# The collisional frequency shift of a trapped-ion optical clock

## TL;DR

This paper introduces a quantum channel-based framework to accurately calculate the collisional frequency shift in trapped-ion optical clocks, exemplified by elastic collisions of Sr+ ions with helium, improving understanding of collision-induced perturbations.

## Contribution

It presents a novel non-perturbative quantum channel approach and derives an analytic expression for the collisional frequency shift in trapped-ion clocks.

## Key findings

- Derived a simple analytic formula for frequency shifts due to collisions
- Applied the method to Sr+ ions with helium collisions
- Enhanced understanding of collision effects in optical clocks

## Abstract

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a non-perturbative framework based on a quantum channel description of the scattering process, and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr$^+$ optical atomic clock transition due to elastic collisions with helium.