Analysis of collision shift assessments in ion-based clocks

TL;DR

This paper presents a unified classical and quantum approach to assessing collision shifts in ion-based clocks, providing a simple, general bound that aids in understanding and measuring collision effects without complex simulations.

Contribution

It introduces a consistent classical and quantum model for collision shifts, deriving a simple bound applicable to any single ion clock, simplifying analysis and measurement.

Findings

Collision shift bound determined by classical Langevin collision rate and recoil decoupling.

Model applies to Lennard-Jones potentials, not just hard-sphere interactions.

Provides a straightforward method to measure collision rates in ion clocks.

Abstract

We consider back-ground gas collision shifts in ion-based clocks. We give both a classical and quantum description of a collision between an ion and a polarizable particle with a simple hard-sphere repulsion. Both descriptions give consistent results, which shows that a collision shift bound is determined by the classical Langevin collision rate reduced by a readily calculated factor describing the decoupling of the clock laser from the ion due to the recoil motion. We also show that the result holds when using a more general Lennard-Jones potential to describe the interaction between the ion and its collision partner. This leads to a simple bound for the collision shift applicable to any single ion clock without resorting to large-scale Monte-Carlo simulations or determination of molecular potential energy curves describing the collision. It also provides a relatively straightforward means to measure the relevant collision rate.