- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

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
  • Open Access

Role of quantum dynamics in coherent and incoherent radiation during tunneling ionization

Michael Klaiber*, Karen Z. Hatsagortsyan†, and Christoph H. Keitel

  • *Contact author: klaiber@mpi-hd.mpg.de
  • †Contact author: k.hatsagortsyan@mpi-hd.mpg.de
PDF

Phys. Rev. A 113, 033110 – Published 12 March, 2026

DOI: https://doi.org/10.1103/dwsm-lt6x

Abstract

Radiation during strong-field tunneling ionization is investigated. The spontaneous as well as the coherent components of the radiation are calculated describing the ionization dynamics via the strong-field approximation, and the role of the quantum dynamics at tunneling is analyzed. The competition between different mechanisms in different spectral regions is examined. Transitionlike radiation (Brunel radiation) is dominant at low frequencies, Thomson scattering at the laser frequency, and radiative recombination via the three-step process at high-order harmonics. To distinguish the role of the quantum dynamics, simple man Drude models are developed for coherent as well as for spontaneous radiation; the models are based on the electron trajectory out of the tunneling barrier. The quantum dynamics is shown to modify the coherent Brunel radiation for near-zero frequencies in asymmetric laser pulses. The significant role of free-free transitions is demonstrated for spontaneous radiation in the low-frequency region.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. P. B. Corkum, Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
  2. 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: At., Mol. Opt. Phys. 21, L31 (1988).
  3. 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).
  4. P. Agostini and L. F. DiMauro, The physics of attosecond light pulses, Rep. Prog. Phys. 67, 813 (2004).
  5. M. C. Kohler, C. Ott, P. Raith, R. Heck, I. Schlegel, C. H. Keitel, and T. Pfeifer, High harmonic generation via continuum wave-packet interference, Phys. Rev. Lett. 105, 203902 (2010).
  6. P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces, Phys. Rev. E 69, 066415 (2004).
  7. K. Kim, A. Taylor, J. Glownia, and G. Rodriguez, Coherent control of terahertz supercontinuum generation in ultrafast laser–gas interactions, Nat. Photonics 2, 605 (2008).
  8. K.-Y. Kim, Generation of coherent terahertz radiation in ultrafast laser-gas interactions, Phys. Plasmas 16, 056706 (2009).
  9. J. Dai, N. Karpowicz, and X.-C. Zhang, Coherent polarization control of terahertz waves generated from two-color laser-induced gas plasma, Phys. Rev. Lett. 103, 023001 (2009).
  10. H. Wen and A. M. Lindenberg, Coherent terahertz polarization control through manipulation of electron trajectories, Phys. Rev. Lett. 103, 023902 (2009).
  11. I. Babushkin, S. Skupin, and J. Herrmann, Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides, Opt. Express 18, 9658 (2010).
  12. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases, Phys. Rev. Lett. 105, 053903 (2010).
  13. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, Tailoring terahertz radiation by controlling tunnel photoionization events in gases, New J. Phys. 13, 123029 (2011).
  14. Y. S. You, T. I. Oh, and K. Y. Kim, Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments, Phys. Rev. Lett. 109, 183902 (2012).
  15. M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguére, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, Wavelength scaling of terahertz generation by gas ionization, Phys. Rev. Lett. 110, 253901 (2013).
  16. T. Balciunas, A. Verhoef, A. Mitrofanov, G. Fan, E. Serebryannikov, M. Ivanov, A. Zheltikov, and A. Baltuska, Optical and thz signatures of sub-cycle tunneling dynamics, Chem. Phys. 414, 92 (2013).
  17. T. I. Oh, Y. J. Yoo, Y. S. You, and K. Y. Kim, Generation of strong terahertz fields exceeding 8 MV/cm at 1 kHz and real-time beam profiling, Appl. Phys. Lett. 105, 041103 (2014).
  18. N. V. Vvedenskii, A. I. Korytin, V. A. Kostin, A. A. Murzanev, A. A. Silaev, and A. N. Stepanov, Two-color laser-plasma generation of terahertz radiation using a frequency-tunable half harmonic of a femtosecond pulse, Phys. Rev. Lett. 112, 055004 (2014).
  19. V. A. Tulsky, M. Baghery, U. Saalmann, and S. V. Popruzhenko, Boosting terahertz-radiation power with two-color circularly polarized midinfrared laser pulses, Phys. Rev. A 98, 053415 (2018).
  20. I. Babushkin, C. Bree, C. M. Dietrich, A. Demircan, U. Morgner, and A. Husakou, Terahertz and higher-order brunel harmonics: From tunnel to multiphoton ionization regime in tailored fields, J. Mod. Opt. 64, 1078 (2017).
  21. I. Babushkin, Á. J. Galán, J. R. C. de Andrade, A. Husakou, F. Morales, M. Kretschmar, T. Nagy, V. Vaičaitis, L. Shi, D. Zuber, L. Bergé, S. Skupin, I. A. Nikolaeva, N. A. Panov, D. E. Shipilo, O. G. Kosareva, A. N. Pfeiffer, A. Demircan, M. J. J. Vrakking, U. Morgner, et al., All-optical attoclock for imaging tunnelling wavepackets, Nat. Phys. 18, 417 (2022).
  22. I. I. Abbasov, B. M. Bolotovskii, and V. A. Davydov, High-frequency asymptotic behavior of radiation spectra of moving charges in classical electrodynamics, Usp. Fiz. Nauk. 149, 709 (1986) [Sov. Phys. Usp. 29, 788 (1986)].
  23. V. L. Ginzburg, Theoretical Physics and Astrophysics (Pergamon Press, New York, 1979).
  24. F. Brunel, Not-so-resonant, resonant absorption, Phys. Rev. Lett. 59, 52 (1987).
  25. F. Brunel, Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit, J. Opt. Soc. Am. B 7, 521 (1990).
  26. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Under-the-tunneling-barrier recollisions in strong-field ionization, Phys. Rev. Lett. 120, 013201 (2018).
  27. M. Klaiber, Q. Z. Lv, S. Sukiasyan, D. Bakucz Canário, K. Z. Hatsagortsyan, and C. H. Keitel, Reconciling conflicting approaches for the tunneling time delay in strong field ionization, Phys. Rev. Lett. 129, 203201 (2022).
  28. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Sub-barrier pathways to freeman resonances, Phys. Rev. A 102, 053105 (2020).
  29. T. Khurelbaatar, M. Klaiber, S. Sukiasyan, K. Z. Hatsagortsyan, C. H. Keitel, and D. E. Kim, Unveiling under-the-barrier electron dynamics in strong field tunneling, Phys. Rev. Lett. 134, 213201 (2025).
  30. D. B. Milošević, Quantum theory of photon emission during strong-laser-field-induced ionization, Phys. Rev. A 108, 033110 (2023).
  31. L. V. Keldysh, Ionization in the field of a strong electromagnetic wave, Zh. Eksp. Teor. Fiz. 37, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
  32. B. Sundaram and P. W. Milonni, High-order harmonic generation: Simplified model and relevance of single-atom theories to experiment, Phys. Rev. A 41, 6571 (1990).
  33. P. Krekora, R. E. Wagner, Q. Su, and R. Grobe, Retardation and kinematic relativistic effects in scattered light, Laser Phys. 12, 455 (2002).
  34. E. A. Chowdhury, I. Ghebregziabiher, and B. C. Walker, Larmor radiation from the ultra-intense field ionization of atoms, J. Phys. B: At., Mol. Opt. Phys. 38, 517 (2005).
  35. J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, Photoemission of a single-electron wave packet in a strong laser field, Phys. Rev. Lett. 100, 153601 (2008).
  36. J. P. Corson and J. Peatross, Quantum-electrodynamic treatment of photoemission by a single-electron wave packet, Phys. Rev. A 84, 053832 (2011).
  37. G. Tarbox, E. Cunningham, R. Sandberg, J. Peatross, and M. Ware, Radiation from free electrons in a laser focus at 1018W/cm2: modeling of photon yields and required focal conditions, J. Opt. Soc. Am. B 32, 743 (2015).
  38. M. Ware, E. Cunningham, C. Coburn, and J. Peatross, Measured photoemission from electron wave packets in a strong laser field, Opt. Lett. 41, 689 (2016).
  39. Y. Pan and A. Gover, Spontaneous and stimulated emissions of a preformed quantum free-electron wave function, Phys. Rev. A 99, 052107 (2019).
  40. D. Marcuse, Emission of radiation from a modulated electron beam, J. Appl. Phys. 42, 2255 (1971).
  41. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, Above-threshold ionization by few-cycle pulses, J. Phys. B 39, R203 (2006).
  42. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  43. 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).
  44. D. M. Wolkow, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Phys. 94, 250 (1935).
  45. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Elsevier, Oxford, 1975).
  46. A. M. Perelomov, V. S. Popov, and V. M. Terent'ev, Ionization of atoms in an alternating electric field. II, Zh. Exp. Theor. Fiz. 51, 309 (1966).
  47. V. S. Popov, Tunneling and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory), Phys. Usp. 47, 855 (2004).
  48. N. Suárez, A. Chacón, M. F. Ciappina, J. Biegert, and M. Lewenstein, Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields, Phys. Rev. A 92, 063421 (2015).
  49. M. Klaiber, Q. Z. Lv, K. Z. Hatsagortsyan, and C. H. Keitel, Tunneling ionization in ultrashort laser pulses: Edge effect and remedy, Phys. Rev. A 105, 063109 (2022).
  50. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Signatures of under-the-barrier dynamics in a tunneling electron wavepacket, Commun. Phys. 7, 384 (2024).
  51. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitevskii, Quantum Electrodynamics (Pergamon, Oxford, 1982).

Outline

Information

Phys. Rev. A 113, 033110– Published 12 March, 2026
  • Received 27 August 2025
  • Revised 19 December 2025
  • Accepted 23 February 2026
Crossmark - Check for updates button
Creative Commons Logo

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. Open access publication funded by Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation