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Bound impurities in a one-dimensional Bose lattice gas: low-energy properties and quench-induced dynamics

by Felipe Isaule, Abel Rojo-Francàs, Bruno Juliá-Díaz

Submission summary

Authors (as registered SciPost users): Felipe Isaule
Submission information
Preprint Link:  (pdf)
Data repository:
Date accepted: 2024-06-18
Date submitted: 2024-05-24 15:05
Submitted by: Isaule, Felipe
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
Approaches: Theoretical, Computational


We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

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

Author comments upon resubmission

Dear Editor,

We thank the reviewers for the detailed evaluation of our manuscript. We have revised several parts of our manuscript, taking into account all questions and suggestions of the reviewers. We believe these changes have greatly improved the quality of our work.

While it is true that our work shares an overlap with a previous article, this partial overlap only applies to Secs. 3.1 and 3.2, where we summarized some previous results to present a cohesive manuscript. In the current revision, we have provided details on the possible experimental realization of our model and emphasized the novelty of our results. We believe our work includes enough new and relevant results to be published in Scipost Physics. However, should the Editorial College and reviewers consider that Scipost Physics Core is the most appropriate journal for our manuscript, we would accept it to reduce the delay in getting our work published.

Please find below a list of the changes made. We also provide a version of our manuscript with the changes highlighted on:

Additionally, we provide complete responses to each report on the original submission page.

Thank you for receiving our manuscript, and we hope that it is now acceptable for publication.

Yours sincerely,

Dr. Felipe Isaule
Corresponding author

List of changes

*Updated published preprints.
*Added some references, mostly to justify some additions to the new manuscript:
-New Journal of Physics 25, 093032 (2023)
-Nature Physics 17 (6), 731-735 (2021)
-Physical Review A 105, L021303 (2022)
-New Journal of Physics 21, 053024 (2019)
-Physical Review B 99, 205414 (2019)
-Physical Review Letters 95, 063201 (2005)
-New Journal of Physics 11, 043030 (2009)
-Reviews of Modern Physics 82, 1225 (2010)
-Reports on Progress in Physics 75, 046401 (2012).
*A sentence in the abstract was rewritten to avoid referring to critical points, as suggested by the reviewers.
*A few words have been rewritten in the last paragraphs of the introduction.
*Several parts of Sec. 2 have been rewritten to explain questions raised by the reviewers.
*The first paragraph of Sec. 3 has been rewritten to better explain the di-impurity states.
*The last three paragraphs of Sec. 3.1 have been rewritten to better explain some aspects of our results.
*Added a sentence after Eq. (9) explaining how to obtain the formula for r0.
*A sentence before Table 1 has been rewritten to highlight the crossover.
*A typo in Table 1 has been fixed.
*The second paragraph of page 8 has been rewritten to better explain the phase separation.
*The first paragraph of Sec. 3.3 has been rewritten to better explain the crossover and the tunneling correlator Ct.
*The last three paragraphs of Sec. 4.1 have been rewritten to better explain the energy gaps.
*The fourth and fifth paragraphs of Sec. 4.2 have been rewritten to better explain the excited states.
*The first paragraphs of Sec. 5 (before 5.1) have been rewritten to explain the possible experimental observation of revivals and to justify the choice for the number of sites.
*Selected sentences of Sec. 5.1 have been rewritten to highlight the crossover behavior of our model.
*A new paragraph has been added at the end of Sec. 5 to explain the dependence of our results on the number of sites.
*The second paragraph of the conclusions has been rewritten to better explain the formation of dimers.
*A new paragraph has been added to the conclusions to highlight the possible experimental realization of our model.
*The last paragraph of the conclusions has been revised to include additional future directions for our work.
*The paragraph after (A.3) has been rewritten to better explain the degeneracy of the ground state.
*The gray lines in the figures have been updated with thicker and darker lines.
*The notation of the lattice’s spacing was changed from “a” to “d”.
*A typo in Table 1 was fixed.

Current status:
Accepted in alternative Journal

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Reports on this Submission

Anonymous Report 2 on 2024-6-13 (Invited Report)


Comprehensive and detailed study
Well formed narrative that provides a clear physical picture
Experimentally relevant predictions


Not much new physics apart from the collapse and revival dynamics
Limited to small system sizes


I thank the authors for adequately addressing all of the technical points in the previous report. However, as before, I think the work is better suited for SciPost Physics Core. The main physical phenomenon the work centers around—that of dimer formation via bath-mediated interaction—was already known from past work, which also explored interaction quenches [49, 44]. I agree that the present work is more comprehensive and perhaps more physically illuminating, but I wouldn’t say that it opens a new pathway for research. Thus, it does not meet the criteria for SciPost Physics for me. As I see it, the really new finding here is the collapse and revival dynamics of the dimer for small systems, which would be interesting to observe experimentally. However, I think this is more appropriate for SciPost Physics Core.


Accept in alternative Journal (see Report)

  • validity: high
  • significance: good
  • originality: ok
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2024-5-30 (Invited Report)


1) Comprehensive description
2) Detailed characterization of microscopic properties
3) Exact calculations
4) Indications of persistent behavior from small to larger systems


1) Some of the presented results, such as the formation of impurity dimers, have also been reported elsewhere


The authors addressed the comments in response to the previous referee report. As such, the revised manuscript is significantly improved in several aspects. Indeed, the description and interpretation of the results are now more solid. For instance, the behavior of the bipolaron energy and its transition behavior is clear, the competition between interspecies phase-separation and Mott-insulator of the bath is better understandable, the role and properties of the di-impurity are better conveyed and the method description is improved. Such systems, despite being few-body, are valuable for our understanding on the microscopic processes and are certainly accessible experimentally nowadays. For these reasons, I recommend this work for publication in Sci Post Physics.


Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: high
  • originality: good
  • clarity: good
  • formatting: excellent
  • grammar: good

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