Competition of light- and phonon-dressing in microwave-dressed Bose polarons

Dear Editor-in-charge of SciPost Physics,

We would like to thank you very much for your handling of the above
manuscript submitted to SciPost Physics. According to the referee
reports we have performed all the suggested changes in the revised
version of our manuscript. In the following you can find our detailed
reply to all of the comments of the referees. A list of changes is also
appended following our point-by-point reply to the referee's comments.
On behalf of the authors,

Georgios M. Koutentakis

List of changes in the revised manuscript:

1. Introduction, last paragraph of page 3. Added a short discussion on past effective potential models "We reveal that the system ...discussed [75]."

2. Sec. 3.1, page 6. Modified Fig. 1, removed previous panels (c), (d) and added a new panel (c) with a magnification of the near resonant region of panel (b). The caption was updated accordingly.

3. Sec. 3.1, page 6. Added a discussion on the existence of one-dimensional Bose polaron "Let us stress here ...one-dimensional confined systems."

4. Sec. 3.1, page 6. Added references to panel 1(c) in the text "however since ...see Fig. (1)". On the same note, in page 7 we modified the sentence "However, since $|E_{2\uparrow} - 2 E_{1 \uparrow}|$ ...see Fig. 1(c)."

5. Sec. 3.2, page 7. We have combined Fig. 1(c) and 1(d) into the new Fig. 2.

6. Sec 3.2, page 8. modified the symbols in the inline equations of the sentence "To establish the validity ...[Eq. (6), Eq. (7)]" with more accurate equations also a few lines below the correct expression for the residue is used $Z = | \langle \Psi_{B+0\uparrow} | \hat{a}_0 | \Psi_{B+1\uparrow} \rangle | $ .

7. Sec 4, page 13. Modified the sentence on Tan's contact, " This behavior can be explained ...effective potential method", to stress the modification of the momentum distribution when a polaron is formed.

8. Sec 4, page 14, Table I. Updated the table with the percentages of change in residue attributed to the change of impurity and bath state. The caption is updated accordingly.

9. Sec 4, page 14. The last two paragraphs of Sec. 4 were rewritten to highlight the behavior of the residue and the different contributions and also to explicitly state that we are confident that the effective potential works only up to the $|g_{BI}| \approx g_{BB}$ case we have checked within ML-MCTDHX.

10. Sec 5.1, page 16. Modified Fig. 6 by removing panels (a$_2$), (b$_2$), (c$_2$), and (d$_2$). These were added to the new Fig. 7 appearing in page 17 of the same section. The caption was updated accordingly for both figures.

11. Page 19, last paragraph of Sec. 5.2, the specification "$\Delta \leq -3 \omega_B$ for $g_{BI} = 1.5~\sqrt{\hbar^3 \omega_B/m_B}$" was added to avoid confusion. Also a few lines below we have added the sentence "As Fig. 8(b) reveals ...for varying" to explain how the regime of the stabilized polaron can be extracted from effective potential calculations.

12. Last paragraph of conclusions, page 20. Modified the sentence "The case of strong attraction ...emerges in this regime." To highlight strong attractive interactions as an important future perspective.

13. Page 15, added the new Appendix C containing the new Fig. 9, with the residue quantities $Z_{\sigma}$ directly connected to many-body overlaps.