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Proposal for an autonomous quantum heat engine
by Miika Rasola, Vasilii Vadimov, Tuomas Uusnäkki, Mikko Möttönen
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Miika Rasola · Vasilii Vadimov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2502.08359v4 (pdf) |
| Date submitted: | Aug. 22, 2025, 3:17 p.m. |
| Submitted by: | Miika Rasola |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We propose and theoretically analyse a superconducting electric circuit which can be used to experimentally realize an autonomous quantum heat engine. Using a quasiclassical, non-Markovian theoretical model, we demonstrate that coherent microwave power generation can emerge solely from the heat flow through the circuit determined by non-linear circuit quantum electrodynamics. The predicted energy generation rate is sufficiently high for experimental observation with contemporary techniques, rendering this work a significant step toward the first experimental realization of an autonomous quantum heat engine based on Otto cycles.
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
Main changes:
- Improved intuitive discussion and better schematics describing device and the dynamics in the introduction
- Added analysis about the limiting quality factors of the 'driving mode': when can the QHE start spontaneously vs. when will it stop working altogether
- Improved comparison with Otto cycle: added figures describing the thermodynamic cycle of the working fluid in (photon number, angular frequency) plane
- Fixed typos and misleading / confusing sentences
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-9-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2502.08359v4, delivered 2025-09-04, doi: 10.21468/SciPost.Report.11869
Report
Requested changes
1 - The authors to some degree address the comment on the quantum noise. A remaining technical question is to show there is no significant unphysical energy extraction from ZPF. If the quasiclassical equations were linear, this should work out automatically. As the authors reply, the results (plots) appear to indicate also the model here is OK, but the reason why and to what degree is not clear from the manuscript. Directly commenting on this question would be relevant in the manuscript, given that a heat engine at low temperatures is discussed.
E.g., at zero temperature, Eq. (23) seems to imply phi_s(t)^2 > 0 generally, so phi_b=const. is not exact solution to (24), hence P>0 in (29), although it may be small due to the time scale separation. The dissipation gamma_b is not associated with a Langevin term, so resonator B is damped by a classical T=0 bath, so there should always be energy flow out. Apparently, it is not significant, but some arguments should be given why.
2 - Eq. (22) has some typos, variable n is summation variable in LHS but also appears on RHS.
Recommendation
Ask for minor revision
Report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Miika Rasola on 2025-09-25 [id 5863]
(in reply to Report 2 on 2025-09-04)Comments by Referee #2:
1 - The authors to some degree address the comment on the quantum noise. A remaining technical question is to show there is no significant unphysical energy extraction from ZPF. If the quasiclassical equations were linear, this should work out automatically. As the authors reply, the results (plots) appear to indicate also the model here is OK, but the reason why and to what degree is not clear from the manuscript. Directly commenting on this question would be relevant in the manuscript, given that a heat engine at low temperatures is discussed.
E.g., at zero temperature, Eq. (23) seems to imply phi_s(t)^2 > 0 generally, so phi_b=const. is not exact solution to (24), hence P>0 in (29), although it may be small due to the time scale separation. The dissipation gamma_b is not associated with a Langevin term, so resonator B is damped by a classical T=0 bath, so there should always be energy flow out. Apparently, it is not significant, but some arguments should be given why.
Our response:
Within our model, the energy exchange between the resonators A and B is provided only by performing work on working mode A. We neglect the heat exchange, which is suppressed due to high frequency difference between the modes $\omega_\mathrm b \ll \omega_\mathrm a'$ . Therefore, the model may give zero output even though mode B is treated fully classically without account of quantum noise. We have added a brief clarification in the beginning of Sec. 3.3.
Equation (24) actually allows a zero output power solution $\phi_\mathrm b = const$ which physically corresponds to a dc current in the SQUID. This solution is not quite consistent with the ansatz (18), but we neglect all the off-resonant harmonics in the dynamics of slow mode B, including this one. In Eq. (29), the power is given by amplitude of resonant harmonic at frequency $\omega_\mathrm b$, the possible constant offset is not present in it. We have provided a more detailed discussion on approximations to Eq. (24) in the following paragraph.
Comments by Referee #2:
2 - Eq. (22) has some typos, variable n is summation variable in LHS but also appears on RHS.
Our response:
There is no summation in Eq. (22). The summation sign was a residual typo from earlier version of the Eq. Each equation is labeled by index $n$ as well each component of Green's function. We have removed the summation sign and added $n=0, \pm 1, \pm 2, \ldots$ in the equation to emphasize that it is a numbering, not summation index.