Few-body states of bosons interacting with a heavy quantum impurity

Shuhei M. Yoshida, Zhe-Yu Shi, Jesper Levinsen, Meera M. Parish

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We consider the problem of a fixed impurity coupled to a small number N of noninteracting 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 analyzing 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 "multibody 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.

Original languageEnglish
Article number062705
Number of pages14
JournalPhysical Review A
Volume98
Issue number6
DOIs
Publication statusPublished - 11 Dec 2018

Keywords

  • Bodies
  • Three-body parameter
  • Trimers

Cite this

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title = "Few-body states of bosons interacting with a heavy quantum impurity",
abstract = "We consider the problem of a fixed impurity coupled to a small number N of noninteracting 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 analyzing 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 {"}multibody 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.",
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Few-body states of bosons interacting with a heavy quantum impurity. / Yoshida, Shuhei M.; Shi, Zhe-Yu; Levinsen, Jesper; Parish, Meera M.

In: Physical Review A, Vol. 98, No. 6, 062705, 11.12.2018.

Research output: Contribution to journalArticleResearchpeer-review

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N2 - We consider the problem of a fixed impurity coupled to a small number N of noninteracting 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 analyzing 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 "multibody 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.

AB - We consider the problem of a fixed impurity coupled to a small number N of noninteracting 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 analyzing 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 "multibody 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.

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