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Time rescaling of nonadiabatic transitions
by Takuya Hatomura
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Submission summary
| Authors (as registered SciPost users): | Takuya Hatomura |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202211_00014v1 (pdf) |
| Date submitted: | 2022-11-08 14:31 |
| Submitted by: | Hatomura, Takuya |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by inducing additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023-3-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00014v1, delivered 2023-03-28, doi: 10.21468/SciPost.Report.6964
Strengths
The topic is very interesting, presented in a concise and self-standing way.
Weaknesses
None
Report
The author applies the fast-forward scaling theory to a system by rescaling its non-adiabatic transitions. They find that the "fast-forwarded" Hamiltonian consists of the original Hamiltonian plus two additional terms, namely the counterdiabatic term (as in shortcuts to adiabaticity) and another similar term. They also explicit two ways in which this new term can be calculated. Furthermore they show how the theory of shortcuts to adiabaticity can be recovered from fast-forward scaling theory of non-adiabatic transitions in the adiabatic limit of the reference Hamiltonian.
Their results allow to connect the fast-forward scaling theory with the theory of shortcuts to adiabaticity and is thus very interesting and I suggest the publication in SciPost Physics.
Requested changes
The paper is well written, my only suggestion, at the discretion of the author, is to improve the last paragraph of the introduction (in which they summarize the points discussed in the paper) in order to make it easier to understand. To me it became clear only after reading the paper.
Anonymous Report 1 on 2023-3-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00014v1, delivered 2023-03-07, doi: 10.21468/SciPost.Report.6858
Strengths
Provides a direct bridge between two popular theoretical approaches to quantum control. Presentation is to the point.
Weaknesses
None that I was able to identify.
Report
In this paper, the author studies the relation between the so-called fast-forward driving scheme and the shortcut to adiabaticity by counterdiabatic driving, as applied to the time-dependent evolution of a quantum system.
The former approach considers how to modify the Hamiltonian to recover the result of a slow parameter quench by driving that is performed at shorter time scales. The latter considers how to modify the Hamiltonian to recover the adiabatic limit of a very slow evolution along the ground states (eigenstates) manifold with parameter driving that is performed at a finite time. As can be naturally expected, both approaches are closely related, which gets nicely and pedagogically elucidated in this article.
The article bridges two popular theoretical approaches to quantum control that appear in the literature. The text is well written, both concise and self-standing. The citation list looks appropriate. I believe the article satisfies the expected acceptance criteria. As such, I can only recommend the publication of this article in SciPost Physics in its current form.