  The physics of impurities in a bosonic quantum environment is a paradigmatic
and challenging many-body problem that remains to be understood in its full
complexity. Here, this problem is investigated for impurities with strong
repulsive interactions based on Ramsey interferometry in a quantum degenerate
gas of 39K atoms. We observe an oscillatory signal that is consistent with a
quantum beat between two co-existing coherent quasiparticle states: the
attractive and repulsive polarons. The interferometric signal allows us to
extract the polaron energies for a wide range of interaction strengths,
complimenting earlier spectroscopic measurements. We furthermore identify
several dynamical regimes towards the formation of the Bose polaron in good
agreement with theory. Our results improve the understanding of quantum
impurities interacting strongly with a bosonic environment, and demonstrate how
quasiparticles as well as short-lived non-equilibrium many-body states can be
probed using Ramsey interferometry.
