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Dephasing enhanced transport of spin excitations in a two dimensional lossy lattice
by Andrei Skalkin, Razmik Unanyan, Michael Fleischhauer
Submission summary
Authors (as registered SciPost users): | Michael Fleischhauer |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2502.10854v1 (pdf) |
Date submitted: | March 8, 2025, 4:11 p.m. |
Submitted by: | Fleischhauer, Michael |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approaches: | Theoretical, Computational |
Abstract
Noise is commonly regarded as an adverse effect disrupting communication and coherent transport processes or limiting their efficiency. However, as has been shown for example for small light-harvesting protein complexes decoherence processes can play a significant role in facilitating transport processes, a phenomenon termed environment-assisted quantum transport (ENAQT). We here study numerically and analytically how dephasing noise improves the efficiency of spin excitation transport in a two dimensional lattice with small homogeneous losses. In particular we investigate the efficiency and time of excitation transfer from a random initial site to a specific target site and show that for system sizes below a characteristic scale it can be substantially enhanced by adding small dephasing noise. We derive approximate analytic expressions for the efficiency which become rather accurate in the two limits of small (coherent regime) and large noise (Zeno regime) and give a very good overall estimate. These analytic expressions provide a quantitative description of ENAQT in spatially extended systems and allow to derive conditions for its existence.
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:
Reports on this Submission
Report
ENAQT is characterised by a non-monotonic behaviour of the transfer efficiency as a function of a dephasing noise, with the efficiency increasing for small noise amplitudes, and decreasing for large ones. This phenomenon has been studied in previous works on different geometries.
This work extends it to the case of a 2D square lattice. In this case, it recovers the expected ENAQT behaviour and its explanation in terms of the presence of dark states, and it explains the dark states existence from geometrical considerations. It derives analytic approximations for the efficiency, in the two regimes of small and large dephasing noise, and identifies a characteristic length scale up to which ENAQT is appreciable.
In my opinion, these results are technically correct and valuable, but I have several concerns regarding the paper claims and its presentation, that I would ask the Authors to address before publication in a journal.
In addition, I believe that the paper results do not constitute a significant advance with respect to previous work, and therefore do not meet the acceptance criteria of SciPost Physics, namely of a groundbreaking discovery or a breakthrough on a long-standing problem. I find it instead more appropriate for SciPost Physics Core.
Requested changes
In the following, I will first address the presentation aspects that I found confusing or need improvement, as this might be helpful for the editor as well. These are briefly described here, but more detailed comments are reported as annotations in the attached PDF.
A. Using the symbol pn,m(t) and the name "density matrix" for \operatorname{tr} \left{\rho(t) \sigma_m^{\dagger} \sigma_n\right} is very confusing in this open system context in which there's also ρ that is also called "density matrix". In particular p is not a probability, and Eq. (27) does not describe a conservation of probability, but of particle density (this initially led me to think that the right-hand-side should have been 0!). To make these things unambiguous, I would use a different symbol and name.
B. The transfer efficiency (11) and average time (12) are crucial quantities for the paper. Nevertheless, what they actually represent is not sufficiently discussed. For (11), for example, I found the discussion given in Ref. clear [15]: The excitation is trapped with a rate Γs. The probability that the exciton is successfully captured at a target site within the time interval [t,t+dt] is given by Γs⟨s|ρ(t)|s⟩dt. Thus the transfer efficiency can be described as the probability of trapping during the time interval [0,t] ([15] actually has a 2, I am not sure why...). Actually, I think the name "trapping probability" would be much clearer than "transfer efficiency", although I understand that the latter is already established. Please find more comments (in particular on the average transfer time) in the PDF attached.
C. Several lengths are defined, such as (6) and (9), but their formulas do not have the dimensions of a length. These should be multiplied by the lattice constant a.
D. Overall I found the paper quite long, and often redundant. I think the results on the analytic approximations for the efficiency should come earlier. Instead, several technical aspects could be moved into Appendices. For example the entire section "3.1 Monte-Carlo wavefunction approach" describes a well established approach, and would better be an Appendix.
Apart from these presentation aspects, my main concerns with the claims of the paper are the following.
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I find Eq. (27) and its discussion unclear and actually very misleading. This equation assumes that there are no dark states in the problem, thus the excitation prepared is completely dissipated at long times (otherwise the right-hand-side wouldn't be 1). Nevertheless, this is not true in most cases of interest for the paper, and the predictions of Eq. (27), of η=1 for μ=0 and η≈1 at small μ, are never realized in any results obtained in the rest of the paper. In fact, for μ=0,γ=0, as discussed in 4.1, the efficiency η is far from 1 precisely because several dark states are present. For small μ, η is also generically far from 1, as shown in Fig. 2. For μ=0 and finite γ, the Authors report that η=1 in all cases and therefore this is a bad quantitative measure of transport. It's then not clear to me why to present and discuss such equation at all, but anyway I found the present discussion quite confusing.
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One of the main claims of the paper is that "ENAQT disappears for a system size larger than a characteristic value". While the results behind this statement are technically correct, and the corresponding length scale identified seems valuable, I find this statement misleading. In fact, this is a result of how the transfer efficiency η is defined, namely by averaging over the site choices where the excitation is initially prepared, which are chosen randomly and uniformly distributed across the entire lattice with linear dimension L. As discussed in Fig. 7, for a large L such efficiency is small (decreases with L), because most (more) initial sites are just too far from the sink site, and cannot reach it. Instead, stating that the efficiency decreases with L makes one think that this is true keeping the source and sink positions fixed, which is not what the Authors have shown. I understand that the chosen randomly located initial excitation might reflect the physical behaviour of photons collected by an antenna, as commented somewhere in the paper, but all these aspects should be explained more clearly.
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An explanation of how the bound (9) (or (34)) arises physically/intuitively is missing.
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Following the discussion in point 1., I would also suggest to replace Eq. (28) with η=η0(1−τμ), with η0=lim and without assuming that the latter is 1. In addition, this result relating transfer efficiency \eta to the average transport time \tau at small \mu is not sufficiently commented, but seems non-trivial to me. One aspect that I remarked is that \eta is a trapping probability, and as such depends explicitly on the trapping rate \Gamma_s, as by Eq. (11). Instead, \tau does not explicitly depend on the trapping rate, as it is better seen if this is re-written as
\tau= \frac{\int_0^{\infty} d t \; t \left\langle\uparrow_s\right| \rho(t)\left|\uparrow_s\right\rangle } {\int_0^{\infty} d t \left\langle\uparrow_s\right| \rho(t)\left|\uparrow_s\right\rangle }This writing clarifies that this is just an average time, taken over a probability density in time, and the denominator is just its normalization -- in passing, I raiterate that what \tau represents should be better discussed in the paper, and perhaps (12) would be better replaced with expression I wrote here that seems clearer to me. Then, it seems a non-trivial fact that, at small \mu, the transfer efficiency \eta is completely determined by the average transport time \tau, and that it depends on the trapping rate \Gamma_s only through it, as shown by Eq. (28) (or the one I suggested instead). This indeed shows that the trapping rate is not the limiting factor to the efficiency in this small-\mu regime. (Perhaps surprisingly, this is also true in the Zeno regime of \Gamma_s \gg J, for which the small efficiency is also due to a large \tau, because hopping into site s is highly inefficient, as shown in Fig. 4.).
Given these considerations, I think the paper needs to be clarified in several ways before publication. In addition, as I said I believe that its results do not meet the acceptance criteria of SciPost Physics, and that it is more appropriate for SciPost Physics Core.
Recommendation
Ask for major revision
Strengths
- Interesting and original methodological approach to the problem of energy transport in dissipative hopping lattices. Potential to apply this approach to other model transport systems.
- Strong and rigorous analytical results, particularly the bounds on efficiency and transport time and the crucial impact of dephasing in enhancing ( or even allowing) excitations to reach a target site.
- Numerical results have been carefully obtained and convincingly compared against analytical predictions.
- To the best of my knowledge the discussion and analysis of system size is potentially novel.
- Clear and well-presented article, easily accessible to expert and non-expert, alike. The details surrounding the mathematical develop of the numerical monte carlo method and the derivations of the various bounds were particularly welcome.
Weaknesses
- The underlying problem and theory of ENAQT ( or noise-assisted dephasing NAT) is now rather old ( 2008 - ) . The lattice system and model studied in this paper is essentially the same as in the first papers looking at ENAQT in the context of exciton transport in photosynthetic proteins. Consequently, the amount of new qualitative insight into ENAQT is somewhat limited.
- Introduction focuses a great deal on biological systems, but many relevant citations are missing and some of the presentation of the previous work, particularly w.r.t. this article's contribution, needs to be corrected for the record.
- Given the single-particle nature of the dynamics, I was surprised by the small lattice sizes used in the numerical simulations, especially given that previous studies have been able to look at much larger and more complex dynamics.
- The main conclusions seem to repeat a number of general facts that have been known/stated in the ENAQT literature many times before. The conclusion concerning critical antenna (lattice) size might be new, but I think this needs to be checked by looking at some of the 'missing' citations, as mentioned above.
Report
Requested changes
- The introduction focuses heavily on ENAQT in biological systems such as the FMO complex. Indeed, most of the references relate to studies of this complex, ignoring the vast number of studies on other - typically much larger - complexes such as LHII, LHI, Chlorosomes...given that several of these systems are much closer to the extended 2D lattice considered here, some of these other works should be cited and scanned for any similarities (methods, conclusions concering ENAQT) with the present work. Similarly, an oft-repeated fallacy is that the FMO complex has '100%' efficiency. It can actually be much lower - https://pubs.rsc.org/en/content/articlehtml/2023/cp/d3cp01321a (and refs therein)
As stated, the claims about 'coherence between distant aggregates persist...despite being subjected to noise' isn't true. The Authors should explain carefully what is meant by 'distant', and even by 'coherence ' (do they mean that exciton eigenstates are spread over several monomers, or the coherence between these extended states, as prepared by ultrafast pumping, 'persist'?).
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The authors should consider/comment if their results are in any way specific to the highly ordered arrangement of dipoles they use in their model. Real biomolecular aggregates often have misaligned dipoles - would random dipole-dipole (anisotropic) interaction make a difference? Also, given the key conclusions of this article revolve around the lattice size scaling, how does this depend on the range of the dipole interaction w.r.t. the lattice site separations?
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The Authors state some standard results for random walks on page 3. Are these quantum or classical walks? Given the existence in this work of both coherent and classical hopping, this is important. Please add clarifications and citations, particularly for the statement about tree-like networks. It should be noted that dissipative quantum walks on bio-like lattices have been studied before, including speed limits and various types of bound. The authors should check their findings against some of this material. For example ( & non-exhaustively):
https://pubs.rsc.org/en/content/articlelanding/2022/cp/d1cp02727a/unauth https://iopscience.iop.org/article/10.1088/1367-2630/12/6/065041/meta https://iopscience.iop.org/article/10.1088/0953-4075/44/18/184012/meta?casa_token=qtWond9LYDcAAAAA:kFyuUxMPjB5SfXpmkGtRuRLD5KUJB61Ryb0ZIS7t_Gu4NrMRJELy9pwZA26Hii-kh-lTkbcFwcctUJbYvIW27WiDLA https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.180601
Minor points: Intro mentions 'dark states' with explanation or citations. What are these?
Recommendation
Ask for major revision