Abstract
Time-driven systems provide a framework for controlling waves through spatio-temporal modulation, which enables the synthesis of effective motion without mechanical displacement1,2,3,4,5,6,7. Within this framework, travelling-wave modulations can emulate moving media and give rise to phenomena such as Doppler-induced non-reciprocity8,9,10. A related effect is the extraction of energy from rotating media, which has been theoretically predicted to occur when waves experience sufficiently large rotational Doppler shifts11,12,13,14,15,16,17. Experimental access to this regime has remained limited due to the extreme rotation speeds required in mechanically rotating systems18,19,20,21. Here we show that Floquet-induced rotation enables access to such ultrafast rotational regimes using purely spatio-temporal modulation. When spinning at effective superluminal speeds, angular-momentum bandgaps emerge in the band structure of the underlying space–time crystal. These gaps host parametric processes that efficiently extract energy from the Floquet-rotating medium, resulting in angular-momentum-selective amplification of orbital waves within a dissipation-shaped spectral bandwidth. We realize this effect experimentally in a ring network of time-modulated resonators, where we observe a Floquet regime of rotational super-radiance mediated by non-Hermitian and parametric dynamics in space–time structured media. These results demonstrate a controllable platform for studying rotational energy transfer and angular-momentum-dependent wave amplification in space–time-modulated media.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$32.99 / 30 days
cancel any time
Subscribe to this journal
Receive 52 print issues and online access
$199.00 per year
only $3.83 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout
Data availability
All data supporting the findings of this study are available within the paper and the Supplementary Information and are available from the corresponding author upon request.
References
Galiffi, E. et al. Photonics of time-varying media. Adv. Photonics 4, 014002 (2022).
Engheta, N. Four-dimensional optics using time-varying metamaterials. Science 379, 1190–1191 (2023).
Jaffray, W. et al. Spatio-spectral optical fission in time-varying subwavelength layers. Nat. Photon. 19, 558–566 (2025).
Konforty, N. et al. Second harmonic generation and nonlinear frequency conversion in photonic time-crystals. Light Sci. Appl. 14, 152 (2025).
Ren, Y. et al. Observation of momentum-gap topology of light at temporal interfaces in a time-synthetic lattice. Nat. Commun. 16, 707 (2025).
Ozlu, M. G., Mkhitaryan, V., Fruhling, C. B., Boltasseva, A. & Shalaev, V. M. Floquet engineering of polaritonic amplification in dispersive photonic time crystals. Phys. Rev. Res. 7, 023214 (2025).
Moussa, H. et al. Observation of temporal reflection and broadband frequency translation at photonic time interfaces. Nat. Phys. 19, 863–868 (2023).
Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic transitions. Nat. Photon. 3, 91–94 (2009).
Estep, N. A., Sounas, D. L., Soric, J. & Alù, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. Nat. Phys. 10, 923–927 (2014).
Harwood, A. C. et al. Space-time optical diffraction from synthetic motion. Nat. Commun. 16, 5147 (2025).
Penrose, R. Gravitational collapse: the role of general relativity. Riv. Nuovo Cimento 1, 252–276 (1969).
Penrose, R. & Floyd, R. M. Extraction of rotational energy from a black hole. Nat. Phys. Sci. 229, 177–179 (1971).
Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973).
Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975).
Zel’dovich, Ya. B. Generation of waves by a rotating body. ZhETF Pis. Red. 14, 270–272 (1971).
Zel’dovich, Ya. B., Rozhanskij, L. V. & Starobinskii, A. A. Rotating bodies and electrodynamics in a rotating reference frame. Radiofizika 29, 1008–1016 (1986).
Zel’dovich, Ya. B. Amplification of cylindrical electromagnetic waves reflected from a rotating body. Sov. Phys. JETP 35, 1085–1087 (1972).
Torres, T. et al. Rotational superradiant scattering in a vortex flow. Nat. Phys. 13, 833–836 (2017).
Cromb, M. et al. Amplification of waves from a rotating body. Nat. Phys. 16, 1069–1073 (2020).
Braidotti, M. C. et al. Amplification of electromagnetic fields by a rotating body. Nat. Commun. 15, 5453 (2024).
Cromb, M., Braidotti, M. C., Vinante, A., Faccio, D. & Ulbricht, H. Creation of a black hole bomb instability in an electromagnetic system. Sci. Adv. 11, eadz4595 (2025).
Fante, R. Transmission of electromagnetic waves into time-varying media. IEEE Trans. Antennas Propag. 19, 417–424 (1971).
Wang, X. et al. Expanding momentum bandgaps in photonic time crystals through resonances. Nat. Photon. 19, 149–155 (2025).
Feis, J., Weidemann, S., Sheppard, T., Price, H. M. & Szameit, A. Space-time-topological events in photonic quantum walks. Nat. Photon. 19, 518–525 (2025).
Feinberg, J., Fernandes, D. E., Shapiro, B. & Silveirinha, M. G. Plasmonic time crystals. Phys. Rev. Lett. 134, 183801 (2025).
Nasari, H. et al. Observation of chiral state transfer without encircling an exceptional point. Nature 605, 256–261 (2022).
Shaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019).
Wang, X. et al. Metasurface-based realization of photonic time crystals. Sci. Adv. 9, eadg7541 (2023).
Park, J. et al. Spontaneous emission decay and excitation in photonic time crystals. Phys. Rev. Lett. 135, 133801 (2025).
Pacheco-Peña, V., Fink, M. & Engheta, N. Temporal chirp, temporal lensing, and temporal routing via space-time interfaces. Phys. Rev. B 111, L100306 (2025).
Liberal, I. & Manjavacas, A. Synthetic crystal rotation with spacetime metamaterials. Phys. Rev. Lett. 136, 146903 (2026).
Sounas, D. L., Caloz, C. & Alù, A. Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials. Nat. Commun. 4, 2407 (2013).
Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774–783 (2017).
Cassedy, E. S. & Oliner, A. A. Dispersion relations in time-space periodic media: Part I—Stable interactions. Proc. IEEE 51, 1342–1359 (1963).
Taravati, S., Chamanara, N. & Caloz, C. Nonreciprocal electromagnetic scattering from a periodically space–time modulated slab and application to a quasisonic isolator. Phys. Rev. B 96, 165144 (2017).
Noether, E. Invariante Variationsprobleme. Nachr. Ges. Wiss. Gött. Math. Kl. 1918, 235–257 (1918).
Lustig, E., Sharabi, Y. & Segev, M. Topological aspects of photonic time crystals. Optica 5, 1390 (2018).
Choquet-Bruhat, Y. General Relativity and Einstein’s Equations (Oxford Univ. Press, 2009).
Braidotti, M. C. et al. Measurement of Penrose superradiance in a photon superfluid. Phys. Rev. Lett. 128, 013901 (2022).
Reimann, R. et al. GHz Rotation of an optically trapped nanoparticle in vacuum. Phys. Rev. Lett. 121, 033602 (2018).
Bekenstein, J. D. & Schiffer, M. The many faces of superradiance. Phys. Rev. D 58, 064014 (1998).
Yu, D. et al. Comprehensive review on developments of synthetic dimensions. Photonics Insights 4, R06 (2025).
Gibson, G. M. et al. Reversal of orbital angular momentum arising from an extreme Doppler shift. Proc. Natl Acad. Sci. USA 115, 3800–3803 (2018).
Asgari, M. M. et al. Theory and applications of photonic time crystals: a tutorial. Adv. Opt. Photonics 16, 958–1063 (2024).
Khurgin, J. B. Photonic time crystals and parametric amplification: similarity and distinction. ACS Photonics 11, 2150–2159 (2024).
Maghrebi, M. F., Jaffe, R. L. & Kardar, M. Spontaneous emission by rotating objects: a scattering approach. Phys. Rev. Lett. 108, 230403 (2012).
Zhao, R., Manjavacas, A., García De Abajo, F. J. & Pendry, J. B. Rotational quantum friction. Phys. Rev. Lett. 109, 123604 (2012).
Oka, T. & Kitamura, S. Floquet engineering of quantum materials. Annu. Rev. Condens. Matter Phys. 10, 387–408 (2019).
Duggan, R., Mann, S. A. & Alù, A. Nonreciprocal photonic topological order driven by uniform optical pumping. Phys. Rev. B 102, 100303 (2020).
de Oliveira, M. & Ambrosio, A. Subcycle modulation of light’s orbital angular momentum via a Fourier space-time transformation. Sci. Adv. 11, eadr6678 (2025).
Lee, K. et al. Analogs of spontaneous emission and lasing in photonic time crystals. Phys. Rev. Lett. 136, 093802 (2026).
Funding
We acknowledge financial support from the Air Force Office of Scientific Research (Grant No. FA9550-25-1-0168 and SBIR Grant No. W911NF23C0025), the Science and Technology Center New Frontiers of Sound through the US National Science Foundation (Cooperative Agreement No. 2242925), the BARI programme (Grant No. N000142412779) and the Simons Foundation.
Author information
Authors and Affiliations
Contributions
H.N. and H.M. developed the theory in consultation with A.A. H.N. designed the circuit, conducted the numerical simulations and executed the measurements with contributions from H.M., Y.K. and A.T. Y.K. fabricated the circuit. H.N. and A.A. wrote the Article with input from all the authors. A.A. conceived the idea and supervised the project.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature thanks Daniele Faccio and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information (download PDF )
Supplementary sections 1–6, Figs. 1–8, Tables 1–3 and references.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Nasari, H., Moussa, H., Kasahara, Y. et al. Observation of Floquet rotational super-radiance. Nature (2026). https://doi.org/10.1038/s41586-026-10725-y
Received:
Accepted:
Published:
Version of record:
DOI: https://doi.org/10.1038/s41586-026-10725-y