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Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

by F. Theel, S. I. Mistakidis, P. Schmelcher

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Simeon Mistakidis · Friethjof Theel
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-12-28
Date submitted: 2023-09-26 15:06
Submitted by: Theel, Friethjof
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

Author comments upon resubmission

Dear SciPost editor,

Thank you very much for sending us the referee reports on our above manuscript. In this resubmission we address in detail all issues raised by all three referees and performed the required changes in the revised manuscript as well as additional simulations in order to clarify the referees inquiries whenever deemed necessary. A list of changes is provided at the end of the reply letter.

We hope that the referees and yourself will find the revised manuscript suitable for publication in SciPost Physics and we are very much looking forward to your Editorial decision. Thank you very much in advance for your handling of our manuscript.

Sincerely yours,
on behalf of the authors
Friethjof Theel

Please find the letter to the editor, our individual replies to each of the referee reports, the list of changes and the revised manuscript with highlighted text under the following link:

List of changes

• In the introduction we have specified the statement regarding the attractive nature of the induced impurity-impurity interaction in a fluctuating medium and added relevant works, see Refs. [27–29].

• In the introduction we have included relevant works regarding open quantum systems and added the corresponding references [30–37].

• In Section 2, we have provided more details regarding a possible experimental realization of our setup.

• In Section 3, we have elaborated in more detail about the limitations of the applied numerical method and its region of applicability in terms of the involved interaction strengths.

• Figure 2 has been updated. We have modified the label of the horizontal axis from xB1to xB 2,1 to account for both, G(2)AB (xA1 , xB2 ) and G(2)BC (xB1 , xC2 ).

• In the captions of Figures 2, 5 and 6 we have specified the units of the two-body densities and the respective correlation functions.

• In Section 5, we commented on the experimental measurement of the two-body correlation functions and also added relevant works, i.e., we have included Refs. [2–6].

• In Section 6.2, we have included a statement about the interaction regime for which the employed effective two-body model with contact interactions is not applicable due to the appearance of non-local correlations.

• In Section 6.2, we have changed the definition of the fidelity (see footnote 5) and correspondingly updated Figure 4(c). However, no qualitative change of the fidelity behavior emerges from the new definition.

• We have added a comment into Section 6.2 of the manuscript confirming the possibility of retrieving different observables from the effective two-body model.

• In Section 7, we have included an additional specification for the formation of a bipolaron. Namely, in our setup we refer to a two-body bound state as a bipolaron when the participating impurities reside at the same spatial region, thereby, distinguishing the bipolaron from the coalescence of the impurities.

• We have improved the readability of Section 8 and hope that with the applied changes the access to the concept of three-body observables such as the Jacobi relative distances are facilitated. In this context, we have slightly modified the abstract and included in Section 8 Refs. [26] and [38].

• We have included additional discussions in the conclusions regarding possible future studies containing for instance finite size scaling analysis of the bath atoms or the usage of different external traps.

• In Appendix A, we have added relevant references regarding the application of the positive partial transpose (PPT) criterion and the logarithmic entanglement, i.e., Refs. [30–35].

• In Appendix D, we have included a comment stating that the general correlation behavior between the impurities is expected to be retained also for a larger number of bath atoms.

[2] S. Hofferberth, I. Lesanovsky, T. Schumm, A. Imambekov, V. Gritsev, E. Demler, and J. Schmiedmayer, Nat. Phys. 4, 489 (2008).
[6] F. Borselli, M. Maiwöger, T. Zhang, P. Haslinger, V. Mukherjee, A. Negretti, S. Montangero, T. Calarco, I. Mazets, M. Bonneau, and J. Schmiedmayer, Phys. Rev. Lett. 126, 083603 (2021).
[26] T. Schweigler, V. Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges, and J. Schmiedmayer, Nature 545, 323 (2017).
[27] A. I. Pavlov, J. Van Den Brink, and D. V. Efremov, Phys. Rev. B 98, 161410 (2018).
[28] M. Pasek and G. Orso, Phys. Rev. B 100, 245419 (2019).
[29] G. E. Astrakharchik, L. A. P. Ardila, K. Jachymski, and A. Negretti, Nat. Commun. 14, 1647 (2023).
[30] D. Braun, Phys. Rev. Lett. 89, 277901 (2002).
[31] F. Benatti, R. Floreanini, and M. Piani, Phys. Rev. Lett. 91, 070402 (2003).
[32] C. Hörhammer and H. Büttner, Phys. Rev. A 77, 042305 (2008).
[33] O. S. Duarte and A. O. Caldeira, Phys. Rev. A 80, 032110 (2009).
[34] T. Zell, F. Queisser, and R. Klesse, Phys. Rev. Lett. 102, 160501 (2009).
[35] K. Shiokawa, Phys. Rev. A 79, 012308 (2009).
[36] F. Benatti, R. Floreanini, and U. Marzolino, Phys. Rev. A 81, 012105 (2010).
[37] C. H. Fleming, N. I. Cummings, C. Anastopoulos, and B. L. Hu, J. Phys. A: Math. Theor. 45, 065301 (2012).
[38] K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. A 78, 023615 (2008).

Published as SciPost Phys. 16, 023 (2024)

Reports on this Submission

Anonymous Report 3 on 2023-11-24 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2303.04699v2, delivered 2023-11-24, doi: 10.21468/SciPost.Report.8185




1. Numerical technique widely used yet unsupported by a theoretical model.

2. Lack of proper experimental protocol which renders the work unplausible for experimental observation.

3. Considerable overlap with previous works.


I acknowledge the authors for providing a response to the points I raised previously. However, concerning a feasible experimental implementation, the authors lack a pragmatic scheme, including the numerical values utilized in their calculations.

The presence of bound states between polarons might be achievable within a two-component system, while the intriguing transition from attractive to repulsive interactions introduces yet another noteworthy and interesting phenomenon. Nevertheless, I am having a hard time foreseeing its interest beyond pure theoretical interest. While I find the system challenging from an experimental point of view, I am intrigued by the crossover between attractive and repulsive interactions, especially since it has not been reported in binary mixtures. However, apart from the numerical values, there is not an intuitive picture of how to understand the phenomena.

Last, but not least, I am still not convinced about how this work is substantially different from previous references, such as PRA 104, L031301 (2021) and PRA 105, 053314 (2022). Essentially, the system is the same—a triple mixture—but you consider the case of two ultra-highly imbalanced components representing the two polarons. Furthermore, the methodology remains the same.

While different physics is explored in this work, I think the present results do not align with the stringent requirements for publications in Scipost. Publication in a more specialized journal, however, is encouraged.

  • validity: ok
  • significance: ok
  • originality: low
  • clarity: ok
  • formatting: acceptable
  • grammar: good

Report 2 by Arturo Camacho Guardian on 2023-11-5 (Invited Report)


The authors have addressed my comments and I now recommend publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2023-11-3 (Invited Report)


1. Clear description of a very wide collection of phenomena.

2. Simple models are presented which capture the relevant physics.

3. Powerful numerical methods which help ellucidate relevant physics and sustain the simple models.


1. Many topics addressed, though this is cured upon honest comments in the manuscript - therefore further research is possible in subsequent papers.


The authors have improved the manuscript with a thoughtful revision, which I honestly acknowledge. One paper I believe is interesting but I gave wrongly the reference in previous report is PRL 97, 250601. Duarte and Caldeira did, in my opinion , a great job here.

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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