Effective two- and three-body interactions between dressed impurities in a tilted double-well potential

We explore the impact and scaling of effective interactions between two and three impurity atoms, induced by a bosonic medium, on their density distributions. To facilitate the detection of mediated interactions, we propose a setup where impurities are trapped in a tilted double-well potential, while the medium is confined to a ring. The tilt of the potential breaks the spatial inversion symmetry allowing us to exploit the population of the energetically elevated well as a probe of induced interactions. For two impurities, the interaction with the medium reduces the impurity population at the energetically elevated well, which we interpret as evidence of induced impurity-impurity attraction. Furthermore, the impact of an induced three-body interaction is unveiled by comparing the predictions of an effective three-body model with many-body simulations. We extend our study for induced interactions to a three-component mixture containing distinguishable impurities. Our results suggest pathways to detect and tune induced two- and three-body interactions.