Polaron physics in hybrid ion-atom systems

Hybrid systems of ultracold ions and atoms are characterized by relatively long-range interactions which compete with the other length scales in the system. This opens the possibility to study new regimes of polaron physics. We show that a single ion immersed in a degenerate Bose gas can acquire very large effective mass, binding multiple bosons in a cluster state. The presence of the ion induces correlations in the gas which can be interpreted as effective interaction. We also discuss the properties of an ion crystal with an atomic impurity, where the polaron is formed by dressing with the lattice distortion. We show that the system can be described in terms of an extended Hubbard-Holstein model with exotic long-ranged interactions.