  Recently, two independent experiments reported the observation of long-lived
polarons in a Bose-Einstein condensate, providing an excellent setting to study
the generic scenario of a mobile impurity interacting with a quantum reservoir.
Here, we expand the experimental analysis by disentangling the effects of trap
inhomogeneities and the many-body continuum in one of these experiments. This
makes it possible to extract the energy of the polaron at a well-defined
density as a function of the interaction strength. Comparisons with quantum
Monte-Carlo as well as diagrammatic calculations show good agreement, and
provide a more detailed picture of the polaron properties at stronger
interactions than previously possible. Moreover, we develop a semi-classical
theory for the motional dynamics and three-body loss of the polarons, which
partly explains a previously unresolved discrepancy between theory and
experimental observations for repulsive interactions. Finally, we utilize
quantum Monte-Carlo calculations to demonstrate that the findings reported in
the two experiments are consistent with each other.
