  Predicting the emergent properties of impurities immersed in a quantum bath
is a fundamental challenge that can defy quasiparticle treatments. Here, we
measure the spectral properties and real-time dynamics of mobile impurities
injected into a homogeneous Bose--Einstein condensate, using two Feshbach
resonances to tune both the impurity-bath and intrabath interactions. We map
out both attractive and repulsive branches of polaron quasiparticles, resolving
the repulsive polaron and the molecular state associated with the Feshbach
resonance in the strongly interacting regime, and show that the latter also has
a many-body character. Our measurements reveal remarkably universal behavior,
controlled by the bath density and a single dimensionless interaction
parameter; for near-resonant interactions the polarons are no longer well
defined, but the universality still holds.
