We address the Bose polaron problem of a mobile impurity interacting strongly with a host Bose-Einstein condensate (BEC) through a Feshbach resonance. On the repulsive side at strong couplings, theoretical approaches predict two distinct polaron branches corresponding to attractive and repulsive polarons, but it remains unclear how the two are related. This is partly due to the challenges resulting from a competition of strongly attractive (destabilizing) impurity-boson interactions with weakly repulsive (stabilizing) boson-boson interactions, whose interplay is difficult to describe with contemporary theoretical methods. Here we develop a powerful variational framework that combines Gaussian correlations among impurity-boson scattering states, including up to an infinite number of bosonic excitations, with exact non-Gaussian correlations among bosons occupying an impurity-boson bound state. This variational scheme enables a full treatment of strong nonlinearities arising in the Feshbach molecule on the repulsive side of the resonance. Within this framework, we demonstrate that the interplay of impurity-induced instability and stabilization by repulsive boson-boson interactions results in a discrete set of metastable many-body bound states at intermediate energies between the attractive and repulsive polaron branches. These states exhibit strong quantum statistical characteristics in the form of non-Gaussian quantum correlations, requiring non-perturbative beyond mean-field treatments for their characterization. Furthermore, these many-body bound states have sizable molecular spectral weights, accessible via molecular spectroscopy techniques. This work provides a unified theory of attractive and repulsive Bose polarons on the repulsive side of the Feshbach resonance.
1. In § 5 of the Introduction, "In the simple model described above..." is replaced by the more elaborate phrase "To illustrate this effect ... . In this single orbital model,...".
2. In § 5 of the Introduction, "In reality,..." is replaced by the more elaborate phrase "While this simplified model ... . In practice,...".
3. In § 7 of the Introduction, "On the other hand, ... remains extremely challenging." is added before "The proper inclusion ...".
4. In § 8 of the Introduction, "In this work, ... are energetically favorable" is replaced by "However, not much work ... the attractive polaron.".
5. In § 8 of the Introduction, "While for Bose polaron ... have not been included so far" is replaced by "As mentioned, ... understanding of the problem is still lacking.".
6. In § 9 of the Introduction, "In this work, ... repulsive polarons" is added to the beginning of the paragraph.
7. In § 9 of the Introduction, "solidly grounded" is added to the sentence "This variational principle ... Bose polarons.".
8. In § 10 of the Introduction, "in contrast to ... on many-body resonances" is added to the sentence "For instance, ... (see Fig. 1)".
9. In § 10 of the Introduction, "Such non-Gaussian ... impurity-boson interaction" is added before "While the quantitative aspects ...".
10. In § 10 of Sec. II C "Effective model and variational principle", "impurities" in "Nevertheless, for heavy impurities ... a negligible role." is changed to the more elaborate phrase "mobile impurities where ... is highly suppressed".
11. In Conclusion and Outlook, the paragraphs "The improvement ... with the condensate." and "Furthermore, ... decay rates" are added before the paragraph "The theoretical developments ... Bose polarons."
12. In Conclusion and Outlook, the paragraph "One future direction ... open problems." is removed, and the paragraph "We emphasize that ... a truncated basis variational state." is added.
13. In Conclusion and Outlook, the paragraph "In conclusion, ... spectroscopic techniques." is added after "In the present context, ... magnon impurity bound states.".
14. In Appendix B, the sentence "In the rest of this appendix, .... in all the expressions" is removed.
