One-dimensional Bose polarons beyond the Fröhlich paradigm: localized impurities

Grusdt et al. [New J. Phys. 19, 103035 (2017)] recently made a renormalization group study of a one-dimensional (1D) Bose polaron in cold atoms that goes beyond the usual Fröhlich description. We study the same model in the localized impurity limit where the ground state is described by a multimode squeezed state instead of the multimode coherent state in the static Fröhlich model. We solve the system exactly by applying the generalized Bogoliubov transformation, an approach that can be straightforwardly adapted to higher dimensions. Using our exact solution, we obtain a polaron energy free of infrared divergences and construct analytically the polaron phase diagram. We find the repulsive polaron is stable on the positive side of the impurity-boson interaction but is always thermodynamically unstable on the negative side of the impurity-boson interaction, featuring a bound state, whose binding energy we obtain analytically. We find the attractive polaron is always dynamically unstable, featuring a pair of imaginary energies which we obtain analytically.