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Optimizing Floquet engineering for non-equilibrium steady states 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:  (pdf)
Date accepted: 2023-05-22
Date submitted: 2023-05-01 11:05
Submitted by: Castro, Alberto
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


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.

Published as SciPost Phys. 15, 029 (2023)

Author comments upon resubmission

Dear Editor,

We would like to thank the referees for carefully reading our revised manuscript. The first referee recognized the significance of our work (“the work does indeed open a new avenue in the field, which will be picked up by other researchers”), and recommended the publication in the flagship journal SciPost Physics. The second referee also recommended the publication. In contrast, the third referee seems to favor the publication in SciPost Physics Core. The main concerns of the third referee in the last report are about the title and introduction – and we have addressed those concerns in our response –, but the referee does not have practical/scientific objections to the contents of the manuscript.

Regarding the lack of the references that the referee suggests for the introduction, we think that the referee favours a comprehensive review-type introduction, while we had prepared a more compact introduction to quickly arrive to the gist of the present work. In any case, given the explicit request to add more context, we have now added some paragraphs with a number of citations that we have deemed relevant – although the list cannnot be comprehensive, of course. However, note that those references are not strictly speaking “prior art” to the method described in our article, as they refer to the computation and / or experimental realization of NESSs, and not to their optimization, as it is the object of our work – which is the reason why, originally, we did not deem it necessary to cite them. In summary, we believe that the revised manuscript has been improved, and it is suitable for publication in SciPost Physics. Our work is the first one to propose a systematic computational procedure for the optimization of driven NESSs, and as such it should prompt other reserarchers to build on it, propose alternative methods, etc.

List of changes

o We have changed the title.

o We have enlarged the introduction, adding the references of a number of previous works that have approached the problem of non-equilibrium steady states.

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