# Rydberg Electrometry for Optical Lattice Clocks

## TL;DR

This paper demonstrates a Rydberg-based electrometry technique to precisely evaluate and constrain the quadratic Stark shift in strontium optical lattice clocks, achieving uncertainties below 1 V/m and fractional frequency uncertainties of 2×10⁻²⁰.

## Contribution

The study introduces a novel Rydberg electrometry method for optical lattice clocks, enabling highly precise electric field measurements and systematic shift constraints.

## Key findings

- Measured Stark shift of Rydberg state using EIT
- Constrained electric field with sub-1 V/m uncertainty
- Limited fractional frequency uncertainty to 2×10⁻²⁰

## Abstract

Electrometry is performed using Rydberg states to evaluate the quadratic Stark shift of the $5s^2$ $^1\textrm{S}_0-5s5p$ $^3\textrm{P}_0$ clock transition in strontium. By measuring the Stark shift of the highly excited $5s75d\;^1\textrm{D}_2$ state using electromagnetically induced transparency, we characterize the electric field with sufficient precision to provide tight constraints on the systematic shift to the clock transition. Using the theoretically derived, and experimentally verified, polarizability for this Rydberg state we can measure the residual field with an uncertainty well below $1 \textrm{V} \textrm{m}^{-1}$. This resolution allows us to constrain the fractional frequency uncertainty of the quadratic Stark shift of the clock transition to $2\times10^{-20}$.