported in [Phys. Rev. A 62 032503 （2000）] and [Phys. Rev. A 71 032504 （2005）]. The other one is magic wavelengths for the 4s2S1/2-3d2Ds/2 clock transition; λ ｜mj｜=1/2= 395.7992（7） nm and λ｜m｜=3/2 = 395.7990（7） nm are reported, and it is the first time that two magic wavelengths for the 40Ca＋ clock-transition have been reported.
Research on the development of the optical frequency standard based on trapped and cold 40 Ca+ with the 4s2S1/2-3d2D5/2 clock transition at 729nm is reported. A single calcium ion was trapped and laser cooled in the Paul trap and stay in trap for more than 15 days. The linewidth of a 729nm laser was reduced to less than 10Hz by locking to a cavity for longer than 50 hours uninterruptedly. The overall systematic uncertainty of the clock transition has been characterized to be better than 6.5×10 16 . The absolute frequency of the clock transition was measured at 10 15 level using an optical frequency comb referenced to a Hydrogen maser, which was calibrated to the SI second through the global positioning system (GPS). The frequency value was 411042129776393.0(1.6)Hz after the correction of the systematic shifts.
