Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A photonic quantum engine driven by superradiance


Performance of nano- and microscale heat engines can be improved with the help of quantum-mechanical phenomena. Recently, heat reservoirs with quantum coherence have been proposed to enhance engine performance beyond the Carnot limit even with a single reservoir. However, no physical realizations have been achieved so far. Here we report the first proof-of-principle experimental demonstration of a photonic quantum engine driven by superradiance employing a single heat reservoir composed of atoms and photonic vacuum. Reservoir atoms prepared in a quantum coherent superposition state underwent superradiance as they traversed the cavity. This led to about 40-fold increase in the effective engine temperature, resulting in near-unity engine efficiency. Moreover, the observed engine output power grew quadratically with respect to the atomic injection rate. Our work can be utilized in quantum-mechanical heat transfer as well as in boosting engine powers, opening a pathway to the development of photomechanical devices that run on quantum coherence embedded in heat baths.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Engine cycle and the pressure–volume diagram of the superradiant quantum engine.
Fig. 2: Second-order correlation and enhanced engine power by superradiance.
Fig. 3: Effective engine temperature and observed engine efficiency.

Data availability

Source data are provided with this paper.

Code availability

The code that supports the findings of this study are available from the corresponding author upon reasonable request.


  1. Scovil, H. E. & Schulz-DuBois, E. O. Three-level masers as heat engines. Phys. Rev. Lett. 2, 262 (1959).

    Article  ADS  Google Scholar 

  2. Allahverdyan, A. E., Johal, R. S. & Mahler, G. Work extremum principle: structure and function of quantum heat engines. Phys. Rev. E 77, 041118 (2008).

    Article  ADS  Google Scholar 

  3. Zou, Y., Jiang, Y., Mei, Y., Guo, X. & Du, S. Quantum heat engine using electromagnetically induced transparency. Phys. Rev. Lett. 119, 050602 (2017).

    Article  ADS  Google Scholar 

  4. Ma, Y.-H., Xu, D., Dong, H. & Sun, C.-P. Universal constraint for efficiency and power of a low-dissipation heat engine. Phys. Rev. E 98, 042112 (2018).

    Article  ADS  Google Scholar 

  5. Klatzow, J. et al. Experimental demonstration of quantum effects in the operation of microscopic heat engines. Phys. Rev. Lett. 122, 110601 (2019).

    Article  ADS  Google Scholar 

  6. Von Lindenfels, D. et al. Spin heat engine coupled to a harmonic-oscillator flywheel. Phys. Rev. Lett. 123, 080602 (2019).

    Article  Google Scholar 

  7. Van Horne, N. et al. Single-atom energy-conversion device with a quantum load. npj Quantum Inf. 6, 37 (2020).

    Article  ADS  Google Scholar 

  8. Bouton, Q. et al. A quantum heat engine driven by atomic collisions. Nat. Commun. 12, 2063 (2021).

    Article  ADS  Google Scholar 

  9. Scully, M. O., Zubairy, M. S., Agarwal, G. S. & Walther, H. Extracting work from a single heat bath via vanishing quantum coherence. Science 299, 862–864 (2003).

    Article  ADS  Google Scholar 

  10. Huang, X., Wang, T. & Yi, X. et al. Effects of reservoir squeezing on quantum systems and work extraction. Phys. Rev. E 86, 051105 (2012).

    Article  ADS  Google Scholar 

  11. Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K. & Lutz, E. Nanoscale heat engine beyond the Carnot limit. Phys. Rev. Lett. 112, 030602 (2014).

    Article  ADS  Google Scholar 

  12. Dağ, C. B., Niedenzu, W., Müstecaplıoğlu, Ö. E. & Kurizki, G. Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines. Entropy 18, 244 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  13. Klaers, J., Faelt, S., Imamoglu, A. & Togan, E. Squeezed thermal reservoirs as a resource for a nanomechanical engine beyond the Carnot limit. Phys. Rev. X 7, 031044 (2017).

    Google Scholar 

  14. Peterson, J. P. et al. Experimental characterization of a spin quantum heat engine. Phys. Rev. Lett. 123, 240601 (2019).

    Article  ADS  Google Scholar 

  15. Scully, M. O., Chapin, K. R., Dorfman, K. E., Kim, M. B. & Svidzinsky, A. Quantum heat engine power can be increased by noise-induced coherence. Proc. Natl Acad. Sci. USA 108, 15097–15100 (2011).

    Article  ADS  Google Scholar 

  16. Gelbwaser-Klimovsky, D., Niedenzu, W., Brumer, P. & Kurizki, G. Power enhancement of heat engines via correlated thermalization in a three-level ‘working fluid’. Sci. Rep. 5, 14413 (2015).

    Article  ADS  Google Scholar 

  17. Wang, J., He, J. & Wu, Z. Efficiency at maximum power output of quantum heat engines under finite-time operation. Phys. Rev. E 85, 031145 (2012).

    Article  ADS  Google Scholar 

  18. Hardal, A. Ü. & Müstecaplıoğlu, Ö. E. Superradiant quantum heat engine. Sci. Rep. 5, 12953 (2015).

    Article  ADS  Google Scholar 

  19. Yamamoto, Y. & Imamoglu, A. Mesoscopic quantum optics. Mesoscopic Quantum Optics (1999).

  20. Niedenzu, W., Gelbwaser-Klimovsky, D., Kofman, A. G. & Kurizki, G. On the operation of machines powered by quantum non-thermal baths. New J. Phys. 18, 083012 (2016).

    Article  ADS  Google Scholar 

  21. Francica, G. et al. Quantum coherence and ergotropy. Phys. Rev. Lett. 125, 180603 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  22. Friedberg, R. & Manassah, J. Dicke states and Bloch states. Laser Phys. Lett. 4, 900 (2007).

    Article  ADS  Google Scholar 

  23. Le Kien, F., Scully, M. & Walther, H. Generation of a coherent state of the micromaser field. Found. Phys. 23, 177–184 (1993).

    Article  ADS  Google Scholar 

  24. Kim, J., Yang, D., Oh, S.-H & An, K. Coherent single-atom superradiance. Science 359, 662–666 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  25. Steck, D. A. Quantum and atom optics. (2007).

  26. Türkpençe, D. & Román-Ancheyta, R. Tailoring the thermalization time of a cavity field using distinct atomic reservoirs. J. Opt. Soc. Am. B 36, 1252–1259 (2019).

    Article  ADS  Google Scholar 

  27. Ma, Y.-H., Liu, C. & Sun, C. Works with quantum resource of coherence. Preprint at (2021).

  28. Liu, S. & Ou, C. Maximum power output of quantum heat engine with energy bath. Entropy 18, 205 (2016).

    Article  ADS  Google Scholar 

  29. Rodríguez-Rosario, C. A., Frauenheim, T. & Aspuru-Guzik, A. Thermodynamics of quantum coherence. Preprint at (2013).

  30. Ronzani, A. et al. Tunable photonic heat transport in a quantum heat valve. Nat. Phys. 14, 991–995 (2018).

    Article  Google Scholar 

  31. Lee, M. et al. Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array. Nat. Commun. 5, 3441 (2014).

    Article  ADS  Google Scholar 

  32. Yang, D. et al. Realization of superabsorption by time reversal of superradiance. Nat. Photon. 15, 272–276 (2021).

    Article  ADS  Google Scholar 

  33. Quan, H.-T., Liu, Y.-X, Sun, C.-P. & Nori, F. Quantum thermodynamic cycles and quantum heat engines. Phys. Rev. E 76, 031105 (2007).

    Article  ADS  MathSciNet  Google Scholar 

Download references


K.A. acknowledges financial support from the Korea Research Foundation (grant no. 2020R1A2C3009299) and the Ministry of Science and ICT of Korea under ITRC program (grand no. IITP-2021-2018-0-01402).

Author information

Authors and Affiliations



Jinuk Kim and K.A. conceived the experiment. Jinuk Kim performed the experiment with help from S.O. and analysed the data and carried out the theoretical investigations. K.A. supervised the overall experimental and theoretical works. Jinuk Kim and K.A. wrote the manuscript. All the authors participated in the analyses and discussions.

Corresponding author

Correspondence to Kyungwon An.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Marlan Scully and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 The pressure-volume diagram.

The pressure-volume diagram of the superradiant quantum engine. The radiation pressure is represented by the photon number. The x axis is the cavity resonance frequency, which is inversely proportional to the cavity mode volume.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5 and Notes 1–6.

Source data

Source Data Fig. 1

Statistical source data for Fig. 1

Source Data Fig. 2

Statistical source data for Fig. 2

Source Data Fig. 3

Statistical source data for Fig. 3

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kim, J., Oh, Sh., Yang, D. et al. A photonic quantum engine driven by superradiance. Nat. Photon. 16, 707–711 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing