## 1 Introduction  
Recently, the possibility of merging together ultracold atoms and trapped ions in the same experiment for creating a hybrid atom-ion quantum system has raised much interest [1]. In fact, this composite system inherits the properties of its constituents, i.e., the possibility of controlling space-localized trapped ions and creating large ensembles of coherent matter with quantum gases, and makes it possible to use a new feature: atom-ion interactions. Atom-ion interactions are much longer range than atom-atom interactions (if Rydberg states are not considered) and can in principle be tuned via Feshbach resonances [2]. Systems of ultracold atoms and trapped ions represent an extremely versatile and powerful experimental platform, in which both atoms and ions can simultaneously play the role of probe and system [3]. For instance, a single ion immersed in an ultracold bath of neutral atoms can be conceived of as a localized impurity in a many-body system. In this scenario, the ion can be exploited as a probe for measuring local properties of the atomic gas, like its densitiesor correlations [4]. Analogously, the atomic cloud at low temperatures can act as an ultracold buffer gas that continuously cools the ions through elastic collisions, realizing a transparent coolant at the wavelengths used to manipulate the internal states of the ions [5]. Ultracold buffer gas cooling can thus be an efficient alternative to laser cooling for preparing ion crystals in quantum technology applications. Atom-ion hybrid systems are also suitable for studying in a controlled way chemical reactions at low temperature, since the ions increase the local density of the neutral atom cloud, thus acting as reaction centers for chemical processes, e.g., charge-exchange and molecule formation [6; 7]. In most atom-ion experiments, the collisional energy is set by the driven component of the ions' dynamics in radiofrequency (RF) traps (i.e., micromotion), since collisions with cold atoms cause a coupling of energy from the driving field to the ions' secular motion, thus making the systems energetically open [8]. A relatively large collisional energy represents a limitation for experiments aiming at exploiting the quantum nature of atom-ion interactions, which arise mainly when atom-ion interactions can be characterized solely by the s-wave phase shift, i.e., the scattering length. In this so-called s-wave scattering regime, the collisions could be controlled via Feshbach resonances, and atom-ion interactions could lead to a coherent evolution of the two quantum systems [3]. However, this regime has not been reached so far due to the presence of micromotion, and Feshbach resonances have never been experimentally observed in atom-ion mixtures. A possible solution to reach the quantum regime with RF-trapped ions in an ultracold bath of atoms is to properly choose the atomic species on the basis of their mass ratio, thus limiting the energy transfer from the RF trapping field to the atom-ion system due to the presence of micromotion and lowering the experimentally attainable temperature [9]. Following this strategy, the group of [PERSON] recently observed atom-ion collisional energies for which only s- and p-waves contribute to the collisions [10]. An alternative strategy to circumvent the detrimental effects of micromotion is to change the ion confinement technique. For instance, ions can be trapped in optical dipole traps [11; 12]. Purely optical trapping of a single barium ion has been realized for up to a few seconds with a trapping scheme based on two lasers having different frequencies [13]. Moreover, optical trapping has also been achieved by employing one-dimensional optical lattices formed by two counter-propagating beams [14], and very recently, small crystals of up to six barium ions were trapped in a single-beam dipolar trap [15]. Hence, ion optical trapping represents an encouraging solution to reach ultracold atom-ion collisions.