SciPost Submission Page
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
Submission summary
| Authors (as registered SciPost users): | Carles Altimiras |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202506_00058v2 (pdf) |
| Data repository: | https://zenodo.org/records/15038602 |
| Date accepted: | Oct. 14, 2025 |
| Date submitted: | Oct. 8, 2025, 4:57 p.m. |
| Submitted by: | Carles Altimiras |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| 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 acts as a current source for the detection circuit 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
Author comments upon resubmission
List of changes
Answers to report #2: 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.
Answers to report #1: We thank the referees 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: Line 35: what we had in mind is that classically one could in principle track all the microscopic degrees of freedom of the physical system and predict the time evolution of a physical signal, which might otherwise look like a fluctuating stochastic signal to an observer not having this information. However, one cannot find such a causal origin to the time dependence of quantum fluctuating signals. Nevertheless, we agree with the referee this is not a standard definition, and decided to remove the reference to causality in the new version. Line 80: We implemented the suggested change, it now reads : “This perturbative expression …” Line 88: We implemented the suggested change, it now reads : “… into the detection circuit …” Abstract: We implemented the suggested change, it now reads : “… the conductor acts as a current source” Line 332: We implemented the suggested change, it now reads : “Expanding it to lowest order in…”
Published as SciPost Phys. 19, 127 (2025)