Magic intensity trapping of the Mg lattice clock with light shift suppressed below $10^{-19}$

TL;DR

This paper demonstrates a method to suppress light shifts in magnesium lattice clocks below 10^{-19} by identifying a specific magic lattice intensity, advancing optical clock precision.

Contribution

It introduces a combined computational approach to determine optimal lattice intensity for minimal light shift in Mg clocks, enabling higher accuracy.

Findings

Identified a magic lattice intensity of 5.33(2)E_R for Mg clocks.

Achieved suppression of light shift below 10^{-19} over 14% trap depth variation.

Provided detailed calculations of multipolar polarizabilities and hyperpolarizabilities.

Abstract

Progress in atomic optical clocks with total uncertainty of $10^{-18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of $5.33(2)E_R$ ($E_R$ is the lattice photon recoil energy) that reduces the total light shift below $1\times 10^{-19}$ over 14\% of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.