Non-Gaussian quantum correlations in many-body bound states of Bose polarons

A mobile impurity resonantly coupled to a Bose-Einstein Ccondensate (BEC) forms a quasiparticle termed Bose polaron. Understanding the physical properties of Bose polarons can provide crucial insights into the formation of few-to-many body quantum correlations in Bose-condensed systems. In cold atom realizations of Bose polarons, the impurity-boson interaction strength is tunable via Feshbach resonances, allowing access to interaction regimes beyond the capacity of conventional solid-state platforms. In the strong-coupling regime, the impurity can induce an unstable Bogoliubov mode causing an indefinite cascaded decay of the BEC. We show that the interplay of impurity-induced instability and stabilization by repulsive inter-boson interactions results in a discrete set of bound-states at intermediate energies between attractive and repulsive polaron branches. These states demonstrate strong non-Gaussian correlations, requiring non-perturbative beyond-mean field treatments for their characterization. Furthermore, they exhibit vanishing quasiparticle residue and thus are inaccessible by conventional impurity spectroscopy techniques. Nevertheless, we show that they have observable signatures in molecular spectroscopy- based detection techniques.