Interaction of Impurity Atoms in Bose-Einstein-Condensates
  The interaction of two spatially separated impurity atoms through phonon exchange in a Bose-Einstein condensate is studied within a Bogoliubov approach. The impurity atoms are held by deep and narrow trap potentials and experience level shifts which consist of a mean-field part and vacuum contributions from the Bogoliubov-phonons. In addition there is a conditional energy shift resulting from the exchange of phonons between the impurity atoms. 
Alexander Klein, Michael Fleischhauer