Medium-induced interaction between impurities in a Bose-Einstein condensate

We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.

Automated summary

In this study, we investigate the mutual interaction between two heavy particles immersed in a three-dimensional Bose-Einstein condensate and its correlation with excitations of the medium. For an ideal Bose gas, the induced interaction follows Newtonian mechanics with a shift in distance that depends on the coupling strength between impurities and bosons. However, for a real Bose-Einstein condensate, we find that the induced potential is dominated by three-body physics of a single boson bound to the impurities at short distances, resulting in an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. We demonstrate that both regimes can be realized for all impurity-boson couplings and determine the corresponding crossover scales. Additionally, we investigate the transition from the real to the ideal condensate at low gas parameters.