Properties of Dipolar Impurities in a Dipolar Medium

We calculate properties of a static impurity placed into a three dimensional Bose gas made of trapped dipoles. We assume that the impurity-boson interaction potential has a short-range part and a long-range tail. To find the self-energy of the impurity, we solve a Gross-Pitaevski equation. We also compute the induced impurity-impurity interaction, which can be highly anisotropic for strong dipolar interactions. Finally, we relate our findings to a Bose-polaron problem. In this case, we transform into a frame co-moving with the impurity, and obtain a modified Gross-Pitaevskii equation, which we numerically solve. The polaron self-energy is obtained as a function of the strength of the dipole-dipole interaction and trap confinement parameters.