# Improved estimate of the collisional frequency shift in Al$^+$ optical clocks

## TL;DR

This paper presents a refined, non-perturbative calculation of collisional frequency shifts in Al$^+$ optical clocks, reducing uncertainties and confirming negligible shifts due to helium and hydrogen collisions.

## Contribution

It introduces a non-perturbative analytic framework to accurately estimate collisional shifts, improving precision over previous methods.

## Key findings

- Collisional shifts for Al$^+$ are effectively zero within uncertainty.
- Uncertainties in collisional shift coefficients are significantly reduced.
- The method enhances the accuracy of systematic corrections in optical clocks.

## Abstract

Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequency shifts for Al$^+$ are zero to within uncertainty.