# Precision measurement of atomic isotope shifts using a two-isotope entangled state

## TL;DR

This paper introduces a noise-insensitive method for precisely measuring atomic isotope shifts using trapped ions, achieving high accuracy and revealing differences in electron g-factors, with implications for new physics and nuclear studies.

## Contribution

The authors present a robust, element- and isotope-independent technique for measuring isotope shifts with unprecedented precision in trapped ions.

## Key findings

- Measured isotope shift in Sr+ with 1.6×10⁻¹¹ relative uncertainty.
- Detected a 3.46(23)×10⁻⁸ difference in orbital g-factors.
- Method is simple, robust, and suitable for future fundamental physics tests.

## Abstract

Atomic isotope shifts (ISs) are the isotope-dependent energy differences in the atomic electron energy levels. These shifts serve an important role in atomic and nuclear physics, and particularly in the latter as signatures of nuclear structure. Recently ISs have been suggested as unique probes of beyond Standard Model (SM) physics, under the condition that they be determined significantly more precisely than current state of the art. In this work we present a simple and robust method for measuring ISs with ions in a Paul trap, by taking advantage of Hilbert subspaces that are insensitive to common-mode noise yet sensitive to the IS. Using this method we evaluate the IS of the $5S_{1/2}\leftrightarrow4D_{5/2}$ transition in $^{86}\text{Sr}^+$ and $^{88}\text{Sr}^+$ with a $1.6\times10^{-11}$ relative uncertainty to be 570,264,063.435(9) Hz. Furthermore, we detect a relative difference of $3.46(23)\times10^{-8}$ between the orbital g-factors of the electrons in the $4D_{5/2}$ level of the two isotopes. Our method is relatively easy to implement and is indifferent to element or isotope, paving the way for future tabletop searches for new physics and posing interesting prospects for testing quantum many-body calculations and for the study of nuclear structure.