Polaron originaly means the conducting electron dressed by phonon cloud in a dielectric crystal, described as a quasiparticle with a medium dependent effective mass.
Recently a cold-atomic many body system mimics the polaron, where an impurity atom immersed in atomic BEC is dressed by Bogoliubov phonon cloud to be a "Bose polaron". The Bose polaron has been observed in some experiments in a very controlled way: dimensionality, interaction between impurity and BEC atoms, and property of BEC can be designed almost at will.
Theoretical works so far entirely assumed uniform systems, although the experiments were done in traps.The local density approximation is not an adequate tool for detailed description of polaron structure, because the impurity itself causes inhomogeneity.
So, we directly calculate properties of Bose polarons in trap potentials, taking care of the angular momentum conservation, instead of the momentum conservation in uniform systems.