  Mixing two kinds of particles that repel each other usually results in either
a homogeneous mixture when the repulsion is weak, or a complete phase
separation of the two kinds when their repulsion is too strong. It is shown
however that there is an intermediate regime where the two kinds can coexist in
their ground state as a bubble immersed in a gas of one kind. Such a situation
is obtained by adding heavy repulsive impurities into a Bose-Einstein
condensate. Above a certain strength of the mutual repulsion, a stable bubble
of impurities and bosons can be formed, resulting from the equilibrium between
the interactions induced by the bosons inside the bubble and the outside
pressure from the surrounding bosons. At some particular strength, the
effective interactions between the impurities consist of only three-body
interactions. Finally, above a critical strength, the bosons are ejected from
the bubble and the impurities collapse into a pure bubble of impurities. This
phenomenon could be observed with an imbalanced mixture of ultra-cold atoms of
different masses. Moreover, it appears possible to reach a regime where the
impurities form a dense bubble of strongly-interacting particles.
