# Impurity-Induced Multibody Resonances in a Bose Gas

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

December 2018
### Abstract

We investigate the problem of $N$ identical bosons that are coupled to an impurity
particle with infinite mass. For noninteracting bosons, we show that a dynamical
impurity-boson interaction, mediated by a closed-channel dimer, can induce an
effective boson-boson repulsion which strongly modifies the bound states consisting of
the impurity and $N$ bosons. In particular, we demonstrate the existence of two
universal “multibody” resonances, where all multibody bound states involving any $N$
emerge and disappear. The first multibody resonance corresponds to infinite
impurity-boson scattering length, $a\to +\infty$, while the second corresponds to the
critical scattering length $a^∗>0$ beyond which the trimer ($N=2$ bound state) ceases
to exist. Crucially, we show that the existence of $a^∗$ ensures that the ground-state
energy in the multibody bound-state region, $\infty>a>a^∗$, is bounded from below,
with a bound that is independent of $N$. Thus, even though the impurity can support
multibody bound states, they become increasingly fragile beyond the dimer state. This
has implications for the nature of the Bose polaron currently being studied in
cold-atom experiments.

Publication

Physical Review Letters **121**, 243401 (2018)