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Testing Kubo formula on a nonlinear quantum conductor driven far from equilibrium via power exchanges
by Zubair Iftikhar, Jonas Müller, Yuri Mukharsky, Philippe Joyez, Patrice Roche, Carles Altimiras
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Carles Altimiras |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202506_00058v1 (pdf) |
| Data repository: | https://zenodo.org/records/15038602 |
| Date submitted: | June 30, 2025, 11:07 a.m. |
| Submitted by: | Carles Altimiras |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Experimental |
Abstract
We present an experimental test of Kubo formula performed on a nonlinear quantum conductor, a Superconductor-Insulator-Superconductor tunnel junction, driven far from equilibrium by a DC voltage bias. We implement the proposal of Lesovik & Loosen [1] and demonstrate experimentally that it is possible to extract both the emission and absorption noise of the conductor by measuring the power it exchanges with a linear detection circuit whose occupation is tuned close to vacuum levels. We then compare their difference to the real part of the admittance which is independently measured by coherent reflectometry, finding that Kubo formula holds within experimental accuracy. Last, we show theoretically that the spectral density of power exchanged between a quantum conductor and its linear detection circuit follows a Lesovik & Loosen like formula, even in the presence of strong detection back-action. This result applies as long as the conductor is in the good current source limit and the detection circuit is not singular.
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 #2 by Anonymous (Referee 2) on 2025-7-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202506_00058v1, delivered 2025-07-29, doi: 10.21468/SciPost.Report.11659
Strengths
1) Clear goal of the research, experimental verification of a sound theoretical concept
Weaknesses
1) The manuscript needs proofreading and possibly some clarifications.
Report
Requested changes
I only have minor comments to the manuscript:
1) Where does Eq. (D.2) come from? It seems essential for calibration of the number of photons. Either a reference, or a hint at a derivation are needed.
2) A related question: A number of photons in Fig. D.3 is small and never exceeds 3. There is no problem with it per se as soon as the authors have enough points, but I guess the precision would be higher if a greater range of n would be used. Did the authors explore this (at different voltages)?
3) The manuscript must be proofread, there are quite some typos, and Refs. 3 and 56 are the same.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report #1 by Anonymous (Referee 1) on 2025-7-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202506_00058v1, delivered 2025-07-11, doi: 10.21468/SciPost.Report.11547
Strengths
- The emission from a superconducting circuit out of equilibrium is a timely topic.
- Investigating the fluctuation-dissipation relation in far-from-equilibrium regimes is relevant to a wide audience.
- The manuscript offers a nice interplay between theoretical and experimental results.
Report
Overall, the paper is clearly written, and the results are both timely and relevant. The manuscript easily meets the standards of the journal and should be accepted with only minor revisions.
Requested changes
I have only a few small things that I would like the authors to clarify:
- line 35: what do you mean with " the noise arising from quantum fluctuations is non-causal"? Causality is a concept that I do not really understand in the context of fluctuations...
- line 80: it is not clear what is ment by "This lower order expression is well justified". Do you mean "This approximate expression" or "This perturbative expression"?
- line 88: for clarity "coupled circuit" would be better called "detection circuit"
- in the abstract " in the good current source limit " is not completely clear; maybe "acts as a current source for the detection circuit"
- line 332: "Developing it to lowest" could be clearer formulated as "Expanding it to lowest"
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
We thank the referee for their positive report; their remarks contributed to improve the quality of the manuscript. We have implemented the requested changes in the resubmitted version.
Author: Carles Altimiras on 2025-10-08 [id 5903]
(in reply to Report 2 on 2025-07-29)We thank the referee for their positive report; their remarks contributed to improve the quality of the manuscript. We detail below how we addressed the specific comments and request:
1/ We agree with the referee the manuscript was missing a derivation of Eq. D.2. We have changed the first paragraph of section D.2.2 to provide it now.
2/ The referee is right that the absorption noise extracted from our protocol has a better precision when increasing the occupation number. This fact can be clearly seen in the data shown in Fig. 3, especially at low SIS biases. However, exploring larger occupations/NIN biases would not help much since i) the accuracy achieved for the absorption noise at the largest NIN bias is similar to the one we obtained for the emission noise. ii) the occupation numbers we used already provide a far better precision than our accuracy, which is limited by the spurious RF return losses neglected by our calibration protocol as stressed in section D.2.3. We added a sentence in line 542, clarifying that the occupation number shown in Figure D.3 is a prediction based on other measurements and calibrations.
3/ We corrected the problem with the references and proofread the manuscript thoroughly. We tried to correct the typos and the grammar as much as possible.