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  • Letter
  • Open Access

Intensity-dependent enhancements in strong-field ionization by quantum light

D. Habibović1 and D. B. Milošević1,2,*

  • *Contact author: milo@bih.net.ba

Phys. Rev. A 112, L051103 – Published 14 November, 2025

DOI: https://doi.org/10.1103/1fsq-ffsv

Abstract

We study strong-field ionization by quantum lights with emphasis on high-order above-threshold ionization and the intensity-dependent enhancements in the photoelectron spectra. We find that the length of the plateau in the photoelectron energy spectrum generated by such quantum lights can be extended by an order of magnitude in comparison with that generated by the classical coherent laser light and that within this plateau resonantly enhanced groups of sharp peaks appear at energies which are integer multiple of the photon energy. We relate the observed intensity-dependent enhancements to the channel closing effect. Our results are particularly interesting in the context of the recent interplay and merging of quantum optics with strong-field physics and attoscience.

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References (100)

  1. P. Salières, A. L' Huillier, P. Antoine, and M. Lewenstein, Study of the spatial and temporal coherence of high-order harmonics, Adv. At. Mol. Phys. 41, 83 (1999).
  2. W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, Above-threshold ionization: From classical features to quantum effects, Adv. At. Mol. Opt. Phys. 48, 35 (2002).
  3. D. B. Milošević and F. Ehlotzky, Scattering and reaction processes in powerful laser fields, Adv. At. Mol. Opt. Phys. 49, 373 (2003).
  4. A. Becker and F. H. M. Faisal, Intense field many-body S-matrix theory, J. Phys. B 38, R1 (2005).
  5. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, Above-threshold ionization by few-cycle pulses, J. Phys. B 39, R203 (2006).
  6. M. Lein, Molecular imaging using recolliding electrons, J. Phys. B 40, R135 (2007).
  7. C. Figueira de Morisson Faria and X. Liu, Electron-electron correlation in strong laser fields, J. Mod. Opt. 58, 1076 (2011).
  8. W. Becker, X. Liu, P. J. Ho, and J. H. Eberly, Theories of photoelectron correlation in laser-driven multiple atomic ionization, Rev. Mod. Phys. 84, 1011 (2012).
  9. M. C. Kohler, T. Pfeifer, K. Z. Hatsagortsyan, and C. H. Keitel, Frontiers of atomic high-harmonic generation, Adv. At. Mol. Opt. Phys. 61, 159 (2012).
  10. P. Agostini and L. F. DiMauro, Atomic and molecular ionization dynamics in strong laser fields: From optical to x-rays, Adv. At. Mol. Opt. Phys. 61, 117 (2012).
  11. S. V. Popruzhenko, Keldysh theory of strong field ionization: History, applications, difficulties and perspectives, J. Phys. B 47, 204001 (2014).
  12. B. Wolter, M. G. Pullen, M. Baudisch, M. Sclafani, M. Hemmer, A. Senftleben, C. D. Schröter, J. Ullrich, R. Moshammer, and J. Biegert, Strong-field physics with mid-IR fields, Phys. Rev. X 5, 021034 (2015).
  13. W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus, The plateau in above-threshold ionization: The keystone of rescattering physics, J. Phys. B 51, 162002 (2018).
  14. K. Amini, J. Biegert, F. Calegari, A. Chacón, M. F. Ciappina, A. Dauphin, D. K. Efimov, C. Figueira de Morisson Faria, K. Giergiel, P. Gniewek et al., Symphony on strong field approximation, Rep. Prog. Phys. 82, 116001 (2019).
  15. C. Figueira de Morrison Faria and A. S. Maxwell, It is all about phases: Ultrafast holographic photoelectron imaging, Rep. Prog. Phys. 83, 034401 (2020).
  16. S. Eckart, Strong field-induced quantum dynamics in atoms and small molecules, J. Phys. B 57, 202001 (2024).
  17. P. Agostini and L. F. DiMauro, The physics of attosecond light pulses, Rep. Prog. Phys. 67, 813 (2004); 67, 1563 (2004).
  18. A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, Attosecond physics, J. Phys. B 39, R1 (2006).
  19. F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
  20. A. S. Landsman and U. Keller, Attosecond science and the tunnelling time problem, Phys. Rep. 547, 1 (2015).
  21. R. Pazourek, S. Nagele, and J. Burgdörfer, Attosecond chronoscopy of photoemission, Rev. Mod. Phys. 87, 765 (2015).
  22. F. Calegari, G. Sansone, S. Stagira, C. Vozzi, and M. Nisoli, Advances in attosecond science, J. Phys. B 49, 062001 (2016).
  23. P. Agostini, Nobel lecture: Genesis and applications of attosecond pulse trains, Rev. Mod. Phys. 96, 030501 (2024).
  24. F. Krausz, Nobel lecture: Sub-atomic motions, Rev. Mod. Phys. 96, 030502 (2024).
  25. A. L' Huillier, Nobel lecture: The route to attosecond pulses, Rev. Mod. Phys. 96, 030503 (2024).
  26. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, New York, 2000).
  27. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  28. M. Scully and M. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  29. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, 2001).
  30. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases, J. Opt. Soc. Am. B 4, 595 (1987).
  31. M. Ferray, A. L' Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, Multiple-harmonic conversion of 1064 nm radiation in rare gases, J. Phys. B 21, L31 (1988).
  32. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, Free-free transitions following six-photon ionization of xenon atoms, Phys. Rev. Lett. 42, 1127 (1979).
  33. G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, Plateau in above threshold ionization spectra, Phys. Rev. Lett. 72, 2851 (1994).
  34. L. V. Keldysh, Ionization in the field of a strong electromagnetic wave, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
  35. A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, Ionization of atoms in an alternating electric field, Zh. Eksp. Teor. Fiz. 50, 1393 (1966) [Sov. Phys. JETP 23, 924 (1966)]
  36. F. H. M. Faisal, Multiple absorption of laser photons by atoms, J. Phys. B 6, L89 (1973).
  37. H. R. Reiss, Effect of an intense electromagnetic field on a weakly bound system, Phys. Rev. A 22, 1786 (1980).
  38. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A 49, 2117 (1994).
  39. W. Becker, A. Lohr, and M. Kleber, Effects of rescattering on above-threshold ionization, J. Phys. B 27, L325 (1994); 28, 1931 (1995).
  40. M. Lewenstein, K. C. Kulander, K. J. Schafer, and P. H. Bucksbaum, Rings in above-threshold ionization: A quasiclassical analysis, Phys. Rev. A 51, 1495 (1995).
  41. T. Rook, D. Habibović, L. Cruz Rodriguez, D. B. Milošević, and C. Figueira de Morisson Faria, Impact of the continuum Coulomb interaction in quantum-orbit-based treatments of high-order above-threshold ionization, Phys. Rev. A 109, 033115 (2024).
  42. A. Gorlach, O. Neufeld, N. Rivera, O. Cohen, and I. Kaminer, The quantum-optical nature of high harmonic generation, Nat. Commun. 11, 4598 (2020).
  43. M. Lewenstein, M. F. Ciappina, E. Pisanty, J. Rivera-Dean, P. Stammer, T. Lamprou, and P. Tzallas, Generation of optical Schrödinger cat states in intense laser–matter interactions, Nat. Phys. 17, 1104 (2021).
  44. P. Stammer, Theory of entanglement and measurement in high-order harmonic generation, Phys. Rev. A 106, L050402 (2022).
  45. P. Stammer, J. Rivera-Dean, T. Lamprou, E. Pisanty, M. F. Ciappina, P. Tzallas, and M. Lewenstein, High photon number entangled states and coherent state superposition from the extreme ultraviolet to the far infrared, Phys. Rev. Lett. 128, 123603 (2022).
  46. R. Dahan, G. Baranes, A. Gorlach, R. Ruimy, N. Rivera, and I. Kaminer, Creation of optical cat and GKP states using shaped free electrons, Phys. Rev. X 13, 031001 (2023).
  47. A. Gorlach, M. E. Tzur, M. Birk, M. Krüger, N. Rivera, O. Cohen, and I. Kaminer, High harmonic generation driven by quantum light, Nat. Phys. 19, 1689 (2023).
  48. U. Bhattacharya, T. Lamprou, A. S. Maxwell, A. Ordonez, E. Pisanty, J. Rivera-Dean, P. Stammer, M. F. Ciappina, M. Lewenstein, and P. Tzallas, Strong–laser–field physics, non–classical light states and quantum information science, Rep. Prog. Phys. 86, 094401 (2023).
  49. M. Khalaf and I. Kaminer, Compton scattering driven by intense quantum light, Sci. Adv. 9, eade0932 (2023).
  50. P. Stammer, J. Rivera-Dean, A. Maxwell, T. Lamprou, A. Ordóñez, M. F. Ciappina, P. Tzallas, and M. Lewenstein, Quantum electrodynamics of intense laser-matter interactions: A tool for quantum state engineering, PRX Quantum 4, 010201 (2023).
  51. P. Stammer, J. Rivera-Dean, A. S. Maxwell, T. Lamprou, J. Argüello-Luengo, P. Tzallas, M. F. Ciappina, and M. Lewenstein, Entanglement and squeezing of the optical field modes in high harmonic generation, Phys. Rev. Lett. 132, 143603 (2024).
  52. A. Rasputnyi, Z. Chen, M. Birk, O. Cohen, I. Kaminer, M. Krüger, D. Seletskiy, M. Chekhova, and F. Tani, High-harmonic generation by a bright squeezed vacuum, Nat. Phys. 20, 1960 (2024).
  53. C. S. Lange, T. Hansen, and L. B. Madsen, Electron-correlation-induced nonclassicality of light from high-order harmonic generation, Phys. Rev. A 109, 033110 (2024).
  54. E. S. Andrianov and O. I. Tolstikhin, Formation of nonclassical and non-Gaussian states of a strong electromagnetic field due to its interaction with free electrons produced by ionization of a target gas, Phys. Rev. A 110, 023115 (2024).
  55. W. Qin, A. F. Kockum, C. S. Muñoz, A. Miranowicz, and F. Nori, Quantum amplification and simulation of strong and ultrastrong coupling of light and matter, Phys. Rep. 1078, 1 (2024).
  56. M. E. Tzur, M. Birk, A. Gorlach, I. Kaminer, M. Krüger, and O. Cohen, Generation of squeezed high-order harmonics, Phys. Rev. Res. 6, 033079 (2024).
  57. S. J. Wang, S. G. Yu, X. Y. Lai, and X. J. Liu, High harmonic generation from an atom in a squeezed-vacuum environment, Phys. Rev. Res. 6, 033010 (2024).
  58. P. Stammer, Absence of quantum optical coherence in high harmonic generation, Phys. Rev. Res. 6, L032033 (2024).
  59. L. Cruz-Rodriguez, D. Dey, A. Freibert, and P. Stammer, Quantum phenomena in attosecond science, Nat. Rev. Phys. 6, 691 (2024).
  60. J. Heimerl, A. Mikhaylov, S. Meier, H. Höllerer, I. Kaminer, M. Chekhova, and P. Hommelhoff, Multiphoton electron emission with non-classical light, Nat. Phys. 20, 945 (2024).
  61. H. Laurell, S. Luo, R. Weissenbilder, M. Ammitzböll, S. Ahmed, H. Söderberg, C. Leon, M. Petersson, V. Poulain, C. Guo et al., Measuring the quantum state of photoelectrons, Nat. Photon. 19, 352 (2025).
  62. C. S. Lange and L. B. Madsen, Hierarchy of approximations for describing quantum light from high-harmonic generation: A Fermi-Hubbard-model study, Phys. Rev. A 111, 013113 (2025).
  63. Z. Lyu, F. Sun, Y. Fang, Q. He, and Y. Liu, Effect of photon quantum statistics on electrons in above-threshold ionization, Phys. Rev. Res. 7, L012072 (2025).
  64. S. Yi, N. D. Klimkin, G. G. Brown, O. Smirnova, S. Patchkovskii, I. Babushkin, and M. Ivanov, Generation of massively entangled bright states of light during harmonic generation in resonant media, Phys. Rev. X 15, 011023 (2025).
  65. Y.-B. Wang and X.-B. Bian, High-order harmonic generation in quantum light by a generalized von Neumann lattice method, Phys. Rev. A 111, 043111 (2025).
  66. S. Lemieux, S. A. Jalil, D. N. Purschke, N. Boroumand, T. J. Hammond, D. Villeneuve, A. Naumov, T. Brabec, and G. Vampa, Photon bunching in high-harmonic emission controlled by quantum light, Nat. Photon. 19, 767 (2025).
  67. J. Rivera-Dean, P. Stammer, A. S. Maxwell, T. Lamprou, P. Tzallas, M. Lewenstein, and M. F. Ciappina, Light-matter entanglement after above-threshold ionization processes in atoms, Phys. Rev. A 106, 063705 (2022).
  68. D. B. Milošević, Quantum theory of photon emission during strong-laser-field-induced ionization, Phys. Rev. A 108, 033110 (2023).
  69. M. E. Tzur, M. Birk, A. Gorlach, M. Krüger, I. Kaminer, and O. Cohen, Photon-statistics force in ultrafast electron dynamics, Nat. Photon. 17, 501 (2023).
  70. M. E. Tzur and O. Cohen, Motion of charged particles in bright squeezed vacuum, Light Sci. Appl. 13, 41 (2024).
  71. Y. Fang, F.-X. Sun, Q. He, and Y. Liu, Strong-field ionization of hydrogen atoms with quantum light, Phys. Rev. Lett. 130, 253201 (2023).
  72. S. J. Wang and X. Y. Lai, High-order above-threshold ionization of an atom in intense quantum light, Phys. Rev. A 108, 063101 (2023).
  73. U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, 30 years of squeezed light generation, Phys. Scr. 91, 053001 (2016).
  74. P. Hansch, M. A. Walker, and L. D. Van Woerkom, Resonant hot-electron production in above-threshold ionization, Phys. Rev. A 55, R2535 (1997).
  75. M. P. Hertlein, P. H. Bucksbaum, and H. G. Muller, Evidence for resonant effects in high-order ATI spectra, J. Phys. B 30, L197 (1997).
  76. M. J. Nandor, M. A. Walker, L. D. Van Woerkom, and H. G. Muller, Detailed comparison of above-threshold-ionization spectra from accurate numerical integrations and high-resolution measurements, Phys. Rev. A 60, R1771 (1999).
  77. E. Cormier, D. Garzella, P. Breger, P. Agostini, G. Chériaux, and C. Leblanc, Above-threshold ionization contrast and channel closure in argon, J. Phys. B 34, L9 (2001).
  78. G. G. Paulus, F. Grasbon, H. Walther, R. Kopold, and W. Becker, Channel-closing-induced resonances in the above-threshold ionization plateau, Phys. Rev. A 64, 021401(R) (2001).
  79. W. Quan, X. Lai, Y. Chen, C. Wang, Z. Hu, X. Liu, X. Hao, J. Chen, E. Hasović, M. Busuladžić, W. Becker, and D. J. Milošević, Resonancelike enhancement in high-order above-threshold ionization of molecules, Phys. Rev. A 88, 021401(R) (2013).
  80. E. S. Toma, P. Antoine, A. de Bohan, and H. G. Muller, Resonance-enhanced high-harmonic generation, J. Phys. B 32, 5843 (1999).
  81. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd ed., Course of Theoretical Physics, Vol. 3 (Butterworth-Heinemann, Amsterdam, 2005), Sec. 147.
  82. D. B. Milošević, E. Hasović, M. Busuladžić, A. Gazibegović-Busuladžić, and W. Becker, Intensity-dependent enhancements in high-order above-threshold ionization, Phys. Rev. A 76, 053410 (2007).
  83. D. B. Milošević and W. Becker, Channel-closing effects in strong-field ionization by a bicircular field, J. Phys. B 51, 054001 (2018).
  84. P. D. Drummond and C. W. Gardiner, Generalised P-representations in quantum optics, J. Phys. A: Math. Gen. 13, 2353 (1980).
  85. M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, Properties of squeezed number states and squeezed thermal states, Phys. Rev. A 40, 2494 (1989).
  86. Computational Strong-Field Quantum Dynamics: Intense Light-Matter Interactions, edited by D. Bauer (de Gruyter, Berlin, 2016).
  87. X. Y. Lai, C. Poli, H. Schomerus, and C. Figueira de Morisson Faria, Influence of the Coulomb potential on above-threshold ionization: A quantum-orbit analysis beyond the strong-field approximation, Phys. Rev. A 92, 043407 (2015).
  88. V. Tulsky and D. Bauer, Qprop with faster calculation of photoelectron spectra, Comput. Phys. Commun. 251, 107098 (2020).
  89. B. Fetić, M. Tunja, W. Becker, and D. B. Milošević, Extracting photoelectron spectra from the time-dependent wave function. II. Validation of two methods: Projection on plane waves and time-dependent surface flux, Phys. Rev. A 105, 053121 (2022).
  90. T. Rook, D. Habibović, and C. Figueira de Morisson Faria, Energy-conservation conditions in the saddle-point approximation for the strong-field ionization of atoms, Phys. Rev. A 111, 023107 (2025).
  91. D. B. Milošević, W. Becker, M. Okunishi, G. Prümper, K. Shimada, and K. Ueda, Strong-field electron spectra of rare-gas atoms in the rescattering regime: Enhanced spectral regions and a simulation of the experiment, J. Phys. B 43, 015401 (2010).
  92. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, Laser ionization of noble gases by Coulomb-barrier suppression, J. Opt. Soc. Am B 8, 858 (1991).
  93. L. F. DiMauro and P. Agostini, Ionization dynamics in strong laser fields, Adv. At. Mol. Opt. Phys. 35, 79 (1995).
  94. E. Hasović, M. Busuladžić, A. Gazibegović-Busuladžić, D. B. Milošević, and W. Becker, Simulation of above-threshold ionization experiments using the strong-field approximation, Laser Phys. 17, 376 (2007).
  95. The cutoff formula for the BSV light, 20Ip[Up0/(3ω)]2/3, proposed in [72], for our parameters gives the cutoff energy 85.3Up0, which is very close to our result 86.4Up0. However, for our example, presented in Fig. 4, this formula gives 103.4Up0, which is different from our result 86.6Up0 and the results in which the saturation effects are calculated numerically (see the red curve in Fig. 4).
  96. This cutoff is sharp since we cut the integral over the quantum field strength Eα0 at a fixed value determined by Isat. (The survival probability is suddenly set to zero for I>Isat. On the other hand, for the red line in Fig. 4, the results are obtained using a different method, which takes into account the atom survival probability for I>Isat and leads to a smooth decrease of the rate.)
  97. M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević, Off-axis low-energy structures in above-threshold ionization, Phys. Rev. A 90, 023412 (2014).
  98. J. Heimerl, A. Rasputnyi, J. Pölloth, S. Meier, M. Chekhova, and P. Hommelhoff, Quantum light drives electrons strongly at metal needle tips, Nat. Phys. (2025), doi:10.1038/s41567-025-03087-1.
  99. D. Habibović, K. R. Hamilton, O. Neufeld, and L. Rego, Emerging tailored light sources for studying chirality and symmetry, Nat. Rev. Phys. 6, 663 (2024).
  100. D. Habibović and D. B. Milošević, Complete classification and additional saddle-point solutions for high-order above-threshold ionization induced by a strong laser field. III. Two-component fields, Phys. Rev. A 112, 043114 (2025).

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