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 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 $a^{\ast }$ 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 $a^{\ast }$. Indeed, since the critical point $a^{\ast }$ 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.

arXiv comment15 pages including 6 figures, 3 appendices and references

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• Electronic properties and polaronic dynamics of semi-Dirac system within ladder approximation
• Observation of a Halo Trimer in an Ultracold Bose-Fermi Mixture
• Universal Efimov Scaling in the Rabi-Coupled Few-Body Spectrum
• A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states