SciPost Submission Page
A unified theory of strong coupling Bose polarons: From repulsive polarons to non-Gaussian many-body bound states
by Nader Mostaan, Nathan Goldman, Fabian Grusdt
Submission summary
| Authors (as registered SciPost users): | Nathan Goldman · Nader Mostaan |
| Submission information | |
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| Preprint Link: | scipost_202406_00029v2 (pdf) |
| Date submitted: | 2024-10-06 15:41 |
| Submitted by: | Mostaan, Nader |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
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.
Current status:
Reports on this Submission
Strengths
- Nicely written, with an extensive review of Bose polarons
- Promising variational approach
Weaknesses
- The calculations use an unphysical (zero range) boson-boson repulsion
- The results are not consistent with the few-body limit
Report
This work theoretically investigates the problem of a mobile impurity in a Bose Einstein condensate — the so-called Bose polaron problem. A variational framework is developed, which extends Gaussian-state approaches to include non-Gaussian correlations. Using this approach, the authors find a series of “many-body bound states” that exist in the energy spectrum between the attractive and repulsive polaron branches for positive scattering lengths.
Overall, I think this provides a worthwhile contribution to the study of the Bose polaron, and I would be interested to see the variational framework applied to the case of a more physical boson-boson repulsion (i.e., not zero range like in this work). However, as it currently stands, I am not convinced this provides a “unified theory” of the strong coupling Bose polaron.
The fundamental issue with theories that only treat the boson-boson repulsion as a low-energy zero-range interaction is that the energy is unbounded from below when the scattering length is positive, and there is nothing to restrict multiple bosons from binding to the impurity. It does not account for the short-range repulsion and the resulting correlations that are necessary to correctly describe bound states. Thus, one ends up with pathologies in the spectrum like the multiple many-body bound states of Ref [49], which also only treats the boson repulsion at the low-energy level.
In particular, I find the many-body bound states observed in this work very puzzling, since they do not agree with the expected behavior in the few-body limit. Note that, while the Bose polaron problem is many body, it should recover the few-body bound states in the limit of low density, i.e., large $E/E_n$ and $1/k_na$, which is accessed in this work.
For small positive impurity-boson scattering lengths and realistic boson-boson repulsion, one expects the ground state to correspond to a tightly bound dimer that cannot bind any more bosons and is weakly interacting with the surrounding Bose gas, i.e., similar to the regime where the scattering length is small and negative. This is the behavior that was obtained for the case of an infinitely heavy impurity using QMC and other exact methods (e.g., Ref [69,70]). One can also arrive at this conclusion by estimating the energy to bind a second boson: $\Delta E \approx -1/ma^2 + U_0/a^3$, where $U_0$ is the repulsion. Thus, we require the impurity-boson scattering length $a \gtrsim U_0 m$ for the boson to bind (i.e., $\Delta E <0$).
Furthermore, according to the few-body spectra for both mobile and infinitely heavy impurities, I would expect the higher body bound states to lie below the two-body bound state in the region near unitarity, rather than above like in Fig 1 and 2.
To conclude, I think this work should certainly be published in some form (e.g., in SciPost Core), but I am not convinced it satisfies the criteria for SciPost Physics given my reservations above.
Recommendation
Accept in alternative Journal (see Report)
Report
I came across the invitation to review the paper again by chance while browsing my SciPost page. It is actually unclear to me if this report is still needed. Anyway, given this turmoil and the clarifications of the Authors I recommend publication in SciPost Phys.
Recommendation
Publish (meets expectations and criteria for this Journal)