Mean-field study of repulsive 2D and 3D Bose polarons

The detailed mean-field (MF) treatment of the Bose polaron problem in two and three dimensions is presented. Particularly, assuming that impurity is immersed in the dilute Bose gas and interacts with bosons via the hard-sphere two-body potential, we calculate the low-momentum parameters of its spectrum, namely, the binding energy and the effective mass. The limits of applicability of the MF approach to a problem of mobile impurity in Bose-Einstein condensates are discussed by comparing our results to the Monte Carlo simulations data.