Grusdt, F.Shchadilova, Y. E.Rubtsov, A. N.Demler, E.2015-08-032015Grusdt, F., Y. E. Shchadilova, A. N. Rubtsov, and E. Demler. 2015. “Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem.” Scientific Reports 5 (1): 12124. doi:10.1038/srep12124. http://dx.doi.org/10.1038/srep12124.2045-2322http://nrs.harvard.edu/urn-3:HUL.InstRepos:17820750When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.en-USJournal Article2015-08-0310.1038/srep12124