The Bose polaron system consists of a Bose-Einstein condensate interacting with one, or few, impurities. Similar polaron models of particles interacting with a bulk system appear in many forms in condensed matter physics, and play an important role, e.g., for the understanding of transport properties.
The topic of my talk will be the derivation of an effective equation starting from an interacting system with a large number N>>1 of bosons and a single impurity. The effective description is given by the Bogoliubov-Fröhlich Hamiltonian, which couples the impurity linearly to Bogoliubov's excitation field in a similar way to other well-known polaron models.
In the first part of the talk I will give an introduction to the Bogoliubov theory of the mean-field Bose gas. In the second part, I will explain how this theory can accommodate the impurity particle and discuss some recent results on the case of a dilute gas.