Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets

We would like to thank the three Referees for providing a positive evaluation of our work and for the interesting raised questions. All the Referees recognise the importance and novelty of our work, and also write that our manuscript is well written and technically solid. The raised questions touch points such as the experimental conditions to observe the predicted effects, limitation of the Floquet formalism, improvement of the notation and discussion of Floquet processes, role of odd-parity magnets for spin-triplet pairing for as well as the clarification of the number of used Floquet bands. Besides these important questions, the Referees also identified a few typos and suggested to improve the resolution of Figures 3 and 4. We provide a detailed response to each of the referees comments in the respective parts, and also list the changes in our manuscript in the 'list of changes section'.

We note that, while these additions enhance the clarity and depth of our work, the core conclusions of the manuscript remain unchanged.

The updated manuscript is attached to this resubmission, with the changes in red color.

(1) To address Comment 1 from the Referee #1, Sec. 6.1 in Page 33, entitled “Experimental observ- ability and feasibility,” has been added to discuss the experimental accessibility of the proposed effects, including quantitative estimates of the relevant parameters, the required driving frequency and inten- sity, and feasible experimental detection schemes.

(2) To address Comment 2 from the Referee #1, Sec. 6.2 in Page 35, entitled “Limitations of the Floquet formalism and mitigation strategies,” has been added to discuss the intrinsic limitations of the present formalism and our strategies for minimizing their impact.

(3) To address Comment 1 from the Referee #2, we have added a remark following Eq. (39) in Page 17 to clarify how this equation is derived from Eq. (31) and why introducing Eq. (39) is necessary.

(4) To address Comment 2 from the Referee #2, we (i) specify the number of Floquet sidebands retained in the calculations in the captions of Figs. 3 and 5, where the Floquet-engineered normal and su- perconducting states are first introduced; and (ii) clarify that we have confirmed our results are not substantially modified by increasing the number of sidebands at the end of Sec. 3 in Page 15.

(5) To address Comment 3 from the Referee #2, we have discussed the robustness of the Floquet-induced spin-triplet states against heating effects in Sec. 6.2 (Page 35], entitled “Limitations of the Floquet formalism and mitigation strategies.”

(6) To address Comment 4 from the Referee #2, we have (i) reformulated the discussion associated with Fig.R1 (Fig.6 in the main text) in Page 26 to clarify why odd-photon processes generate purely light-induced pairing channels, whereas even-photon processes can mix with static correlations; and (ii) added a remark in the Conclusion in Page 36, noting that the effects of disorder in Floquet systems remain an open problem and deserve further investigation in future studies.

(7) To address Comment 5 from the Referee #2, we have replaced Figs. 3 and 4 by Figs. R2 and R3 with a higher resolution.

(8) To address Comment 6 from the Referee #2, the mentioned PhysRevB.112.L201408 [35] is cited with other relevant up-to-date studies on Floquet engineering unconventional magnets are cited, including Ref.[35–56].

(9) To address Comment 7 from the Referee #2, we had added Sec. 6.1 (Page 33) entitled “Experimental observability and feasibility to discuss experimental accessibility, including the possibility to detect Floquet spin-triplet Cooper pair magnitude in feasible experimental schemes

(10) To address Comment 8 from the Referee #2, we had correct (i) the text below Eq. (4) on page 7, (ii) the spacing and notation in Eq. (40), (iii) interchanged panels (b) and (c) in Fig. 4 and (iv) carefully check the manuscirpt to fix the typos.

(11) To address Comment 1 from the Referee #3, in the Sec. 2.1 and Sec. 4 of the revised manuscript, we rephrase the quantities Sz [Eq. (6)] and SF,z [Eq. (37)] as the spin densities in the static and driven normal states, respectively, rather than referring to them as spin-triplet densities in the normal state.

(12) To address Comment 2 from the Referee #3, after demonstrating Eq. (12) in Sec. 2.2. on Page 9, we emphasize that the spin-triplet Cooper pairs in p- and f-wave magnets with spin-singlet s- wave superconductivity exist even with time-reversal symmetry, which is akin to the cases of Rashba superconductors [57–62].