2015/03/31 by Rasmus Søgaard Christensen, Jesper Levinsen, Georg M. Bruun · 1 citation
Physics and Astronomy · #cond-mat.quant-gas
paper · pdf · doi:10.1103/physrevlett.115.160401
published as Phys. Rev. Lett. 115, 160401 (2015) · 5 pages, 3 figures, Supplementary Information
arxiv created 2015/10/19 · arxiv updated 2015/10/20
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 Fröhlich model of an impurity interacting with phonons, provide valuable benchmarks for many-body theories and for experiments.