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  • Open Access

Electron-beam-induced quantum interference effects in a multilevel quantum emitter

H. B. Crispin* and N. Talebi†

  • *Contact author: crispin@physik.uni-kiel.de
  • †Contact author: talebi@physik.uni-kiel.de
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Phys. Rev. B 112, 045419 – Published 17 July, 2025

DOI: https://doi.org/10.1103/xtgl-vccr

Abstract

Cathodoluminescence spectroscopy has recently emerged as a novel platform for nanoscale control of nonclassical features of light. Here, we propose a theoretical model for cathodoluminescence from a multilevel quantum emitter. Employing a master equation approach and treating the electron-beam excitation as an incoherent broadband field source, we show that quantum interference can arise between the different relaxation pathways. The induced interference can significantly modify the time-dependent spectra resulting in the enhancement or suppression of cathodoluminescence. We find that the excitation rate, initial state of the emitter, and excited level spacing play a crucial role in determining the influence of interference. Our findings shed light on electron-beam-induced quantum interference in cathodoluminescence and provides a theoretical basis for exploring quantum optical phenomena in electron-driven multilevel systems.

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References (48)

  1. N. Talebi, Interaction of electron beams with optical nanostructures and metamaterials: from coherent photon sources towards shaping the wave function, J. Opt. 19, 103001 (2017); A. Polman, M. Kociak, and F. J. García de Abajo, Electron-beam spectroscopy for nanophotonics, Nat. Mater. 18, 1158 (2019); N. Talebi, Near-Field-Mediated Photon–Electron Interactions (Springer International Publishing, Berlin, 2019).
  2. P. A. Cherenkov, Visible light from clear liquids under the action of gamma radiation, Dokl. Akad. Nauk SSSR 2, 451 (1934); S. I. Vavilov, On possible causes of dark blue gamma radiation in liquids, ibid. 2, 457 (1934).
  3. V. L. Ginzburg and I. M. Frank, Radiation of a uniformly moving electron arising from its transition from one medium to another, Zh. Éksp. Teor. Fiz. 16, 15 (1946) [J. Phys. (USSR) 9, 353 (1945)].
  4. S. J. Smith and E. M. Purcell, Visible light from localized surface charges moving across a grating, Phys. Rev. 92, 1069 (1953).
  5. R. H. Ritchie, Plasma losses by fast electrons in thin films, Phys. Rev. 106, 874 (1957).
  6. T. Coenen and N. M. Haegel, Cathodoluminescence for the 21st century: Learning more from light, Appl. Phys. Rev. 4, 031103 (2017).
  7. C. Roques-Carmes, S. E. Kooi, Y. Yang, N. Rivera, P. D. Keathley, J. D. Joannopoulos, S. G. Johnson, I. Kaminer, K. K. Berggren, and M. Soljačić, Free-electron-light interactions in nanophotonics, Appl. Phys. Rev. 10, 011303 (2023).
  8. L. H. G. Tizei and M. Kociak, Spatially resolved quantum nano-optics of single photons using an electron microscope, Phys. Rev. Lett. 110, 153604 (2013).
  9. S. Meuret, L. H. G. Tizei, T. Cazimajou, R. Bourrellier, H. C. Chang, F. Treussart, and M. Kociak, Photon bunching in cathodoluminescence, Phys. Rev. Lett. 114, 197401 (2015).
  10. S. Meuret, T. Coenen, H. Zeijlemaker, M. Latzel, S. Christiansen, S. Conesa-Boj, and A. Polman, Photon bunching reveals single-electron cathodoluminescence excitation efficiency in InGaN quantum wells, Phys. Rev. B 96, 035308 (2017).
  11. S. Fiedler, S. Morozov, D. Komisar, E. A. Ekimov, L. F. Kulikova, V. A. Davydov, V. N. Agafonov, S. Kumar, C. Wolff, S. I. Bozhevolnyi, and N. A. Mortensen, Sub-to-super-Poissonian photon statistics in cathodoluminescence of color center ensembles in isolated diamond crystals, Nanophoton. 12, 2231 (2023).
  12. B. Lounis and M. Orrit, Single-photon sources, Rep. Prog. Phys. 68, 1129 (2005).
  13. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
  14. M. Solà-Garcia, K. W. Mauser, M. Liebtrau, T. Coenen, S. Christiansen, S. Meuret, and A. Polman, Photon statistics of incoherent cathodoluminescence with continuous and pulsed electron beams, ACS Photon. 8, 916 (2021).
  15. M. A. Feldman, E. F. Dumitrescu, D. Bridges, M. F. Chisholm, R. B. Davidson, P. G. Evans, J. A. Hachtel, A. Hu, R. C. Pooser, R. F. Haglund, and B. J. Lawrie, Colossal photon bunching in quasiparticle-mediated nanodiamond cathodoluminescence, Phys. Rev. B 97, 081404(R) (2018).
  16. S. Yanagimoto, N. Yamamoto, T. Sannomiya, and K. Akiba, Purcell effect of nitrogen-vacancy centers in nanodiamond coupled to propagating and localized surface plasmons revealed by photon-correlation cathodoluminescence, Phys. Rev. B 103, 205418 (2021).
  17. T. Yuge, N. Yamamoto, T. Sannomiya, and K. Akiba, Superbunching in cathodoluminescence: A master equation approach, Phys. Rev. B 107, 165303 (2023).
  18. M. Taleb, P. H. Bittorf, M. Black, M. Hentschel, W. Sigle, B. Haas, C. Koch, P. A. van Aken, H. Giessen, and N. Talebi, Ultrafast phonon-mediated dephasing of color centers in hexagonal boron nitride probed by electron beams, Nat. Commun. 16, 2326 (2025).
  19. X. Zhang, M. E. Turiansky, L. Razinkovas, M. Maciaszek, P. Broqvist, Q. Yan, J. L. Lyons, C. E. Dreyer, D. Wickramaratne, Á. Gali, A. Pasquarello, and C. G. Van de Walle, First-principles calculations of defects and electron–phonon interactions: Seminal contributions of audrius alkauskas to the understanding of recombination processes, J. Appl. Phys. 135, 150901 (2024).
  20. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  21. Z. Ficek and S. Swain, in Quantum Interference and Coherence, edited by W. T. Rhodes, T. Asakura, K.-H. Brenner, T. W. Hänsch, T. Kamiya, F. Krausz, B. Monemar, H. Venghaus, H. Weber, and H. Weinfurter (Springer-Verlag, Berlin, 2005), Vol. 100.
  22. Z. Mahfoud, A. T. Dijksman, C. Javaux, P. Bassoul, A.-L. Baudrion, J. Plain, B. Dubertret, and M. Kociak, Cathodoluminescence in a scanning transmission electron microscope: A nanometer-scale counterpart of photoluminescence for the study of II–VI quantum dots, J. Phys. Chem. Lett. 4, 4090 (2013).
  23. F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys. 82, 209 (2010).
  24. T. Coenen, B. J. Brenny, E. J. Vesseur, and A. Polman, Cathodoluminescence microscopy: Optical imaging and spectroscopy with deep-subwavelength resolution, MRS Bull. 40, 359 (2015).
  25. F. P. Laussy, E. del Valle, and C. Tejedor, Strong coupling of quantum dots in microcavities, Phys. Rev. Lett. 101, 083601 (2008).
  26. P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, Nonlinear photoluminescence spectra from a quantum-dot–cavity system: Interplay of pump-induced stimulated emission and anharmonic cavity QED, Phys. Rev. B 81, 033309 (2010).
  27. R. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer US, New York, 2011).
  28. A. Rothwarf, Plasmon theory of electron-hole pair production: efficiency of cathode ray phosphors, J. Appl. Phys. 44, 752 (1973).
  29. M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes, Opt. Commun. 87, 109 (1992).
  30. K. T. Kapale, M. O. Scully, S.-Y. Zhu, and M. S. Zubairy, Quenching of spontaneous emission through interference of incoherent pump processes, Phys. Rev. A 67, 023804 (2003).
  31. V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, Inducing quantum coherence via decays and incoherent pumping with application to population trapping, lasing without inversion, and quenching of spontaneous emission, Phys. Rev. A 74, 063829 (2006).
  32. M. Kiffner, M. Macovei, J. Evers, and C. H. Keitel, Vacuum-induced processes in multilevel atoms, Prog. Optics 55, 85 (2010).
  33. G. Adamo, J. Y. Ou, J. K. So, S. D. Jenkins, F. De Angelis, K. F. MacDonald, E. Di Fabrizio, J. Ruostekoski, and N. I. Zheludev, Electron-beam-driven collective-mode metamaterial light source, Phys. Rev. Lett. 109, 217401 (2012).
  34. G. Li, B. P. Clarke, J.-K. So, K. F. MacDonald, and N. I. Zheludev, Holographic free-electron light source, Nat. Commun. 7, 13705 (2016).
  35. J. Christopher, M. Taleb, A. Maity, M. Hentschel, H. Giessen, and N. Talebi, Electron-driven photon sources for correlative electron-photon spectroscopy with electron microscopes, Nanophoton. 9, 4381 (2020).
  36. N. Talebi, S. Meuret, S. Guo, M. Hentschel, A. Polman, H. Giessen, and P. A. van Aken, Merging transformation optics with electron-driven photon sources, Nat. Commun. 10, 599 (2019).
  37. N. van Nielen, M. Hentschel, N. Schilder, H. Giessen, A. Polman, and N. Talebi, Electrons generate self-complementary broadband vortex light beams using chiral photon sieves, Nano Lett. 20, 5975 (2020).
  38. J. H. Eberly and K. Wódkiewicz, The time-dependent physical spectrum of light, J. Opt. Soc. Am. 67, 1252 (1977).
  39. J. H. Eberly, C. V. Kunasz, and K. Wódkiewicz, Time-dependent spectrum of resonance fluorescence, J. Phys. B: At. Mol. Phys. 13, 217 (1980).
  40. S. Prawer and I. Aharonovich, Quantum Information Processing with Diamond: Principles and Applications (Elsevier, Amsterdam, 2014).
  41. M. Taleb, M. Hentschel, K. Rossnagel, H. Giessen, and N. Talebi, Phase-locked photon–electron interaction without a laser, Nat. Phys. 19, 869 (2023).
  42. J. E. Golub and T. W. Mossberg, Transient spectra of strong-field resonance fluorescence, Phys. Rev. Lett. 59, 2149 (1987).
  43. J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly, Theory of spontaneous-emission line shape in an ideal cavity, Phys. Rev. Lett. 51, 550 (1983).
  44. A. S. Jayarao, S. V. Lawande, and R. D'Souza, Time-dependent spectra of a strongly driven three-level atom, Phys. Rev. A 39, 3464 (1989).
  45. R. Román-Ancheyta, O. de los Santos-Sánchez, L. Horvath, and H. M. Castro-Beltrán, Time-dependent spectra of a three-level atom in the presence of electron shelving, Phys. Rev. A 98, 013820 (2018).
  46. D. Groll, T. Hahn, P. Machnikowski, D. Wigger, and T. Kuhn, Controlling photoluminescence spectra of hBN color centers by selective phonon-assisted excitation: a theoretical proposal, Mater. Quantum. Technol. 1, 015004 (2021).
  47. G. S. Agarwal and S. Menon, Quantum interferences and the question of thermodynamic equilibrium, Phys. Rev. A 63, 023818 (2001).
  48. M. Lax, Formal theory of quantum fluctuations from a driven state, Phys. Rev. 129, 2342 (1963).

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Phys. Rev. B 112, 045419– Published 17 July, 2025
  • Received 5 December 2024
  • Revised 22 April 2025
  • Accepted 26 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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