I will discuss how superfluidity manifests itself in the spectrum of the Hamiltonian for a test particle travelling through a Bose Einstein condensate.
In the Bogoliubov-Fröhlich polaron model, a stable polaron with momentum P corresponds to a ground state of the Hamiltonian at fixed total momentum. 

I will explain a result in collaboration with Benjamin Hinrichs, which shows that a ground state exists if the momentum is less than mc, where m is the particle mass and c is the slope at zero momentum of the dispersion relation of the Bogoliubov phonons.