  Polarons, self-localized composite objects formed by the interaction of a
single impurity particle with a host medium, are a paradigm of strong
interaction many-body physics. We show that dilute gas Bose-Einstein
condensates (BEC's) are the first medium known to self-localize the same
impurity particles both in a Landau-Pekar polaron state akin to that of
self-localized electrons in a dielectric lattice, and in a bubble state akin to
that of electron bubbles in helium. We also show that the BEC-impurity system
is fully characterized by just two dimensionless coupling constants, and that
it can be adiabatically steered from the Landau-Pekar regime to the bubble
regime in a smooth crossover trajectory.
