Ultracold atoms and trapped ions are among the most powerful tools to study quantum physics. On the one hand, ultracold atoms provide an exceptional resource for studying many-body physics, since a relatively large number of particles, typically from a few tens of thousands to several million, can be brought to quantum degeneracy. Quantum gases have been used extensively in recent years to realize quantum simulations of fundamental models of condensed matter, the solutions of which are often too complex to be computed. On the other hand, trapped ions provide a great resource to explore the physics of small quantum systems. They provide one of the most successful hardwares for a quantum computer, and clocks made of trapped ions are among the most precise. Moreover, trapped ions have been recently used as a quantum simulator, making the path of the two subjects of ultracold atoms and trapped ions even more entangled.
Only recently, though, ultracold atoms and trapped ions have been brought together in a single experimental setup. The progress in this new research field has been extremely fast (see ref.  for a review of the field), and now about ten groups in the world have built or are currently building experimental setups in which different pairs of atoms and ions are used together. The reason for this interest is based on the several innovative ingredients that are available – many more than in traditional atomic physics experiments. At the fundamental level, atoms and ions interact through a potential that is much more long-ranged with respect to the interaction between ultracold atoms (scaling with R-4 instead of R-6, where R is the internuclear separation), and one can exploit the different techniques to manipulate atoms and ions to exert more control in the hybrid system. With this control at hand, atom-ion quantum systems have been proposed to advance quantum simulation, quantum computation, and quantum chemistry.
In our project, we plan to realize a new generation atom-ion machine in order to realize new quantum simulations of a many-body system in the presence of one or more localized impurities. With this setup, we plan to investigate fundamental atom-ion interactions in the ultracold regime, and to use these controlled interactions to realize a platform for investigating out-of-equilibrium quantum systems and quantum thermodynamics.
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