LAUSR

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of 3P0o clock state for 88Sr and 87Sr atoms. By using this formula and the multi-configuration Dirac–Hartree–Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values C 2 = –23.38(5) MHz/T2 for 88Sr and the 3P0o , F = 9/2, MF = ±9/2 clock states for 87Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the 3P0o , F = 9/2, MF = ±9/2 clock states were also determined in our 87Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed 1 S 0, F = 9/2, MF = ±5/2– 3P0o , F = 9/2, MF = ±3/2 transitions.