  Neutron star observations, as well as experiments on neutron-rich nuclei,
used to motivate one to look at degenerate nuclear matter from its extreme,
namely, pure neutron matter. As an important next step, impurities and clusters
in dilute neutron matter have attracted special attention. In this paper, we
review in-medium properties of these objects on the basis of the physics of
polarons, which have been recently realized in ultracold atomic experiments. We
discuss how such atomic and nuclear systems are related to each other in terms
of polarons. In addition to the interdisciplinary understanding of in-medium
nuclear clusters, it is shown that the quasiparticle energy of a single proton
in neutron matter is associated with the symmetry energy, implying a novel
route toward the nuclear equation of state from the neutron-rich side.
