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Floquet engineering of quantum thermal machines: A gradient-based procedure to optimize their performance
by Alberto Castro
Submission summary
| Authors (as registered SciPost users): | Alberto Castro |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.09126v1 (pdf) |
| Code repository: | https://qocttools.readthedocs.io/en/stable/ |
| Date submitted: | 2024-05-16 09:56 |
| Submitted by: | Castro, Alberto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
A procedure to find optimal regimes for quantum thermal engines (QTMs) is described and demonstrated. The QTMs are modelled as the periodically-driven non-equilibrium steady states of open quantum systems, whose dynamics is approximated in this work with Markovian master equations. The action of the external agent, and the couplings to the heat reservoirs can be modulated with control functions, and it is the time-dependent shape of these control functions the object of optimisation. Those functions can be freely parameterised, which permits to constrain the solutions according to experimental or physical requirements.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
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Report
The paper’s main focus is to find driving protocols (i.e. time dependent functions which correspond to driven coherent and incoherent evolution) that optimise a particular cost function associated with the systems performance as a thermodynamic engine. The reduced system state (after tracing out the thermal baths or environments) is described by a standard Lindblad master equation i.e. it assumes the Born-Markov approximation.
In particular, the current work focussed solely on the power output over a cycle as the key quantity to be optimised. It is assumed that all driving protocols are periodic, which leads the system to relax to a non-equilibrium steady state. The intermediate timescale where some transient effects play a role is not investigated.
My main critique of the paper, is that there does not seem to be a clear novel improvement over previous works e.g. Refs. 16 and 17. The author must make clear why their contribution is not an incremental improvement over previous papers.
I would not recommend the paper in it’s current form for publication. For publication, the author would need to thoroughly address both this main point and my additional comments listed below.
- The introduction is well structured, but does have some strange and redundant phrasing at times. It could be improved upon.
- Fig. 1 is never referenced in the main text that I can see.
- It is not clear what are the main quantum effects being exploited. Does the coherence of the qubit play an important role? What results would one get from an analogous classical master equation?
- Some notation I find a bit awkward such as with f(t) and f_k(t). Maybe the use of vectors would be useful here. Similarly with u and u^{(k)}.
- The author notes that the Lamb-shift “can be ignored in the weak coupling limit”. Recent discussion here [arXiv:2305.08941] suggests that this is a somewhat subtle point. Some more discussion on this is probably warranted.
- The notation \rho is used to denote both the general solution to the master equation and the NESS. I would suggest using a subscript for the NESS for clarity.
- There has been recent work e.g. [Quantum 5, 590 (2021) and Sci. Adv.8, eadd0828 (2022)] which show how the usual Lindblad master equation must be modified to ensure thermodynamic consistency when the system is driven. - Since the current work is focussed on quantifying thermodynamics performance, should this modified master equation be employed?
- The main focus has been on optimising output power. Does this have any tradeoff relations with the efficiency (even from the numerics)? Would it make sense to use a joint cost function which combines the two?
- It is claimed that the Lindblad operators can be modulated in time. This is rather unusual. It would be nice if some physical insight into how this is done in practice was included.
- “…which in a realistic setup cannot be taken to arbitrarily close-to-zero values”. It would be useful to state how small this can really be made for the setups of interest.
- Panel (b) of Figs. 2 and 3 need units for the y-axis.
- For the parameterisation of the control function, would it not be simpler to just use a Fourier series (as in Eq. A2) and just bound the sum of the absolute values of the amplitudes to cap the amplitude?
Recommendation
Ask for major revision