Quasiparticle properties of a mobile impurity in a Bose-Einstein condensate

TL;DR

This paper develops a perturbation theory to analytically determine the quasiparticle properties of a single impurity in a Bose-Einstein condensate, including energy, effective mass, and residue, up to third order in scattering length.

Contribution

It provides the first analytical third-order perturbation results for impurity quasiparticles in a BEC, extending beyond the Fröhlich model.

Findings

Energy depends logarithmically on scattering length at third order.

Residue and effective mass are given by analytical power series.

Results serve as benchmarks for many-body theories and experiments.

Abstract

We develop a systematic perturbation theory for the quasiparticle properties of a single impurity immersed in a Bose-Einstein condensate. Analytical results are derived for the impurity energy, the effective mass, and residue to third order in the impurity-boson scattering length. The energy is shown to depend logarithmically on the scattering length to third order, whereas the residue and effective mass are given by analytical power series. When the boson-boson scattering length equals the boson-impurity scattering length, the energy has the same structure as that of a weakly interacting Bose gas, including terms of the Lee-Huang-Yang and fourth order logarithmic form. Our results, which cannot be obtained within the canonical Fr{\"o}hlich model of an impurity interacting with phonons, provide valuable benchmarks for many-body theories and for experiments.