  The variational Feynman formalism for the polaron, extended to an
all-coupling treatment of bipolarons, is applied for two impurity atoms in a
Bose-Einstein condensate. This shows that if the polaronic coupling strength is
large enough the impurities will form a bound state (the bipolaron). As a
function of the mutual repulsion between the impurities two types of bipolaron
are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell
bipolaron at strong repulsion. Apart from the binding energy, also the
evolution of the bipolaron radius and its effective mass are examined as a
function of the strength of the repulsive interaction between the impurities
and of the polaronic cupling strength. We then apply the strong-coupling
formalism to multiple impuritiy atoms in a condensate which leads to the
prediction of multi-polaron formation in the strong coupling regime. The
results of the two formalisms are compared for two impurities in a condensate
which results in a general qualitative agreement and a quantitative agreement
at strong coupling. Typically the system of impurity atoms in a Bose-Einstein
condensate is expected to exhibit the polaronic weak coupling regime. However,
the polaronic coupling strength is in principle tunable with a Feshbach
resonance.
