Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

We address the problem of lattice light shifts in the Sr clock caused by multipolar M1 and E2 atom-field interactions. We present a simple but accurate formula for the magnetic-dipole polarizability that takes into account the contributions of both the positive- and negative-energy states. We calculate the contribution of

negative-energy states to the M1 polarizabilities of the clock ¹S₀ and ³P₀ states at the magic frequency. Taking these contributions into account, we obtain good agreement with the experimental results, explaining the major discrepancy between theory and experiment.