Contributions of negative-energy states to the E2-M1 polarizability of the Sr clock

TL;DR

This paper investigates the role of negative-energy states in the E2-M1 polarizability of the Sr clock, resolving previous theoretical and experimental discrepancies and providing results consistent with recent measurements.

Contribution

It demonstrates that negative-energy states are crucial for accurately calculating the M1 polarizability, leading to a theoretical result that aligns with recent experimental data.

Findings

Negative-energy states dominate M1 polarizability contributions.

The new theoretical E2-M1 polarizability difference matches recent experimental results.

The study resolves previous inconsistencies between theory and experiment.

Abstract

With the improvement of high-precision optical clock, the higher-order multipolar interaction between atoms and light needs quantitative evaluation. However for the Sr clock, the differential dynamic E2-M1 polarizability at the magic wavelength has contradictions among available theoretical and experimental results. Recently, the new experimental measurement of S. D\"{o}rscher {\em et al.} [arXiv: 2210. 14727] is consistent with measurement of Ushijima {\em et al.}, which poses new challenges to theory and urgently calls for theoretical explanations. In present work, we investigate contributions of negative-energy states to the E2 and M1 polarizabilities. We find that for the M1 polarizability, the contribution from negative-energy states is crucial and dominant. Our new theoretical result for E2-M1 polarizability difference is $-7.74(3.92)\times 10^{-5}$ a.u., which is in good agreement with the recent experiment of S. D\"{o}rscher et al., so the inconsistency problem of E2-M1 polarizability in the Sr clock between theory and experiment is eliminated.