Driving Quantum Heat Engines Beyond Classical Limits through Multilevel Coherence

Hui Wang; Marlan O. Scully; William J. Munro; Yusef Maleki

arxiv: 2604.04873 · v1 · submitted 2026-04-06 · 🪐 quant-ph

Driving Quantum Heat Engines Beyond Classical Limits through Multilevel Coherence

Hui Wang , Yusef Maleki , William J. Munro , Marlan O. Scully This is my paper

Pith reviewed 2026-05-10 18:52 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum heat enginesmultilevel coherenceeffective temperaturequantum thermodynamicscavity QEDthermodynamic control

0 comments

The pith

N-level ground-state coherence enables analytic tuning of effective temperature in quantum heat engines from near zero to divergence.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper sets out to show that coherence prepared across N levels in the ground state of an atom provides a controllable resource for setting the effective temperature seen by a cavity mode in a quantum heat engine. Analytic expressions are obtained that express this temperature directly in terms of the coherence parameters, allowing continuous variation from near-zero values up to divergence. The same expressions incorporate both ground-state and excited-state coherence as parts of one framework, so that their relative strengths determine whether the mode is heated, cooled, or left unaffected. A reader would care because the result supplies a single set of tunable knobs that can switch the thermodynamic behavior of the engine without altering the underlying temperatures or couplings.

Core claim

Analytic expressions for the effective engine temperature are derived using N-level ground-state coherence, demonstrating that the temperature can be driven continuously from near-zero to divergence by varying the coherence amplitudes and phases. Ground-state and excited-state coherence are placed inside one unified analytic framework whose interplay controls the net thermodynamic effect. The resulting description connects and generalizes earlier models of coherence-assisted quantum heat engines and identifies rubidium atoms as a system in which the predicted regimes can be tested.

What carries the argument

N-level ground-state coherence, which appears in the off-diagonal elements of the atomic density matrix and enters the master equation for the cavity mode to produce a modified effective thermal occupation number.

If this is right

The effective temperature of the engine becomes a direct function of the coherence parameters and can therefore be set to any value between near zero and divergence.
The engine can be switched at will among heating, cooling, and cancellation regimes by adjusting only the coherence.
Earlier treatments that considered ground-state coherence or excited-state coherence separately become special cases inside the single framework.
The same coherence resource can be applied to existing quantum heat engine proposals to extend their operating range.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Coherence preparation and stabilization techniques developed for this setting could be reused in other quantum thermal machines such as refrigerators to achieve similar mode switching.
The analytic expressions make it possible to design feedback loops that adjust coherence in real time to maintain a target effective temperature despite slow drifts in other parameters.
Experimental tests with rubidium would also reveal how the predicted divergence behaves when the number of levels N is increased beyond small values.

Load-bearing premise

The derivations assume that the prepared multilevel coherence persists long enough to influence the cavity dynamics before decoherence destroys it, and that the atom-cavity interaction follows the idealized quantum-optical model used to obtain the closed-form expressions.

What would settle it

A measurement of the cavity-mode effective temperature in a rubidium system with controlled N-level coherence that fails to follow the derived analytic formula, or that cannot reach the predicted low or high extremes, would falsify the tunability result.

Figures

Figures reproduced from arXiv: 2604.04873 by Hui Wang, Marlan O. Scully, William J. Munro, Yusef Maleki.

**Figure 2.** Figure 2: FIG. 2. Atomic configurations considered in this work. (a) Coher [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Quantum efficiency [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) Effective cavity temperature normalized to the bath tem [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

Quantum coherence provides a controllable thermodynamic resource that can raise or lower the effective temperature of a cavity mode, enabling efficiency tuning in quantum heat engines. Here, we derive analytic expressions for the effective engine temperature, demonstrating the enhanced temperature tunability achievable via $N$-level ground-state coherence. We further unify ground- and excited-state coherence within a single analytic framework, revealing their interplay as a mechanism for thermodynamic control. Such quantum resources serve as tunable parameters that enable switching between heating, cooling, and cancellation regimes, driving the effective temperature from near-zero to divergence. Ultimately, our framework connects and generalizes previous models of quantum heat engines, and we identify rubidium atoms as a promising candidate for experimentally realizing these coherence-assisted effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives closed-form expressions for how N-level ground-state coherence tunes a cavity's effective temperature from near zero to divergence while unifying it with excited-state effects, but the tunability assumes coherence survives without decay.

read the letter

The key takeaway is that this work derives analytic formulas for the effective temperature of a cavity mode driven by an N-level atom with ground-state coherence, showing it can be tuned from near zero up to divergence by adjusting the coherence strength and level number. It also folds excited-state coherence into the same framework. What stands out is the unification: earlier papers handled ground-state or excited-state coherence separately, but here they sit in one expression that lets you switch between heating, cooling, and nulling regimes. The N-level generalization is straightforward once you set up the density matrix, and they identify rubidium as a candidate system. The derivations appear careful for the closed-system steady state. They get explicit dependence of temperature on the off-diagonal elements, which is cleaner than many numerical studies in this area. The main limitation is the idealized treatment. The model keeps coherence as a fixed input without including dephasing rates or spontaneous emission from the multilevel system. If those are added back in, the steady-state coherence drops and the temperature range narrows sharply, as the stress-test suggests. For realistic Rb parameters, sustaining the required coherence over engine cycles looks challenging. This is worth a look for anyone modeling coherence as a thermodynamic resource. The analytic results give a clear picture of how multilevel effects scale, which is harder to see in more complicated simulations. I would send it for peer review. The unification and closed-form results are solid enough to merit referee feedback, even if the decoherence issue needs more discussion in revision.

Referee Report

2 major / 2 minor

Summary. The paper derives analytic expressions for the effective temperature of a cavity mode in a quantum heat engine, using N-level ground-state coherence as a controllable parameter to achieve tunability from near-zero values to divergence. It unifies ground- and excited-state coherence within a single framework, identifies regimes of heating, cooling, and cancellation, and proposes rubidium atoms as an experimental platform. The central claim is that multilevel coherence acts as a thermodynamic resource generalizing prior quantum heat engine models.

Significance. If the analytic derivations are robust, the work offers a parameter-free unification of coherence effects that could enable new control strategies in quantum thermodynamics beyond classical Carnot limits. The explicit connection to Rb atoms provides a falsifiable experimental target, strengthening the paper's impact if decoherence constraints are addressed.

major comments (2)

[Derivations of effective temperature (analytic expressions section)] The analytic expressions for effective cavity temperature (derived from the steady-state solution of the cavity-atom interaction Hamiltonian) treat N-level ground-state coherence amplitudes as sustained parameters without retaining dephasing or spontaneous-emission terms from the master equation. This assumption is load-bearing for the claimed divergence to infinite temperature and the full tunability range; restoring realistic decoherence rates for Rb D-line transitions would collapse the coherence and narrow the predicted temperature window.
[Framework unification paragraph] The unification of ground- and excited-state coherence is presented as generalizing previous models, but the manuscript does not provide an explicit comparison (e.g., reduction to known limits when N=2 or when coherence is set to zero) that would confirm the expressions are independent of self-referential assumptions.

minor comments (2)

[Abstract] The abstract states 'analytic derivations' but the main text should include at least one explicit equation for the effective temperature to allow immediate verification.
[Model definition] Notation for the multilevel density-matrix elements should be defined consistently when transitioning from the Hamiltonian to the steady-state solution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address the major comments point by point below, and have revised the manuscript to incorporate clarifications and additional discussions as needed.

read point-by-point responses

Referee: The analytic expressions for effective cavity temperature (derived from the steady-state solution of the cavity-atom interaction Hamiltonian) treat N-level ground-state coherence amplitudes as sustained parameters without retaining dephasing or spontaneous-emission terms from the master equation. This assumption is load-bearing for the claimed divergence to infinite temperature and the full tunability range; restoring realistic decoherence rates for Rb D-line transitions would collapse the coherence and narrow the predicted temperature window.

Authors: We agree that our analytic treatment assumes sustained N-level ground-state coherence amplitudes in the steady-state solution of the interaction Hamiltonian, which enables the derivation of the tunable effective temperature expressions including the divergence limit. This is an idealization to highlight the role of coherence as a thermodynamic resource. We acknowledge that a full master equation including dephasing and spontaneous emission would be necessary for quantitative predictions under realistic conditions. In the revised version, we have added a discussion on the decoherence rates for Rb D-line transitions, noting that while coherence lifetimes are finite, the predicted effects can still be observed in regimes where the coherence time exceeds the relevant dynamical timescales, thus partially addressing the narrowing of the temperature window. revision: partial
Referee: The unification of ground- and excited-state coherence is presented as generalizing previous models, but the manuscript does not provide an explicit comparison (e.g., reduction to known limits when N=2 or when coherence is set to zero) that would confirm the expressions are independent of self-referential assumptions.

Authors: We appreciate this observation. To demonstrate the consistency of our unified framework, we have included in the revised manuscript explicit reductions of the general expressions to the N=2 limit and to the zero-coherence case. These reductions recover the effective temperatures and efficiencies reported in prior two-level quantum heat engine models, confirming that our results are not self-referential and properly generalize the existing literature. revision: yes

Circularity Check

0 steps flagged

Analytic derivations treat coherence as an independent tunable parameter in the Hamiltonian; no reduction to fitted inputs or self-citation chains

full rationale

The paper derives effective temperature expressions by inserting N-level ground-state coherence (off-diagonal density-matrix elements) directly into the steady-state solution of an idealized cavity-atom Hamiltonian. This is a standard parametric model rather than a self-definitional loop: the coherence amplitude is an input variable whose value is varied to obtain tunability from near-zero to divergence. No equations are shown that fit coherence to the target temperature and then re-label the result a prediction. The unification of ground- and excited-state coherence is presented as an algebraic extension of prior models, not as a uniqueness theorem imported from the same authors' unverified work. The framework is therefore self-contained against external benchmarks once the coherence-preparation assumption is granted; the derivations do not collapse to their own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only, the central claim rests on standard quantum optical assumptions for cavity-atom interactions and coherence maintenance; no free parameters or invented entities are explicitly introduced in the provided text.

axioms (2)

standard math Standard quantum mechanics and open quantum system dynamics govern the cavity mode and atomic levels
Invoked implicitly to derive effective temperature expressions from coherence
domain assumption Multilevel coherence can be prepared and controlled without specifying decoherence rates
Required for the tunability and regime-switching claims to hold

pith-pipeline@v0.9.0 · 5421 in / 1248 out tokens · 44985 ms · 2026-05-10T18:52:21.819615+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

˙n_Q = α [N P_ee (n_Q+1) - ∑ P_gi gj n_Q]; n_Q = n / (1 + n ε_g + ε_g); T_Q = ħω / k_B ln[(1+ε_g)(1+1/n)]
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

unified four-level configuration with ε_g and ε_e as independent control parameters

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

[1]

(3), which is valid only in the weak-coupling regime

The saturation at finiteNresults from an overestimate of ¯nQ (and consequentlyT Q) by the approximate rate equation in Eq. (3), which is valid only in the weak-coupling regime. We note that to extend the analysis beyond this approximation, numerical analysis such as in Ref. [25] is required. FIG. 3. Quantum efficiencyη Q versusN. (a) Blue dashed, green so...

work page 2023
[2]

Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979)

R. Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979)

work page 1979
[3]

N. M. Myers, O. Abah, and S. Deffner, Quantum thermody- namic devices: From theoretical proposals to experimental re- ality, A VS quantum science4(2022)

work page 2022
[4]

L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Physics Reports1087, 1 (2024)

work page 2024
[5]

H. T. Quan, Y .-x. Liu, C. P. Sun, and F. Nori, Quantum ther- modynamic cycles and quantum heat engines, Phys. Rev. E76, 031105 (2007)

work page 2007
[6]

Horodecki, P

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of modern physics81, 865 (2009)

work page 2009
[7]

G ¨uhne and G

O. G ¨uhne and G. T ´oth, Entanglement detection, Physics Re- ports474, 1 (2009)

work page 2009
[8]

Baumgratz, M

T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying co- herence, Physical review letters113, 140401 (2014)

work page 2014
[9]

Streltsov, G

A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quan- tum coherence as a resource, Reviews of Modern Physics89, 041003 (2017)

work page 2017
[10]

Lostaglio, D

M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires con- straints beyond free energy, Nature communications6, 6383 (2015)

work page 2015
[11]

Vinjanampathy and J

S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemporary Physics57, 545 (2016)

work page 2016
[12]

M. O. Scully, M. S. Zubairy, G. S. Agarwal, and H. Walther, Extracting work from a single heat bath via vanishing quantum coherence, Science299, 862 (2003)

work page 2003
[13]

M. O. Scully, K. R. Chapin, K. E. Dorfman, M. B. Kim, and A. Svidzinsky, Quantum heat engine power can be in- creased by noise-induced coherence, Proceedings of the Na- tional Academy of Sciences108, 15097 (2011)

work page 2011
[14]

working fluid

D. Gelbwaser-Klimovsky, W. Niedenzu, P. Brumer, and G. Kur- izki, Power enhancement of heat engines via correlated ther- malization in a three-level “working fluid”, Scientific reports5, 14413 (2015)

work page 2015
[15]

K. E. Dorfman, D. V . V oronine, S. Mukamel, and M. O. Scully, Photosynthetic reaction center as a quantum heat en- gine, Proceedings of the National Academy of Sciences110, 2746 (2013)

work page 2013
[16]

Ferreri, H

A. Ferreri, H. Wang, F. Nori, F. K. Wilhelm, and D. E. Bruschi, Quantum heat engine based on quantum interferometry: The su(1,1) otto cycle, Phys. Rev. Research7, 013284 (2025)

work page 2025
[17]

Amato, C

F. Amato, C. Pellitteri, G. M. Palma, S. Lorenzo, and R. Lo Franco, Heating and cooling processes via phaseonium- driven dynamics of cascade systems, Physical Review A109, 043705 (2024)

work page 2024
[18]

J. W. Zhang, J. Q. Zhang, G. Y . Ding, J. C. Li, J. T. Bu, B. Wang, L. L. Yan, S. L. Su, L. Chen, F. Nori, c. K. ¨Ozdemir, F. Zhou, H. Jing, and M. Feng, Dynamical control of quantum heat en- gines using exceptional points, Nat. Commun.13, 6225 (2022)

work page 2022
[19]

M. O. Scully, Quantum photocell: Using quantum coherence to reduce radiative recombination and increase efficiency, Physi- cal review letters104, 207701 (2010)

work page 2010
[20]

A. A. Svidzinsky, K. E. Dorfman, and M. O. Scully, Enhancing photovoltaic power by fano-induced coherence, Physical Re- view A84, 053818 (2011)

work page 2011
[21]

Wertnik, A

M. Wertnik, A. Chin, F. Nori, and N. Lambert, Optimizing co- operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine, J. Chem. Phys.149, 084112 (2018)

work page 2018
[22]

A. ¨U. Hardal and ¨O. E. M ¨ustecaplıo˘glu, Superradiant quantum heat engine, Scientific reports5, 12953 (2015)

work page 2015
[23]

Kim, S.-h

J. Kim, S.-h. Oh, D. Yang, J. Kim, M. Lee, and K. An, A pho- tonic quantum engine driven by superradiance, Nature Photon- ics16, 707 (2022)

work page 2022
[24]

M. Kim, M. Scully, and A. Svidzinsky, A supercharged pho- tonic quantum heat engine, Nature Photonics16, 669 (2022)

work page 2022
[25]

Niedenzu, D

W. Niedenzu, D. Gelbwaser-Klimovsky, and G. Kurizki, Perfor- mance limits of multilevel and multipartite quantum heat ma- chines, Physical Review E92, 042123 (2015)

work page 2015
[26]

T ¨urkpenc ¸e and ¨O

D. T ¨urkpenc ¸e and ¨O. E. M ¨ustecaplıo˘glu, Quantum fuel with multilevel atomic coherence for ultrahigh specific work in a photonic carnot engine, Physical Review E93, 012145 (2016)

work page 2016
[27]

Meschede, H

D. Meschede, H. Walther, and G. M ¨uller, One-atom maser, Physical review letters54, 551 (1985)

work page 1985
[28]

M. O. Scully, S.-Y . Zhu, and A. Gavrielides, Degenerate quantum-beat laser: Lasing without inversion and inversion without lasing, Physical review letters62, 2813 (1989)

work page 1989
[29]

Kocharovskaya, Amplification and lasing without inversion, Physics Reports219, 175 (1992)

O. Kocharovskaya, Amplification and lasing without inversion, Physics Reports219, 175 (1992)

work page 1992
[30]

See Supplemental Material at [URL will be inserted by pub- lisher] for derivations and additional details

work page
[31]

Maruyama, F

K. Maruyama, F. Nori, and V . Vedral, The physics of maxwell’s demon and information, Rev. Mod. Phys.81, 1 (2009)

work page 2009
[32]

Leff and A

H. Leff and A. F. Rex,Maxwell’s Demon 2 Entropy, Classical and Quantum Information, Computing(CRC Press, 2002)

work page 2002
[33]

C. H. Bennett, Demons, engines and the second law, Scientific American257, 108 (1987)

work page 1987
[34]

Lloyd, Use of mutual information to decrease entropy: Impli- cations for the second law of thermodynamics, Physical Review A39, 5378 (1989)

S. Lloyd, Use of mutual information to decrease entropy: Impli- cations for the second law of thermodynamics, Physical Review A39, 5378 (1989)

work page 1989
[35]

Oberst, F

M. Oberst, F. Vewinger, and A. Lvovsky, Time-resolved prob- ing of the ground state coherence in rubidium, Optics letters32, 1755 (2007)

work page 2007
[36]

Jiang, H

X. Jiang, H. Zhang, and Y . Wang, Electromagnetically in- duced transparency in a zeeman-sublevelsλ-system of cold 87rb atoms in free space, Chinese Physics B25, 034204 (2016)

work page 2016
[37]

J. Lee, G. Vrijsen, I. Teper, O. Hosten, and M. A. Ka- sevich, Many-atom–cavity QED system with homogeneous atom–cavity coupling, Optics letters39, 4005 (2014) 6 I. SUPPLEMENTAL INFORMATION S1:ATOM-CA VITY INTERACTION HAMILTONIANS AND PHOTON NUMBER DYNAMICS We consider a cavity quantum electrodynamics (QED) setup where atoms interact with a single-mode ph...

work page 2014

[1] [1]

(3), which is valid only in the weak-coupling regime

The saturation at finiteNresults from an overestimate of ¯nQ (and consequentlyT Q) by the approximate rate equation in Eq. (3), which is valid only in the weak-coupling regime. We note that to extend the analysis beyond this approximation, numerical analysis such as in Ref. [25] is required. FIG. 3. Quantum efficiencyη Q versusN. (a) Blue dashed, green so...

work page 2023

[2] [2]

Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979)

R. Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979)

work page 1979

[3] [3]

N. M. Myers, O. Abah, and S. Deffner, Quantum thermody- namic devices: From theoretical proposals to experimental re- ality, A VS quantum science4(2022)

work page 2022

[4] [4]

L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Physics Reports1087, 1 (2024)

work page 2024

[5] [5]

H. T. Quan, Y .-x. Liu, C. P. Sun, and F. Nori, Quantum ther- modynamic cycles and quantum heat engines, Phys. Rev. E76, 031105 (2007)

work page 2007

[6] [6]

Horodecki, P

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of modern physics81, 865 (2009)

work page 2009

[7] [7]

G ¨uhne and G

O. G ¨uhne and G. T ´oth, Entanglement detection, Physics Re- ports474, 1 (2009)

work page 2009

[8] [8]

Baumgratz, M

T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying co- herence, Physical review letters113, 140401 (2014)

work page 2014

[9] [9]

Streltsov, G

A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quan- tum coherence as a resource, Reviews of Modern Physics89, 041003 (2017)

work page 2017

[10] [10]

Lostaglio, D

M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires con- straints beyond free energy, Nature communications6, 6383 (2015)

work page 2015

[11] [11]

Vinjanampathy and J

S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemporary Physics57, 545 (2016)

work page 2016

[12] [12]

M. O. Scully, M. S. Zubairy, G. S. Agarwal, and H. Walther, Extracting work from a single heat bath via vanishing quantum coherence, Science299, 862 (2003)

work page 2003

[13] [13]

M. O. Scully, K. R. Chapin, K. E. Dorfman, M. B. Kim, and A. Svidzinsky, Quantum heat engine power can be in- creased by noise-induced coherence, Proceedings of the Na- tional Academy of Sciences108, 15097 (2011)

work page 2011

[14] [14]

working fluid

D. Gelbwaser-Klimovsky, W. Niedenzu, P. Brumer, and G. Kur- izki, Power enhancement of heat engines via correlated ther- malization in a three-level “working fluid”, Scientific reports5, 14413 (2015)

work page 2015

[15] [15]

K. E. Dorfman, D. V . V oronine, S. Mukamel, and M. O. Scully, Photosynthetic reaction center as a quantum heat en- gine, Proceedings of the National Academy of Sciences110, 2746 (2013)

work page 2013

[16] [16]

Ferreri, H

A. Ferreri, H. Wang, F. Nori, F. K. Wilhelm, and D. E. Bruschi, Quantum heat engine based on quantum interferometry: The su(1,1) otto cycle, Phys. Rev. Research7, 013284 (2025)

work page 2025

[17] [17]

Amato, C

F. Amato, C. Pellitteri, G. M. Palma, S. Lorenzo, and R. Lo Franco, Heating and cooling processes via phaseonium- driven dynamics of cascade systems, Physical Review A109, 043705 (2024)

work page 2024

[18] [18]

J. W. Zhang, J. Q. Zhang, G. Y . Ding, J. C. Li, J. T. Bu, B. Wang, L. L. Yan, S. L. Su, L. Chen, F. Nori, c. K. ¨Ozdemir, F. Zhou, H. Jing, and M. Feng, Dynamical control of quantum heat en- gines using exceptional points, Nat. Commun.13, 6225 (2022)

work page 2022

[19] [19]

M. O. Scully, Quantum photocell: Using quantum coherence to reduce radiative recombination and increase efficiency, Physi- cal review letters104, 207701 (2010)

work page 2010

[20] [20]

A. A. Svidzinsky, K. E. Dorfman, and M. O. Scully, Enhancing photovoltaic power by fano-induced coherence, Physical Re- view A84, 053818 (2011)

work page 2011

[21] [21]

Wertnik, A

M. Wertnik, A. Chin, F. Nori, and N. Lambert, Optimizing co- operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine, J. Chem. Phys.149, 084112 (2018)

work page 2018

[22] [22]

A. ¨U. Hardal and ¨O. E. M ¨ustecaplıo˘glu, Superradiant quantum heat engine, Scientific reports5, 12953 (2015)

work page 2015

[23] [23]

Kim, S.-h

J. Kim, S.-h. Oh, D. Yang, J. Kim, M. Lee, and K. An, A pho- tonic quantum engine driven by superradiance, Nature Photon- ics16, 707 (2022)

work page 2022

[24] [24]

M. Kim, M. Scully, and A. Svidzinsky, A supercharged pho- tonic quantum heat engine, Nature Photonics16, 669 (2022)

work page 2022

[25] [25]

Niedenzu, D

W. Niedenzu, D. Gelbwaser-Klimovsky, and G. Kurizki, Perfor- mance limits of multilevel and multipartite quantum heat ma- chines, Physical Review E92, 042123 (2015)

work page 2015

[26] [26]

T ¨urkpenc ¸e and ¨O

D. T ¨urkpenc ¸e and ¨O. E. M ¨ustecaplıo˘glu, Quantum fuel with multilevel atomic coherence for ultrahigh specific work in a photonic carnot engine, Physical Review E93, 012145 (2016)

work page 2016

[27] [27]

Meschede, H

D. Meschede, H. Walther, and G. M ¨uller, One-atom maser, Physical review letters54, 551 (1985)

work page 1985

[28] [28]

M. O. Scully, S.-Y . Zhu, and A. Gavrielides, Degenerate quantum-beat laser: Lasing without inversion and inversion without lasing, Physical review letters62, 2813 (1989)

work page 1989

[29] [29]

Kocharovskaya, Amplification and lasing without inversion, Physics Reports219, 175 (1992)

O. Kocharovskaya, Amplification and lasing without inversion, Physics Reports219, 175 (1992)

work page 1992

[30] [30]

See Supplemental Material at [URL will be inserted by pub- lisher] for derivations and additional details

work page

[31] [31]

Maruyama, F

K. Maruyama, F. Nori, and V . Vedral, The physics of maxwell’s demon and information, Rev. Mod. Phys.81, 1 (2009)

work page 2009

[32] [32]

Leff and A

H. Leff and A. F. Rex,Maxwell’s Demon 2 Entropy, Classical and Quantum Information, Computing(CRC Press, 2002)

work page 2002

[33] [33]

C. H. Bennett, Demons, engines and the second law, Scientific American257, 108 (1987)

work page 1987

[34] [34]

Lloyd, Use of mutual information to decrease entropy: Impli- cations for the second law of thermodynamics, Physical Review A39, 5378 (1989)

S. Lloyd, Use of mutual information to decrease entropy: Impli- cations for the second law of thermodynamics, Physical Review A39, 5378 (1989)

work page 1989

[35] [35]

Oberst, F

M. Oberst, F. Vewinger, and A. Lvovsky, Time-resolved prob- ing of the ground state coherence in rubidium, Optics letters32, 1755 (2007)

work page 2007

[36] [36]

Jiang, H

X. Jiang, H. Zhang, and Y . Wang, Electromagnetically in- duced transparency in a zeeman-sublevelsλ-system of cold 87rb atoms in free space, Chinese Physics B25, 034204 (2016)

work page 2016

[37] [37]

J. Lee, G. Vrijsen, I. Teper, O. Hosten, and M. A. Ka- sevich, Many-atom–cavity QED system with homogeneous atom–cavity coupling, Optics letters39, 4005 (2014) 6 I. SUPPLEMENTAL INFORMATION S1:ATOM-CA VITY INTERACTION HAMILTONIANS AND PHOTON NUMBER DYNAMICS We consider a cavity quantum electrodynamics (QED) setup where atoms interact with a single-mode ph...

work page 2014