### 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 language | English |
---|---|

Article number | 062705 |

Number of pages | 14 |

Journal | Physical Review A |

Volume | 98 |

Issue number | 6 |

DOIs | |

Publication status | Published - 11 Dec 2018 |

### Keywords

- Bodies
- Three-body parameter
- Trimers

### Cite this

*Physical Review A*,

*98*(6), [062705]. https://doi.org/10.1103/PhysRevA.98.062705

}

*Physical Review A*, vol. 98, no. 6, 062705. https://doi.org/10.1103/PhysRevA.98.062705

**Few-body states of bosons interacting with a heavy quantum impurity.** / Yoshida, Shuhei M.; Shi, Zhe-Yu; Levinsen, Jesper; Parish, Meera M.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Few-body states of bosons interacting with a heavy quantum impurity

AU - Yoshida, Shuhei M.

AU - Shi, Zhe-Yu

AU - Levinsen, Jesper

AU - Parish, Meera M.

PY - 2018/12/11

Y1 - 2018/12/11

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.

KW - Bodies

KW - Three-body parameter

KW - Trimers

UR - http://www.scopus.com/inward/record.url?scp=85058634030&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.062705

DO - 10.1103/PhysRevA.98.062705

M3 - Article

VL - 98

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 6

M1 - 062705

ER -