  The physics of quantum impurities coupled to a many-body environment is among
the most important paradigms of condensed matter physics. In particular, the
formation of polarons, quasiparticles dressed by the polarization cloud, is key
to the understanding of transport, optical response, and induced interactions
in a variety of materials. Despite recent remarkable developments in ultracold
atoms and solid-state materials, the direct measurement of their ultimate
building block, the polaron cloud, has remained a fundamental challenge. We
propose and anlalyze a unique platform to probe time-resolved dynamics of
polaron-cloud formation with an interferometric protocol. We consider an
impurity atom immersed in a two-component Bose-Einstein condensate, where the
impurity generates spin-wave excitations that can be directly measured by the
Ramsey interference of surrounding atoms. The dressing by spin waves leads to
the formation of magnetic polarons and reveals a unique interplay between few-
and many-body physics that is signified by single- and multi-frequency
oscillatory dynamics corresponding to the formation of many-body bound states.
Finally, we discuss concrete experimental implementations in ultracold atoms.
