# Controlled collisions of a single atom and ion guided by movable trapping potentials

## TL;DR

This paper investigates controlled collisions between a single atom and ion in movable traps, revealing trap-induced and confinement-induced resonances that enable quantum state control and spectroscopy of atom-ion molecules.

## Contribution

It introduces a theoretical framework for atom-ion interactions in trapping potentials, including quantum-defect theory and resonance phenomena, extending to quasi-one-dimensional geometries.

## Key findings

- Observation of trap-induced shape resonances.
- Identification of confinement-induced resonances.
- Potential for quantum state control and spectroscopy.

## Abstract

We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an r^{-4} dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the s-wave scattering length. When the separation between traps is changed we observe trap-induced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasi-one-dimensional geometries, when the scattering exhibit confinement-induced resonances, similar to the ones studied before for short-range interactions. For quasi-one-dimensional systems we investigate the effects of coupling between the center of mass and relative motion, which occurs for different trapping frequencies of atom and ion traps. Finally, we show how the two types of resonances can be employed for quantum state control and spectroscopy of atom-ion molecules.