Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Open Access

Spontaneous Emission Decay and Excitation in Photonic Time Crystals

Jagang Park1,*, Kyungmin Lee2,*, Ruo-Yang Zhang3, Hee-Chul Park4, Jung-Wan Ryu5, Gil Young Cho6, Min Yeul Lee7, Zhaoqing Zhang3, Namkyoo Park8 et al.

Wonju Jeon9, Jonghwa Shin7, C. T. Chan3, and Bumki Min2,†

  • *These authors contributed equally to this work.
  • †Contact author: bmin@kaist.ac.kr

Phys. Rev. Lett. 135, 133801 – Published 22 September, 2025

DOI: https://doi.org/10.1103/5v2w-yg7v

Abstract

Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.

View figure in article

Physics Subject Headings (PhySH)

Viewpoint

Controlling Light Emission with Photonic Time Crystals

Published 22 September, 2025

A material whose dielectric properties vary in time could produce exotic light-emission phenomena in a nearby atom, theorists predict.

See more in Physics

Article Text

Supplemental Material

References (60)

  1. F. R. Morgenthaler, Velocity modulation of electromagnetic waves, IRE Trans. Microwave Theory Tech. 6, 167 (1958).
  2. D. Holberg and K. Kunz, Parametric properties of fields in a slab of time-varying permittivity, IEEE Trans. Antennas Propag. 14, 183 (1966).
  3. E. S. Cassedy, Dispersion relations in time-space periodic media: Part II—Unstable interactions, Proc. IEEE 55, 1154 (1967).
  4. R. Fante, Transmission of electromagnetic waves into time-varying media, IEEE Trans. Antennas Propag. 19, 417 (1971).
  5. L. Felsen and G. Whitman, Wave propagation in time-varying media, IEEE Trans. Antennas Propag. 18, 242 (1970).
  6. J. R. Reyes-Ayona and P. Halevi, Observation of genuine wave vector (k or β) gap in a dynamic transmission line and temporal photonic crystals, Appl. Phys. Lett. 107, 074101 (2015).
  7. N. Chamanara, Z. L. Deck-Léger, C. Caloz, and D. Kalluri, Unusual electromagnetic modes in space-time-modulated dispersion-engineered media, Phys. Rev. A 97, 063829 (2018).
  8. M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces, Nat. Commun. 10, 1345 (2019).
  9. E. Galiffi, P. A. Huidobro, and J. B. Pendry, Broadband nonreciprocal amplification in luminal metamaterials, Phys. Rev. Lett. 123, 206101 (2019).
  10. V. Pacheco-Peña and N. Engheta, Effective medium concept in temporal metamaterials, Nanophotonics 9, 379 (2020).
  11. J. Park and B. Min, Spatiotemporal plane wave expansion method for arbitrary space–time periodic photonic media, Opt. Lett. 46, 484 (2021).
  12. S. Lee, J. Park, H. Cho, Y. Wang, B. Kim, C. Daraio, and B. Min, Parametric oscillation of electromagnetic waves in momentum band gaps of a spatiotemporal crystal, Photonics Res. 9, 142 (2021).
  13. D. L. Sounas and A. Alù, Non-reciprocal photonics based on time modulation, Nat. Photonics 11, 774 (2017).
  14. X. Wang, M. S. Mirmoosa, V. S. Asadchy, C. Rockstuhl, S. Fan, and S. A. Tretyakov, Metasurface-based realization of photonic time crystals, Sci. Adv. 9, eadg7541 (2023).
  15. J. Park, H. Cho, S. Lee, K. Lee, K. Lee, H. C. Park, J.-W. Ryu, N. Park, S. Jeon, and B. Min, Revealing non-Hermitian band structure of photonic floquet media, Sci. Adv. 8, eabo6220 (2022).
  16. N. Chamanara, D. G. Cooke, and C. Caloz, Linear pulse compansion based on space-time modulation, in Proceedings of the 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (2019), pp. 239–240.
  17. S. A. R. Horsley and J. B. Pendry, Quantum electrodynamics of time-varying gratings, Proc. Natl. Acad. Sci. U.S.A. 120, e2302652120 (2023).
  18. F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109, 160401 (2012).
  19. A. Shapere and F. Wilczek, Classical time crystals, Phys. Rev. Lett. 109, 160402 (2012).
  20. J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-Gonzalez, Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function, Phys. Rev. A 79, 053821 (2009).
  21. M. Salem and C. Caloz, Temporal photonic crystals: Causality versus periodicity, in Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications (ICEAA) (IEEE, New York, 2015), pp. 490–493.
  22. J. S. Martínez-Romero, O. M. Becerra-Fuentes, and P. Halevi, Temporal photonic crystals with modulations of both permittivity and permeability, Phys. Rev. A 93, 063813 (2016).
  23. J. S. Martínez-Romero and P. Halevi, Parametric resonances in a temporal photonic crystal slab, Phys. Rev. A 98, 053852 (2018).
  24. N. Wang, Z.-Q. Zhang, and C. T. Chan, Photonic floquet media with a complex time-periodic permittivity, Phys. Rev. B 98, 085142 (2018).
  25. Y.-X. Wang and A. A. Clerk, Non-Hermitian dynamics without dissipation in quantum systems, Phys. Rev. A 99, 063834 (2019).
  26. M. Lyubarov, Y. Lumer, A. Dikopoltsev, E. Lustig, Y. Sharabi, and M. Segev, Amplified emission and lasing in photonic time crystals, Science 377, 425 (2022).
  27. S. Franke, J. Ren, M. Richter, A. Knorr, and S. Hughes, Fermi’s golden rule for spontaneous emission in absorptive and amplifying media, Phys. Rev. Lett. 127, 013602 (2021).
  28. J. Ren, S. Franke, B. VanDrunen, and S. Hughes, Classical purcell factors and spontaneous emission decay rates in a linear gain medium, Phys. Rev. A 109, 013513 (2024).
  29. J. Ren, S. Franke, and S. Hughes, Quasinormal modes, local density of states, and classical purcell factors for coupled loss-gain resonators, Phys. Rev. X 11, 041020 (2021).
  30. A. A. Vyshnevyy, Gain-dependent purcell enhancement, breakdown of Einstein’s relations, and superradiance in nanolasers, Phys. Rev. B 105, 085116 (2022).
  31. O. Scarlatella, A. A. Clerk, and M. Schiro, Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator, New J. Phys. 21, 043040 (2019).
  32. K. Petermann, Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding, IEEE J. Quantum Electron. 15, 566 (1979).
  33. M. V. Berry, Mode degeneracies and the Petermann excess-noise factor for unstable lasers, J. Mod. Opt. 50, 63 (2003).
  34. J. Zhang, B. Peng, Ş. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y.-x. Liu, S. Rotter, and L. Yang, A phonon laser operating at an exceptional point, Nat. Photonics 12, 479 (2018).
  35. H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Petermann-factor sensitivity limit near an exceptional point in a brillouin ring laser gyroscope, Nat. Commun. 11, 1610 (2020).
  36. P. W. Milonni and W. A. Smith, Radiation reaction and vacuum fluctuations in spontaneous emission, Phys. Rev. A 11, 814 (1975).
  37. J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities, IEEE J. Quantum Electron. 35, 1168 (1999).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/5v2w-yg7v for derivations of the dyadic Green’s function, kDOS formulation and decomposition, proof of pseudo-Hermiticity, driven Lorentz oscillator analysis, nonorthogonality of Floquet eigenmodes, and kDOS at exceptional points.
  39. A. Pick, B. Zhen, O. D. Miller, C. W. Hsu, F. Hernandez, A. W. Rodriguez, M. Soljačić, and S. G. Johnson, General theory of spontaneous emission near exceptional points, Opt. Express 25, 12325 (2017).
  40. L. Ferrier, P. Bouteyre, A. Pick, S. Cueff, N. H. M. Dang, C. Diederichs, A. Belarouci, T. Benyattou, J. X. Zhao, R. Su, J. Xing, Q. Xiong, and H. S. Nguyen, Unveiling the enhancement of spontaneous emission at exceptional points, Phys. Rev. Lett. 129, 083602 (2022).
  41. P. Garg, J. D. Fischbach, A. G. Lamprianidis, X. Wang, M. S. Mirmoosa, V. S. Asadchy, C. Rockstuhl, and T. J. Sturges, Inverse-designed dispersive time-varying nanostructures, Adv. Opt. Mater. 13, 2402444 (2025).
  42. M. M. Sadafi, A. F. da Mota, and H. Mosallaei, Time-varying Mie resonators for real-time manipulation of quantum emitter radiation, Phys. Rev. B 111, 125419 (2025).
  43. V. P. Bykov, Spontaneous emission in a periodic structure, Sov. J. Exp. Theor. Phys. 35, 269 (1972), https://scholar.google.com/scholar?q=Spontaneous+Emission+in+a+Periodic+Structure&hl=ko&as_sdt=0%2C5&as_ylo=&as_yhi=1973.
  44. V. P. Bykov, Spontaneous emission from a medium with a band spectrum, Sov. J. Quantum Electron. 4, 861 (1975).
  45. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett. 58, 2059 (1987).
  46. J. Joannopoulos, P. R. Villeneuve, and S. Fan, Photonic crystals, Solid State Commun. 102, 165 (1997).
  47. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, High extraction efficiency of spontaneous emission from slabs of photonic crystals, Phys. Rev. Lett. 78, 3294 (1997).
  48. E. P. Petrov, V. N. Bogomolov, I. I. Kalosha, and S. V. Gaponenko, Spontaneous emission of organic molecules embedded in a photonic crystal, Phys. Rev. Lett. 81, 77 (1998).
  49. M. Boroditsky, R. Vrijen, R. Coccioli, R. Bhat, and E. Yablonovitch, Spontaneous emission extraction and purcell enhancement from thin-film 2-d photonic crystals, J. Lightwave Technol. 17, 2096 (1999).
  50. Z.-Y. Li, L.-L. Lin, and Z.-Q. Zhang, Spontaneous emission from photonic crystals: Full vectorial calculations, Phys. Rev. Lett. 84, 4341 (2000).
  51. P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals, Nature (London) 430, 654 (2004).
  52. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal, Phys. Rev. Lett. 95, 013904 (2005).
  53. H. Altug, D. Englund, and J. Vučković, Ultrafast photonic crystal nanocavity laser, Nat. Phys. 2, 484 (2006).
  54. G. Lecamp, P. Lalanne, and J. P. Hugonin, Very large spontaneous-emission β factors in photonic-crystal waveguides, Phys. Rev. Lett. 99, 023902 (2007).
  55. S. Noda, M. Fujita, and T. Asano, Spontaneous-emission control by photonic crystals and nanocavities, Nat. Photonics 1, 449 (2007).
  56. V. S. C. Manga Rao and S. Hughes, Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient “on chip” single photon gun, Phys. Rev. Lett. 99, 193901 (2007).
  57. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, England, 2012).
  58. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators, Phys. Rev. Lett. 110, 237401 (2013).
  59. Z. Lin, A. Pick, M. Lončar, and A. W. Rodriguez, Enhanced spontaneous emission at third-order dirac exceptional points in inverse-designed photonic crystals, Phys. Rev. Lett. 117, 107402 (2016).
  60. W. L. Barnes, S. A. Horsley, and W. L. Vos, Classical antennas, quantum emitters, and densities of optical states, J. Opt. 22, 073501 (2020).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation