Bose polaron in spherical trap potentials: Spatial structure and quantum depletion

We investigate how the presence of a localized impurity in a Bose-Einstein condensate of trapped cold atoms that interact with each other weakly and repulsively affects the profile of the condensed and excited components at zero temperature. By solving the Gross-Pitaevskii and Bogoliubov-de Gennes equations, we find that an impurity-boson contact attraction (repulsion) causes both components to change in spatial structure in such a way as to be enhanced (suppressed) around the impurity, while slightly declining (growing) in a region far from the impurity. Such behavior of the quantum depletion of the condensate can be understood by decomposing the impurity-induced change in the profile of the excited component with respect to the radial and azimuthal quantum numbers. The significant role of the centrifugal potential and the hole excitation level is thus clarified.