Exact results for heavy unitary Bose polarons

We consider the problem of unitary Bose polarons, i.e., impurities interacting via a potential with infinite scattering length with a bath of weakly interacting bosons. We show that this problem can be solved analytically in two regimes, where the impurity-boson interaction potential has a range both much smaller and larger than the healing length of the bath. We provide various expressions for the energy and other quasiparticle properties of the polaron in those regimes. Furthermore, we perform numerically exact Diffusion Monte Carlo calculations and we demonstrate that the simple Gross-Pitaevskii theory provides a remarkably accurate description of heavy unitary Bose polarons throughout the whole experimentally relevant range of gas densities.