  The problem of an impurity particle moving through a bosonic medium plays a
fundamental role in physics. However, the canonical scenario of a mobile
impurity immersed in a Bose-Einstein condensate (BEC) has not yet been
realized. Here, we use radio frequency spectroscopy of ultracold bosonic
$^{39}$K atoms to experimentally demonstrate the existence of a well-defined
quasiparticle state of an impurity interacting with a BEC. We measure the
energy of the impurity both for attractive and repulsive interactions, and find
excellent agreement with theories that incorporate three-body correlations,
both in the weak-coupling limits and across unitarity. The spectral response
consists of a well-defined quasiparticle peak at weak coupling, while for
increasing interaction strength, the spectrum is strongly broadened and becomes
dominated by the many-body continuum of excited states. Crucially, no
significant effects of three-body decay are observed. Our results open up
exciting prospects for studying mobile impurities in a bosonic environment and
strongly interacting Bose systems in general.
