# Operational Magic Intensity for Sr Optical Lattice Clocks

## TL;DR

This paper experimentally investigates and determines the optimal lattice depth for Sr optical lattice clocks, achieving ultra-precise light shift cancellation at the $10^{-19}$ level by controlling atomic motion and polarizabilities.

## Contribution

It provides the first precise measurement of lattice-induced polarizabilities and establishes an operational lattice depth that minimizes light shifts in Sr optical lattice clocks.

## Key findings

- Operational lattice depth of 72(2) E_R for minimal light shift.
- Light shift cancels to the $10^{-19}$ level within 30% intensity variation.
- Controlled atomic motion enables accurate polarizability measurements.

## Abstract

We experimentally investigate the lattice-induced light shift by the electric-quadrupole ($E2$) and magnetic-dipole ($M1$) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the $E2$-$M1$ polarizability difference. Measured polarizabilities determine an operational lattice depth to be $72(2) E_R$, where the total light shift cancels to the $10^{-19}$ level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.