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Floquet engineering non-equilibrium steady states: on the optimization of system properties with gradient-based methods
by Alberto Castro, Shunsuke A. Sato
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Submission summary
| Authors (as registered SciPost users): | Alberto Castro |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2301.02004v2 (pdf) |
| Date submitted: | 2023-04-04 09:24 |
| Submitted by: | Castro, Alberto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment -- as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we propose a computational method to find the multicolor periodic perturbations that lead to the final steady states that are optimal with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable. We exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.
Author comments upon resubmission
We have revised our manuscript, and written response to the reports. We think that the manuscript has improved thanks to their valuable insight. Furthermore, we would like to request publication in the flagship journal SciPost Physics, as we disagree with the third report assessment in this respect. We believe that our work fulfills the criteria, and in particular it does meet the requirement “Open a new pathway in an existing or a new research direction, with clear potential for muletipronged follow-up work”. This is the first work that performs optimizations on the properties of systems in driven NESSs, and as such it will be picked up by other authors as an inspiration to pursue that line of research.
List of changes
o Added paragraphs making the relationship of this work with previous works more explicit.
o Added comments on the scalability and computational feasibility of the method.
o Added a new figure, with examples of convergence histories
o Added a paragraph explaining the possible use of the adjoint method for gradient computations
o Added a few references suggested by the referees
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 1) on 2023-4-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.02004v2, delivered 2023-04-21, doi: 10.21468/SciPost.Report.7086
Report
I appreciate some of their responses and revisions, but I was disappointed to read the others because they make arguments for their own sake and their revision is far from satisfactory. So my recommendation does not change from the previous round. Below I detail how their response is unsatisfactory.
1. 'we would like to comment on the notion of “engineering”: “designing and/or building something useful/desired based on scientific principles”. We are probably using that notion with a meaning that goes beyond what the referee implies. Generally speaking, we think that a simple parameter scan is not engineering; ...'
I think that a simple parameter scan is also engineering and so does, e.g., a standard review article [Annu. Rev. Condens. Matter Phys. 10, 387-408 (2019)]. The authors' idea of using multiple parameters in Floquet engineering more sophisticatedly ("engineer" in their definition) is a generalization of previous studies. If they use the word "engineer" in the title in a non-standard manner, wouldn't it be misleading? I would suggest another title like "Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods."
2. "We also thank the referee for pointing towards arXiv:2203.16358 (already published in Annual Reviews of Condensed Matter). We have added that reference to the text."
This revision did not address my comment. I did not mean to cite this review article only but to cite some relevant references therein (together with describing each work more carefully). I meant to point out the issue that their introduction part fails to mention relevant works for open Floquet systems. I was disappointed that the authors just put this review article at the end of a sequence of original articles.
3. 'We thank the referee for appreciating our work as “valid and interesting”, and worthy of SciPost Physics Core. However, we would like to request a publication in the flagship journal SciPost Physics. We hope that the novelty and significance of the present work have become more clear in the revised manuscript. We believe that our work meets the criterion for publicaction in SciPost Physics. In particular, we think that it fully fulfills one of the expectations: “Open a new pathway in an existing or a new research direction, with clear potential for muletipronged follow-up work”.'
I can say nothing because there is no justification for why they think so.
Strengths
9
Weaknesses
1
Report
I would like to thank the authors for addressing all my questions and comments.
I can recommend the work for publication.
Requested changes
Increase the figures' axis labels font size, as the current size is not readable when printed.
Report
The authors have improved the manuscript based on the reviewers' suggestions. I also agree that the manuscript should be published in the flagship SciPost Physics outlet, since the work does indeed open a new avenue in the field, which will be picked up by other researchers.
Author: Alberto Castro on 2023-05-01 [id 3632]
(in reply to Report 3 on 2023-04-21)Our response: We thank the referee for clarifying his/her take on the meaning of “engineering”: “A simple parameter scan is also engineering”. This is clearly different from the meaning that we had assigned to it: engineering as a more sophisticated concept than a simple parameter scan for designing and/or building something useful/desired. In the present work, we propose a practical prescription for the design of periodic drivings that would lead to useful/desired properties, with a method that goes beyond a simple parameter scan. However, the referee also indicates that “engineering” is normally used in a broader sense in the Floquet engineering community. Perhaps we should not discuss semantics; to avoid possible confusion, we revised the title of our manuscript to the one that the referee suggests: “Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods”.
Our response: We would like to thank the referee’s suggestion, which we have followed, adding some paragraphs in the introduction with a sample of references that we expect is significant enough. Since the present manuscript is not a review paper, we had not reviewed the field in detail in the introduction. We also note that, in the review paper that the referee suggested, it was mentioned: “For instance, the importance of dissipation has been pointed out in recent experimental [33] and theoretical [34] studies on the light-induced anomalous Hall effect in graphene”. One of the authors of the present manuscript is also the leading author of that reference [34]. We had cited and mentioned this point already in our manuscript, albeit without explaining specific phenomena in detail, since we did not intend to review the whole field, but rather provide a compact introduction that would quickly summarize the intent of the present manuscript.
Our response: We are sorry that the referee could not find the justification. One of the ultimate goals of the optics community is to engineer (in our meaning of the word) or design/control material properties/functionalities as desired. Our present manuscript provides a practical prescription for engineering/designing/controlling material properties/functionalities, based on optimal control theory, and demonstrates the control of the material properties by light in the open quantum system setup. Therefore, these tools for the optimization of material functionalities are now settled, and other researchers can also explore optimal fields to realize their desired properties of materials by light. We therefore hope and expect that this will lead to many follow-up works. That is the reason why we believe that our work indeed satisfies the journal criterion: “Open a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work”. Indeed, the first referee explicitly appreciates this point by mentioning “the work does indeed open a new avenue in the field, which will be picked up by other researchers”.