  We study a quantum impurity possessing both translational and internal
rotational degrees of freedom interacting with a bosonic bath. Such a system
corresponds to a `rotating polaron', which can be used to model, e.g., a
rotating molecule immersed in an ultracold Bose gas or superfluid Helium. We
derive the Hamiltonian of the rotating polaron and study its spectrum in the
weak- and strong-coupling regimes using a combination of variational,
diagrammatic, and mean-field approaches. We reveal how the coupling between
linear and angular momenta affects stable quasiparticle states, and demonstrate
that internal rotation leads to an enhanced self-localization in the
translational degrees of freedom.
