# Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps

## TL;DR

This paper explores how ion micromotion in hybrid traps influences atom-ion confinement-induced resonances, showing that these resonances can be controlled via radiofrequency fields despite ion motion effects.

## Contribution

It demonstrates that ion micromotion affects resonance positions but does not prevent the observation of confinement-induced resonances, enabling new control methods in atom-ion systems.

## Key findings

- Ion micromotion shifts resonance positions significantly.
- Resonance phenomena like perfect transmission and reflection remain observable.
- Radiofrequency fields can tune atom-ion interactions in low dimensions.

## Abstract

We investigate confinement-induced resonances in atom-ion quantum mixtures confined in hybrid traps. Specifically, we consider an ion confined in a time-dependent radio-frequency Paul trap with linear geometry, while the atom is constrained to move into a quasi-one-dimensional optical waveguide within the ion trap. We evaluate the impact of the ion intrinsic micromotion on the resonance position. Thus, we solve the atom-ion dynamics semiclassically, namely the atom dynamics is governed by the three-dimensional time-dependent Schr\"odinger equation, whereas the ion motion is described by the classical Hamilton equations. We find that the energy of the ion provided by the oscillating radiofrequency fields can affect the resonance position substantially. Notwithstanding, the peculiar phenomenology of those resonances regarding perfect transmission and reflection is still observable. These findings indicate that the intrinsic micromotion of the ion is not detrimental for the occurrence of the resonance and that its position can be controlled by the radiofrequency fields. This provides an additional mean for tuning atom-ion interactions in low spatial dimensions. The study represents an important advancement in the scattering physics of compound atomic quantum systems in time-dependent traps.