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Phase diagram for strong-coupling Bose polarons

by Arthur Christianen, J. Ignacio Cirac, Richard Schmidt

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Submission summary

Authors (as registered SciPost users): Arthur Christianen
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-02-22
Date submitted: 2024-01-17 10:30
Submitted by: Christianen, Arthur
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
Approach: Theoretical


Important properties of complex quantum many-body systems and their phase diagrams can often already be inferred from the impurity limit. The Bose polaron problem describing an impurity atom immersed in a Bose-Einstein condensate is a paradigmatic example. One of the most interesting features of this model is the competition between the emergent impurity-mediated attraction between the bosons and their intrinsic repulsion. The arising higher-order correlations make the physics rich and interesting, but also complex to describe theoretically. To tackle this challenge, we develop a quantum chemistry-inspired computational technique and compare two state-of-the-art variational methods that fully include both the boson-impurity and boson-boson interactions on a non-perturbative level. For a sweep of the boson-impurity interaction strength, we find two regimes of qualitatively different behaviour. If the impurity-mediated interactions overcome the repulsion between the bosons, the polaron becomes unstable due to the formation of large bound clusters. If instead the interboson interactions dominate, the impurity will experience a crossover from a polaron into a small molecule. We achieve a unified understanding incorporating both of these regimes and the transition between them. We show that both the instability and crossover regime can be studied in realistic cold-atom experiments. Moreover, we develop a simple analytical model that allows us to interpret these phenomena in the typical Landau framework of first-order phase transitions that turn second-order at a critical endpoint, revealing a deep connection of the Bose polaron model to both few- and many-body physics.

Author comments upon resubmission

We thank the referees for their useful feedback, which helped us to improve the clarity of our manuscript and to put it better into context. We have made substantial revisions to the manuscript and we hope that the referees find that their comments were addressed to their satisfaction.

Yours sincerely,
Arthur Christianen

List of changes

Please find below the list of changes with respect to the previous version in their order of appearance.

- We have added the references referee 2 suggested in our discussion of cooperative binding in the beginning of section 3,
- To better explain the connection between our work and our previous work, and the regime of validity of our previous work, we have thoroughly revised the section 3 “Current theoretical status”.
- In this section we have further changed the sentence where we refer to Ref. [68] to state more precisely what was done there, and we added Ref. [85].
- In this section we have explicitly explained now as well how the coherent-state approach compares to the Gross-Pitaevskii equation.
- We have added a comment to table 1 stating that the CS1 approach is equivalent to the GPE approach.
- At the end of section 4.2 we have nuanced our discussion of the Born approximation breaking down and the importance of quantum fluctuations, and we have added a footnote further elaborating on this point.
- In the beginning of the results section we have more clearly explained the limitations of our previous work in Refs. [70,71] and emphasized how our current work connects to this previous work. We have added a footnote explicitly stating that we recover the results from our previous work in the limit of small interboson repulsion.
- In section 5.2 we have rephrased the first sentence of the second paragraph, to reflect more clearly that we are talking about the weakly interacting regime.
- At the end of section 5.4 we have added a paragraph discussing how our results relate to Quantum Monte Carlo results in the literature
- In the beginning of section 5.6 we added a discussion of how inclusion of higher-order correlations would affect the onset of the polaronic instability.
- Later in section 5.6 we rewrote the paragraph discussing the description of the interboson interactions with the double-excitation approach, to more clearly reflect that the problems which arise from our implementation of the double-excitation approach do not appear in other situations.
- In section 6.1 we emphasize once more in the discussion of Eq. (23) that interboson interactions are not included at this point.
- In the conclusion we added a paragraph discussing how the spectral function of the polaron could be extracted from dynamical calculations, and how recombination would affect these results.
- We greatly expanded Appendix C with more explanations and with the newly added Fig. 13.

Published as SciPost Phys. 16, 067 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-2-13 (Invited Report)


I am generally happy with the authors' response to the reports and the changes made to the manuscript. I think there are still some interesting remaining questions regarding the role of higher body correlations (which could affect the cascade process proposed by the authors) and the role of losses (which could also modify the correlations themselves). However, these belong in future work and should not stand in the way of publication.

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Anonymous Report 1 on 2024-1-31 (Invited Report)


I am happy with the authors' response and the changes they made in the revised manuscript. I will recommend this paper to be published in SciPost.

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