BEC polaron in harmonic trap potential at weak coupling regime: Lee-Low-Pines type approach

We have calculated the zero-temperature binding energy of a single impurity atom immersed in a Bose-Einstein condensate of ultracold atoms that are trapped in an axially symmetric harmonic potential, where the impurity interacts with bosonic atoms in the condensate via a low-energy s-wave scattering. In this case, bosons are excited around the impurity to form a quasiparticle, namely, a BEC polaron. We have developed a variational method, {\it a la} Lee-Low-Pines (LLP) theory for electron-phonon systems, for description of the polaron with a conserved angular momentum around the symmetric axis. It is found in numerical results that the binding energy between the impurity and the excited bosons break the degeneracy with respect to the total angular momentum of the polaron. The angular momentum is partially shared by the excited bosons, which is due to a mechanism similar to the drag effect on the polaron momentum by a phonon cloud in the LLP theory.