# Effect of ion-trap parameters on energy distributions of ultra-cold atom-ion mixtures

## TL;DR

This study investigates how ion trap parameters influence the energy distribution and heating rates of ions in ultra-cold atom-ion mixtures, combining theoretical simulations with experimental measurements to understand energy dynamics.

## Contribution

It provides a combined theoretical and experimental analysis of how Paul trap parameters affect ion energy distributions and heating in ultra-cold atom-ion systems, highlighting the minimal impact of trap variations.

## Key findings

- Heating rates are largely unaffected by trap parameter changes.
- Experimental heating is slightly higher than simulation predictions.
- Energy distribution deviations from thermal behavior are discussed.

## Abstract

The holy grail of ion-neutral systems is reaching the s-wave scattering regime. However, most of these systems have a fundamental lower collision energy limit which is higher than this s-wave regime. This limit arises from the time-dependant trapping potential of the ion, the Paul trap. In this work, we studied both theoretically and experimentally, the way the Paul trap parameters affect the energy distribution of an ion that is immersed in a bath of ultra-cold atoms. Heating rates and energy distributions of the ion are calculated for various trap parameters by a molecular dynamics (MD) simulation that takes into account the attractive atom-ion potential. The deviation of the energy distribution from a thermal one is discussed. Using the MD simulation, the heating dynamics for different atom-ion combinations is also investigated. In addition, we performed measurements of the heating rates of a ground-state cooled $\ ^{88}$Sr$^+$ ion that is immersed in an ultra-cold cloud of $\ ^{87}$Rb atoms, over a wide range of trap parameters, and compare our results to the MD simulation. Both the simulation and the experiment reveal no significant change in the heating for different parameters of the trap. However, in the experiment a slightly higher global heating is observed, relative to the simulation.