Solution of the Fr\"ohlich polaron problem at intermediate couplings

We develop a renormalization group approach for analyzing Fr\"ohlich polarons and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate (BEC) of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations [1] for a wide range of interaction strengths. We show analytically that the energy of the Fr\"ohlich polaron in a BEC is logarithmically UV divergent, and present a regularization scheme. This allows us to make predictions for the polaron energy, which can be tested in future experiments. Furthermore we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Our method can be generalized to non-equilibrium polaron problems.\\[4pt] [1] Vlietinck et al., arXiv:1406.6506\\[0pt] [2] Grusdt et al.,arXiv:1410.2203\\[0pt] [3] Shchadilova et al.,arXiv:1410.5691