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High-order above-threshold ionization by squeezed coherent light

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

  • *Contact author: milo@bih.net.ba

Phys. Rev. A 113, 043124 – Published 21 April, 2026

DOI: https://doi.org/10.1103/yrpf-r7p6

Abstract

Squeezed coherent quantum light is described by the complex squeeze parameter ζ=seiϑ and the coherent-state displacement parameter β=|β|eiϕβ. Our study of strong-field ionization [D. Habibović and D. B. Milošević, Phys. Rev. A 112, L051103 (2025)], which focused on bright squeezed vacuum quantum light with β=0 and s≫1, is extended to ionization by squeezed coherent light. It is shown that the amplitudes s and |β| strongly influence the ionization process, whereas phases ϑ and ϕβ play a less significant role. The present work provides a unified treatment of coherent, squeezed vacuum, and squeezed coherent light within a single theoretical framework. The quantum nature of the driving field is incorporated by averaging the strong-field ionization probability over the Husimi-Kano phase-space distribution. Using neon as a representative target, we analyze how the parameters characterizing squeezed coherent light modify photoelectron spectra and intensity-dependent enhancements. We show that nonclassical photon statistics can lead to a pronounced steepening of the rescattering plateau and, at low mean intensities, to an effective suppression of the nominal high-energy cutoff. These effects originate from the reduced weight of high-intensity field components inherent to squeezed states and have no analog in strong-field ionization driven by a coherent light. Our results highlight the potential for quantum-statistical control of strong-field ionization and provide a foundation for exploring laser-matter interactions driven by quantum light.

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References (56)

  1. U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, 30 years of squeezed light generation, Phys. Scr. 91, 053001 (2016).
  2. X. Heng, L. Zhang, Q. Yin, W. Liu, L. Tang, Y. Zhai, and K. Wei, Quantum-enhanced sensing with squeezed light: From fundamentals to applications, Appl. Sci. 15, 10179 (2025).
  3. R. Li, B. An, N. Jiao, J. Liu, L. Chen, Y. Wang, and Y. Zheng, Bright squeezed light in the kilohertz frequency band, Light: Sci. Appl. 14, 310 (2025).
  4. S. L. Braunstein and P. van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77, 513 (2005).
  5. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
  6. P. Agostini, Nobel Lecture: Genesis and applications of attosecond pulse trains, Rev. Mod. Phys. 96, 030501 (2024).
  7. F. Krausz, Nobel Lecture: Sub-atomic motions, Rev. Mod. Phys. 96, 030502 (2024).
  8. A. L' Huillier, Nobel Lecture: The route to attosecond pulses, Rev. Mod. Phys. 96, 030503 (2024).
  9. 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).
  10. 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).
  11. D. B. Milošević and F. Ehlotzky, Scattering and reaction processes in powerful laser fields, Adv. At. Mol. Opt. Phys. 49, 373 (2003).
  12. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, Above-threshold ionization by few-cycle pulses, J. Phys. B 39, R203 (2006).
  13. F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. 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).
  19. L. Cruz-Rodriguez, D. Dey, A. Freibert, and P. Stammer, Quantum phenomena in attosecond science, Nat. Rev. Phys. 6, 691 (2024).
  20. M. Sennary, J. Rivera-Dean, M. ElKabbash, V. Pervak, M. Lewenstein, and M. Th Hassan, Attosecond quantum uncertainty dynamics and ultrafast squeezed light for quantum communication, Light: Sci. Appl. 14, 350 (2025).
  21. 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).
  22. 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).
  23. 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).
  24. J. Heimerl, A. Rasputnyi, J. Pölloth, S. Meier, M. Chekhova, and P. Hommelhoff, Quantum light drives electrons strongly at metal needle tips, Nat. Phys. 21, 1899 (2025).
  25. D.-S. Guo and T. Åberg, Quantum electrodynamical approach to multiphoton ionisation in the high-intensity H field, J. Phys. A 21, 4577 (1988).
  26. D.-S. Guo and G. W. F. Drake, Stationary solutions for an electron in an intense laser field. I. Single-mode case, J. Phys. A 25, 3383 (1992).
  27. D. N. Makarov and V. I. Matveev, Ionization in a two-mode quantized electromagnetic field, Theor. Math. Phys. 191, 491 (2017).
  28. I. A. Gonoskov, G. A. Vugalter, and V. A. Mironov, Ionization in a quantized electromagnetic field, J. Exp. Theor. Phys. 105, 1119 (2007).
  29. P. R. Sharapova and O. V. Tikhonova, Dynamics of ionisation and entanglement in the “atom+quantum electromagnetic field” system, Quantum Electron. 42, 199 (2012).
  30. I. A. Burenkov and O. V. Tikhonova, Ionization and stabilization of an atom in a quantum electromagnetic field, JETP Lett. 97, 362 (2013).
  31. J. Rivera-Dean, P. Stammer, A. S. Maxwell, Th. 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).
  32. 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).
  33. 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).
  34. 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).
  35. D. Habibović and D. B. Milošević, Intensity-dependent enhancements in strong-field ionization by quantum light, Phys. Rev. A 112, L051103 (2025).
  36. J. Rivera-Dean, P. Stammer, C. Figueira de Morisson Faria, and M. Lewenstein, Microscopic analysis of above-threshold ionization driven by squeezed light, Phys. Rev. A 112, 063101 (2025).
  37. D. B. Milošević and W. Becker, Strong-field ionization by thermal light, Ann. Phys. (Berl.) 538, e00620 (2026).
  38. Y.-J. Mao, E.-R. Zhou, Y. Li, P.-L. He, and F. He, Benchmarking atomic ionization driven by strong quantum light, arXiv:2512.15458v1.
  39. 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).
  40. G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, Plateau in above threshold ionization spectra, Phys. Rev. Lett. 72, 2851 (1994).
  41. P. Hansch, M. A. Walker, and L. D. Van Woerkom, Resonant hot-electron production in above-threshold ionization, Phys. Rev. A 55, R2535 (1997).
  42. 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).
  43. 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).
  44. K. Krajewska, I. I. Fabrikant, and A. F. Starace, Threshold effects in strong-field detachment of H− and F−: Plateau enhancements and angular distribution variations, Phys. Rev. A 74, 053407 (2006).
  45. K. Krajewska, I. I. Fabrikant, and A. F. Starace, Threshold effects on plateau electron angular distributions in above-threshold detachment, Phys. Rev. A 78, 023407 (2008).
  46. K. Krajewska, I. I. Fabrikant, and A. F. Starace, Threshold effects in strong-field ionization: Energy shifts and Rydberg structures, Phys. Rev. A 86, 053410 (2012).
  47. S. Azizi, U. Saalmann, and J. M. Rost, Zero-energy photoelectric effect, Phys. Rev. Lett. 134, 103201 (2025).
  48. R. Loudon and P. L. Knight, Squeezed light, J. Mod. Opt. 34, 709 (1987).
  49. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, New York, 2000).
  50. W. P. Schleich, Quantum Optics in Phase Space (Wiley, New York, 2001).
  51. M. Scully and M. Zubairy, Quantum Optics (Cambridge University, Cambridge, England, 1997).
  52. D. B. Milošević and W. Becker, Improved strong-field approximation and quantum-orbit theory: Application to ionization by a bicircular laser field, Phys. Rev. A 93, 063418 (2016).
  53. 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).
  54. B. L. Schumaker and C. M. Caves, New formalism for two-photon quantum optics. II. Mathematical foundation and compact notation, Phys. Rev. A 31, 3093 (1985).
  55. 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).
  56. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).

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