Theoretical calculation of the quadratic Zeeman shift coefficient of the ³P₀^o clock state for strontium optical lattice clock

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of ^3P^\rm o_0 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/T^2 for ^88Sr and the ^3P^\rm o_0, F = 9/2, M_F = \pm9/2 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 ^3P^\rm o_0, F = 9/2, M_F = \pm9/2 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 ^1S_0, F = 9/2, M_F = \pm5/2-^3P^\rm o_0, F = 9/2, M_F = \pm3/2 transitions.