Bipolarons and multipolarons consisting of impurity atoms in a Bose-Einstein condensate

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, the evolution of the bipolaron radius and its effective mass are also examined as a function of the strength of the repulsive interaction between the impurities and of the polaronic coupling strength. We then apply the strong-coupling formalism to multiple-impurity atoms in a condensate, which leads to the prediction of multipolaron 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.