Phases and dynamics of fermionic impurities in a two-dimensional boson droplet

We unravel the ground state properties and emergent non equilibrium dynamics of a mixture consisting of few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. It is found that an increasingly attractive droplet-fermion interaction leads to a transition from a delocalized fermion configuration to a distribution where the fermions are highly localized and isolated from one another. In turn, undulations in the droplet density are observed in the vicinity of the fermions. This process is accompanied by the emergence of induced interactions among the fermions mediated by the droplet. Following interaction quenches from strong attractive to weaker couplings reveals the spontaneous nucleation of complex excitation patterns such as ring-shaped structures building upon the flat-top droplet. Simultaneously, the fermions are dragged along, in the course of the evolution, while remaining predominantly trapped within the droplet. Our results provide a paradigm beyond the reduced single-component droplet model unveiling the role of back-action in droplets and the effect of induced mediated interactions.