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

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: https://wolke.physnet.uni-hamburg.de/index.php/s/RHxn2d3i9H3QrQG

• 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.

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