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, which can be employed for a transfer of quantum information between the atoms.