Many-polaron description of impurities in a Bose-Einstein condensate in the weak coupling regime

The weak coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows to investigate the groundstate properties and the response of the system to Bragg spectroscopy. This theory is then applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak which corresponds to the emission of Bogoliubov excitations. Both ground state properties and the response spectrum show that the polaronic effect vanishes at large densities. We also look at two possibilities to define the polaronic effective mass and observe that this results in a different quantitative behavior if multiple impurities are involved.