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Floquet engineering non-equilibrium steady states
by Alberto Castro, Shunsuke A. Sato
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Submission summary
| Authors (as registered SciPost users): | Alberto Castro |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202301_00037v1 (pdf) |
| Date submitted: | 2023-01-27 15:31 |
| 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 demonstrate how those final states can be optimally tuned with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable, by using multicolor periodic perturbations. We show a computational framework that can be used for that purpose, and 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.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 4) on 2023-3-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202301_00037v1, delivered 2023-03-27, doi: 10.21468/SciPost.Report.6962
Report
This paper offers a way for designing Floquet driving protocols as an optimization problem, maximizing an observable in the nonequilibrium steady states (NESSs). Taking advantage of the simple structure of the Lindblad equation, the authors obtain gradients for the density matrix in terms of driving parameters, which allows the optimization of the NESSs.
Roughly speaking, this work is a direct combination of Ref. 28 and Ref. 36. Reference 28 discusses the optimization problem without Floquet drivings, whereas Ref. 36 discusses the NESS without optimization. In this view, the current title, "Floquet engineering non-equilibrium steady states," is inappropriate and too general since this concept was already proposed, at least in Ref. 36.
Besides, the paragraph "However, ..." in the Introduction is referenced only by Ref. 28, and the authors completely ignore all the relevant works on Floquet engineering in open systems, including the NESS, even stating, "we extend here that previous concept of Floquet engineering to open-quantum systems." The authors' contribution is not to extend Floquet engineering to open systems but to develop an optimization technique for (previously proposed) Floquet engineering of NESSs. I strongly recommend that the authors read a recent review article, arXiv:2203.16358, and revise the Introduction and title so as to highlight their contribution correctly.
Given that this work is a direct combination of Refs. 28 and 36, I do not find it a groundbreaking discovery or a breakthrough that is required in the acceptance criteria. So I cannot recommend publication in this journal. Since the technical results seem valid and interesting, I recommend publication in a non-flagship journal like SciPost Physics core after making appropriate revisions.
Requested changes
1- Modify the title more specifically.
2- Revise the Introduction by adding more references on Floquet engineering in open systems.
Report #2 by Anonymous (Referee 5) on 2023-3-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202301_00037v1, delivered 2023-03-21, doi: 10.21468/SciPost.Report.6936
Strengths
1- concise description of methodology
2- conceptual advance in the field of optimal control of driven-dissipative steady states
Weaknesses
1- computational costs are not discussed
2- limitations of the method are not discussed
Report
Generally, this is an interesting technical piece of work, and can be published in SciPost Physics. The other reviewer has already mentioned a few points of potential improvement that should be addressed. Besides those, it would be good if the authors could also mention the scope of this method -- what are requirements on the model for this method to work efficiently? The chosen example of NV center in diamond is a small model system with limited Hilbert space. Is it clear that the method can be expanded to extended systems -- solids are mentioned in the motivation? If so, what are the restrictions on those systems? E.g., does it only work efficiently for essentially noninteracting problems? Once a more in-depth discussion of these issues is added, I do recommend publication in SciPost Physics.
Requested changes
1- discuss costs and limitations
Author: Alberto Castro on 2023-04-04 [id 3540]
(in reply to Report 2 on 2023-03-21)We thank the referee for the recommendation to publish, and for the suggestion, that we find very appropriate. We have added a discussion about this point to the manuscript at the end of section 2
Strengths
New numerical method.
Clear application.
Weaknesses
Lack of comparison with other methods.
Report
Report attached
Requested changes
Indicated in the report.
Author: Alberto Castro on 2023-04-04 [id 3539]
(in reply to Report 1 on 2023-03-11)(see attached file)
Author: Alberto Castro on 2023-04-04 [id 3541]
(in reply to Report 3 on 2023-03-28)(see attachment)
Attachment:
author-response-3.pdf