- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Attosecond diffraction imaging of electron dynamics in solids

Mingrui Yuan

Nikolay V. Golubev*

  • *Contact author: ngolubev@arizona.edu
PDF

Phys. Rev. Research 7, L022042 – Published 27 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022042

Abstract

Visualizing the electron dynamics in four dimensions of space and time is crucial to the understanding of several ubiquitous processes in nature. Hence, ultrafast x-ray and electron imaging tools have been developed to probe the dynamics of matter by means of the time-resolved diffraction imaging (TRDI). In this work, we report an extension of the theory underlying the TRDI to the case of the laser-driven electron dynamics in solid-state systems. We demonstrate that the TRDI signal encodes essential information about the time-dependent electron density of the system under study and thus makes it possible to decipher the ultrafast quantum dynamics and the electron transfer phenomena in solids. We apply the developed approach to image the laser-driven electron dynamics in neutral graphene showing that the predictions made by the fully quantum version of the TRDI deviate significantly from those obtained with the conventional semiclassical approach.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (66)

  1. F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
  2. E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, Real-time observation of valence electron motion, Nature (London) 466, 739 (2010).
  3. X. Gong, S. Heck, D. Jelovina, C. Perry, K. Zinchenko, R. Lucchese, and H. J. Wörner, Attosecond spectroscopy of size-resolved water clusters, Nature (London) 609, 507 (2022).
  4. F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martin, and M. Nisoli, Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses, Science 346, 336 (2014).
  5. P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horny, 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).
  6. D. T. Matselyukh, V. Despré, N. V. Golubev, A. I. Kuleff, and H. J. Wörner, Decoherence and revival in attosecond charge migration driven by non-adiabatic dynamics, Nat. Phys. 18, 1206 (2022).
  7. I. Jordan, M. Huppert, D. Rattenbacher, M. Peper, D. Jelovina, C. Perry, A. Von Conta, A. Schild, and H. J. Wörner, Attosecond spectroscopy of liquid water, Science 369, 974 (2020).
  8. R. Borrego-Varillas, M. Lucchini, and M. Nisoli, Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics, Rep. Prog. Phys. 85, 066401 (2022).
  9. D. Hui, H. Alqattan, S. Yamada, V. Pervak, K. Yabana, and M. T. Hassan, Attosecond electron motion control in dielectric, Nat. Photon. 16, 33 (2022).
  10. V. Gruson, L. Barreau, Á. Jiménez-Galan, F. Risoud, J. Caillat, A. Maquet, B. Carré, F. Lepetit, J.-F. Hergott, T. Ruchon, L. Argenti, R. Taïeb, F. Martín, and P. Salières, Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron, Science 354, 734 (2016).
  11. G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L'Huillier, M. Yu. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, Electron localization following attosecond molecular photoionization, Nature (London) 465, 763 (2010).
  12. J. M. Cowley, Diffraction Physics, 3rd ed., North-Holland Personal Library (Elsevier Science B.V, Amsterdam, New York, 1995).
  13. I. Schlichting and J. Miao, Emerging opportunities in structural biology with X-ray free-electron lasers, Curr. Opin. Struct. Biol. 22, 613 (2012).
  14. C. Colliex, J. M. Cowley, S. L. Dudarev, M. Fink, J. Gjønnes, R. Hilderbrandt, A. Howie, D. F. Lynch, L. M. Peng, G. Ren, A. W. Ross, V. H. Smith, J. C. H. Spence, J. W. Steeds, J. Wang, M. J. Whelan, and B. B. Zvyagin, Electron diffraction, in International Tables for Crystallography, Vol. C, edited by H. Fuess, Th. Hahn, H. Wondratschek, U. Müller, U. Shmueli, E. Prince, A. Authier, V. Kopský, D. B. Litvin, M. G. Rossmann, E. Arnold, S. Hall, B. McMahon, and E. Prince (International Union of Crystallography, Chester, England, 2006) 1st ed., pp. 259–429.
  15. C. B. Carter, Transmission Electron Microscopy: Diffraction, Imaging, and Spectrometry, 1st ed. (Springer, Berlin, Heidelberg, New York, NY, 2016).
  16. M. Th. Hassan, J. S. Baskin, B. Liao, and A. H. Zewail, High-temporal-resolution electron microscopy for imaging ultrafast electron dynamics, Nat. Photonics 11, 425 (2017).
  17. M. T. Hassan, Attomicroscopy: From femtosecond to attosecond electron microscopy, J. Phys. B: At., Mol. Opt. Phys. 51, 032005 (2018).
  18. T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki et al., A compact X-ray free-electron laser emitting in the sub-ångström region, Nat. Photonics 6, 540 (2012).
  19. C. Pellegrini, A. Marinelli, and S. Reiche, The physics of x-ray free-electron lasers, Rev. Mod. Phys. 88, 015006 (2016).
  20. D. Hui, H. Alqattan, M. Sennary, N. V. Golubev, and M. T. Hassan, Attosecond electron microscopy and diffraction, Sci. Adv. 10, eadp5805 (2024).
  21. P. Coppens, Electron density from x-ray diffraction, Annu. Rev. Phys. Chem. 43, 663 (1992).
  22. P. Coppens, X-Ray Charge Densities and Chemical Bonding, International Union of Crystallography Texts on Crystallography No. 4 (International Union of Crystallography/Oxford University Press, Oxford, New York, 1997).
  23. J. Cao and K. R. Wilson, Ultrafast x-ray diffraction theory, J. Phys. Chem. A 102, 9523 (1998).
  24. A. Authier, Dynamical Theory of X-ray Diffraction, repr ed., Monographs on Crystallography No. 11 (Oxford University Press, Oxford, 2008).
  25. M. Centurion, T. J. Wolf, and J. Yang, Ultrafast Imaging of Molecules with Electron Diffraction, Annu. Rev. Phys. Chem. 73, 21 (2022).
  26. H.-C. Shao and A. F. Starace, Detecting electron motion in atoms and molecules, Phys. Rev. Lett. 105, 263201 (2010).
  27. H. J. Suominen and A. Kirrander, How to observe coherent electron dynamics directly, Phys. Rev. Lett. 112, 043002 (2014).
  28. P. Baum, J. Manz, and A. Schild, Quantum model simulations of attosecond electron diffraction, Sci. China Phys. Mech. Astron. 53, 987 (2010).
  29. V. S. Yakovlev, M. I. Stockman, F. Krausz, and P. Baum, Atomic-scale diffractive imaging of sub-cycle electron dynamics in condensed matter, Sci. Rep. 5, 14581 (2015).
  30. G. Dixit, O. Vendrell, and R. Santra, Imaging electronic quantum motion with light, Proc. Natl. Acad. Sci. 109, 11636 (2012).
  31. G. Dixit, J. M. Slowik, and R. Santra, Theory of time-resolved nonresonant x-ray scattering for imaging ultrafast coherent electron motion, Phys. Rev. A 89, 043409 (2014).
  32. H.-C. Shao and A. F. Starace, Imaging coherent electronic motion in atoms by ultrafast electron diffraction, Phys. Rev. A 88, 062711 (2013).
  33. G. Dixit, J. M. Slowik, and R. Santra, Proposed imaging of the ultrafast electronic motion in samples using x-ray phase contrast, Phys. Rev. Lett. 110, 137403 (2013).
  34. G. Dixit and R. Santra, Role of electron-electron interference in ultrafast time-resolved imaging of electronic wavepackets, J. Chem. Phys. 138, 134311 (2013).
  35. H.-C. Shao and A. F. Starace, Imaging electronic motions in atoms by energy-resolved ultrafast electron diffraction, Phys. Rev. A 90, 032710 (2014).
  36. H.-C. Shao and A. F. Starace, Imaging population transfer in atoms with ultrafast electron pulses, Phys. Rev. A 94, 030702(R) (2016).
  37. G. Dixit and R. Santra, Time-resolved ultrafast x-ray scattering from an incoherent electronic mixture, Phys. Rev. A 96, 053413 (2017).
  38. M. Grosser, J. M. Slowik, and R. Santra, Attosecond x-ray scattering from a particle-hole wave packet, Phys. Rev. A 95, 062107 (2017).
  39. H.-C. Shao and A. F. Starace, Imaging electronic motions by ultrafast electron diffraction, in Ultrafast Nonlinear Imaging and Spectroscopy V, edited by Z. Liu (SPIE, San Diego, 2017), p. 12.
  40. K. Bennett, J. D. Biggs, Y. Zhang, K. E. Dorfman, and S. Mukamel, Time-, frequency-, and wavevector-resolved x-ray diffraction from single molecules, J. Chem. Phys. 140, 204311 (2014).
  41. G. Hermann, V. Pohl, G. Dixit, and J. C. Tremblay, Probing electronic fluxes via time-resolved x-ray scattering, Phys. Rev. Lett. 124, 013002 (2020).
  42. S. Giri, J. C. Tremblay, and G. Dixit, Imaging charge migration in chiral molecules using time-resolved x-ray diffraction, Phys. Rev. A 104, 053115 (2021).
  43. J. R. Rouxel, D. Keefer, and S. Mukamel, Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction, Struct. Dyn. 8, 014101 (2021).
  44. J. C. Tremblay, V. Pohl, G. Hermann, and G. Dixit, Time-resolved imaging of correlation-driven charge migration in light-induced molecular magnets by X-ray scattering, Faraday Discuss. 228, 82 (2021).
  45. M. Kowalewski, K. Bennett, and S. Mukamel, Monitoring nonadiabatic avoided crossing dynamics in molecules by ultrafast X-ray diffraction, Struct. Dyn. 4, 054101 (2017).
  46. K. Bennett, M. Kowalewski, J. R. Rouxel, and S. Mukamel, Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction, Proc. Natl. Acad. Sci. 115, 6538 (2018).
  47. M. Simmermacher, A. Moreno Carrascosa, N. E. Henriksen, K. B. Møller, and A. Kirrander, Theory of ultrafast x-ray scattering by molecules in the gas phase, J. Chem. Phys. 151, 174302 (2019).
  48. S. Giri, J. C. Tremblay, and G. Dixit, Probing the effect of molecular structure saddling on ultrafast charge migration via time-resolved x-ray diffraction, Phys. Rev. A 106, 033120 (2022).
  49. J. C. Tremblay, A. Blanc, P. Krause, S. Giri, and G. Dixit, Probing electronic symmetry reduction during charge migration via time-resolved x-ray diffraction, ChemPhysChem 24, e202200463 (2023).
  50. W. Friedrich, P. Knipping, and M. von Laue, Interferenz-Erscheinungen Bei Röntgenstrahlen (Sitzungsberichte der Mathematisch-Physikalischen Classe der Königlich-Bayerischen Akademie der Wissenschaften zu München, München, 1912).
  51. H. Boersch, Über das primäre und sekundäre Bild im Elektronenmikroskop. II. Strukturuntersuchung mittels Elektronenbeugung, Annalen der Physik 419, 75 (1936).
  52. N. Jones, Crystallography: Atomic secrets, Nature (London) 505, 602 (2014).
  53. M. Gemmi, E. Mugnaioli, T. E. Gorelik, U. Kolb, L. Palatinus, P. Boullay, S. Hovmöller, and J. P. Abrahams, 3D electron diffraction: The nanocrystallography revolution, ACS Central Science 5, 1315 (2019).
  54. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  55. K. L. Ishikawa, Nonlinear optical response of graphene in time domain, Phys. Rev. B 82, 201402(R) (2010).
  56. H. K. Kelardeh, V. Apalkov, and M. I. Stockman, Graphene in ultrafast and superstrong laser fields, Phys. Rev. B 91, 045439 (2015).
  57. C. Liu, J. Manz, K. Ohmori, C. Sommer, N. Takei, J. C. Tremblay, and Y. Zhang, Attosecond control of restoration of electronic structure symmetry, Phys. Rev. Lett. 121, 173201 (2018).
  58. Y. Morimoto, Y. Shinohara, K. L. Ishikawa, and P. Hommelhoff, Atomic real-space perspective of light-field-driven currents in graphene, New J. Phys. 24, 033051 (2022).
  59. P. Baum and C. Ropers, Comment on ‘Attosecond electron microscopy and diffraction', arXiv:2411.14518.
  60. D. Hui, H. Alqattan, M. Sennary, N. V. Golubev, and M. T. Hassan, Comment on “Comment on Attosecond electron microscopy and diffraction”, arXiv:2502.06592.
  61. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022042 for the step-by-step derivations of the equations used in the main text as well as for the details of the performed simulations.
  62. W. V. Houston, Acceleration of electrons in a crystal lattice, Phys. Rev. 57, 184 (1940).
  63. J. B. Krieger and G. J. Iafrate, Time evolution of Bloch electrons in a homogeneous electric field, Phys. Rev. B 33, 5494 (1986).
  64. T. Higuchi, C. Heide, K. Ullmann, H. B. Weber, and P. Hommelhoff, Light-field-driven currents in graphene, Nature (London) 550, 224 (2017).
  65. O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, Nonadiabatic Landau–Zener–Stückelberg–Majorana transitions, dynamics, and interference, Phys. Rep. 995, 1 (2023).
  66. S. Ghimire and D. A. Reis, High-harmonic generation from solids, Nat. Phys. 15, 10 (2019).

Outline

Information

Phys. Rev. Research 7, L022042– Published 27 May, 2025
  • Received 1 July 2024
  • Revised 22 November 2024
  • Accepted 30 April 2025
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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation