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
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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 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 -