  We demonstrate that identical impurities immersed in a two-dimensional
many-particle bath can be viewed as flux-tube-charged-particle composites
described by fractional statistics. In particular, we find that the bath
manifests itself as an external magnetic flux tube with respect to the
impurities, and hence the time-reversal symmetry is broken for the effective
Hamiltonian describing the impurities. The emerging flux tube acts as a
statistical gauge field after a certain critical coupling. This critical
coupling corresponds to the intersection point between the quasiparticle state
and the phonon wing, where the angular momentum is transferred from the
impurity to the bath. This amounts to a novel configuration with emerging
anyons. The proposed setup paves the way to realizing anyons using electrons
interacting with superfluid helium or lattice phonons, as well as using atomic
impurities in ultracold gases.
