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.
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List of changes
1. On page 3, the second to the last paragraph of Sec. I, we corrected the typo "repuslive" to "repulsive". 2. On page 3, the second to the last paragraph of Sec. I, we added an explanation to clarify address point B of referee report. 3. We added Refs. [64] and [65] as asked by the referee in point A. 4. In Eqs. (9), (11) and (12) we changed "n+m=4" to "n+m<=4". 5. On page 7, we added a paragraph after the paragraph containing Eq. (10), explaining the connection of the ansatz to the Born-Oppenheimer approximation in more details, in line with the referee's request for major changes point 1. 6. On pages 7 and 8, we included an explanation regarding the referee's point H, in the paragraph starting with "Some comments on the variational scheme presented above are in order. " 7. In Sec. III, paragraph 5, we added an explanation regarding the role of fluctuations, as asked by the referee in point E. 8. We added Ref. [79] in the revised manuscript. 9. We added paragraph 5 in Sec. V concerning referee's comments in point F. 10. We added the new appendix B concerning referee's request for major changes in point 1, to provide a rigorous justification of the variational ansatz.
