We investigate the contribution of negative-energy states on the $E2$ and $M1$ polarizabilities for the ${}^{1}S_0$ and ${}^{3}P_0$ states of the Sr clock and find that they dominate the $E2\text{−}M1$ polarizability difference. Our calculated result is $-7.74\left(3.92\right)\times {10}^{-5}$ a.u., which resolves the sign inconsistency between theory and experiment. Additionally, we extend our method to other optical clocks, confirming the crucial role of negative-energy states in determining the $M1$ polarizability.

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• Atomic, optical & lattice clocks
• Electronic structure of atoms & molecules
• Stark effect