# Nuclear Spin Effects in Optical Lattice Clocks

## TL;DR

This paper investigates how nuclear spin influences the accuracy of optical lattice clocks, combining experimental measurements and theoretical models to understand and mitigate related systematic effects.

## Contribution

It introduces a comprehensive spin-mixing theory for alkaline-earth-like atoms and demonstrates methods to reduce nuclear spin-related systematic shifts in optical lattice clocks.

## Key findings

- Differential g-factor in $^{87}$Sr agrees with theory
- Tensor light shift effects characterized experimentally
- Nuclear spin polarization can reduce systematic effects below 10$^{-17}$

## Abstract

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^1S_0$-$^3P_0$ clock transition and the differential g-factor between the two clock states for alkaline-earth(-like) atoms, using $^{87}$Sr as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential g-factor in $^{87}$Sr is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below 10$^{-17}$ in lattice clocks.