Impurity-induced multi-body resonances in a Bose gas

We investigate the problem of $N$ identical bosons that are coupled to an impurity particle with infinite mass. For non-interacting 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 ‘multi-body’ resonances, where all multi-body bound states involving any $N$ emerge and disappear. The first multi-body resonance corresponds to infinite impurity-boson scattering length, $a\to +\infty$,whilethesecondcorrespondstothecriticalscatteringlength$a^*>0$beyondwhichthetrimer($N=2$ bound state) ceases to exist. Crucially, we show that the existence of $a^{\ast }$ ensures that the ground-state energy in the multi-body bound-state region, $\mathrm{\infty }>a>a^{\ast }$, is bounded from below, with a bound that is independent of $N$. Thus, even though the impurity can support multi-body 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.