2018/07/26 by Shuhei M. Yoshida, Zhe-Yu Shi, Jesper Levinsen +1 · 1 citation
Physics and Astronomy · #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.98.062705
published as Phys. Rev. A 98, 062705 (2018) · 15 pages including 6 figures, 3 appendices and references
arxiv created 2018/07/26 · arxiv updated 2018/12/19
We consider the problem of a fixed impurity coupled to a small number N of non-interacting bosons. We focus on impurity-boson interactions that are mediated by a closed-channel molecule, as is the case for tuneable interatomic interactions in cold-atom experiments. We show that this two-channel model can be mapped to a boson model with effective boson-boson repulsion, which enables us to solve the three-body (N=2) problem analytically and determine the trimer energy for impurity-boson scattering lengths a>0. By analysing the atom-dimer scattering amplitude, we find a critical scattering length a^* at which the atom-dimer scattering length diverges and the trimer merges into the dimer continuum. We furthermore calculate the tetramer energy exactly for a>0 and show that the tetramer also merges with the continuum at a^*. Indeed, since the critical point a^* formally resembles the unitary point 1/a = 0, we find that all higher-body bound states (involving the impurity and N>1 bosons) emerge and disappear at both of these points. We show that the behavior at these 'multi-body resonances' is universal, since it occurs for any model with an effective three-body repulsion involving the impurity. Thus, we see that the fixed-impurity problem is strongly affected by a three-body parameter even in the absence of the Efimov effect.