Skip to main content
SpringerLink
Log in

Quantum model simulations of attosecond electron diffraction

  • Review
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

Ultrafast diffraction with free attosecond electron pulses promises insight into the four-dimensional motion of charge density in atoms, molecules and condensed matter. Here we consider the quantum dynamics of the electron-electron scattering process on an attosecond time scale. By numerically solving the time-dependent two-electron Schrödinger equation, we investigate the interaction of an incoming keV-range electron wavepacket by the bound electron of an aligned H +2 molecule, using a one-dimensional model. Our findings reveal the ratio of elastic to inelastic contributions, the role of exchange interaction, and the influence of the molecular electron density to diffraction. Momentum transfer during the scattering process, from the incoming to the bound electron mediated by the nuclei, leaves the bound electron in a state of coherent oscillation with attosecond recurrences. Entanglement causes related state-selective oscillations in the phase shift of the scattered electron. Two scenarios of distinguishable and indistinguishable free and bound electrons yield equivalent results, irrespective of the electronic spins. This suggests to employ the scenario of distinguishable electrons, which is computationally less demanding. Our findings support the possibility of using electron diffraction for imaging the motion of charge density, but also suggest the application of free electron pulses for inducing attosecond dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zewail AH. In: Frängsmyr T, ed. Les Prix Nobel: The Nobel Prices 1999. Stockholm: Almqvist & Wiksell, 2000. 110

    Google Scholar 

  2. Baum P, Yang D S, Zewail A H. 4D visualization of transitional structures in phase transformations by electron diffraction. Science, 2007, 318: 788–792

    Article  ADS  Google Scholar 

  3. Remacle F, Levine R D. An electronic time scale in chemistry. Proc Natl Acad Sci USA, 2006, 103: 6793–6798

    Article  ADS  Google Scholar 

  4. Kuleff A I, Cederbaum L S. Tracing ultrafast interatomic electronic decay processes in real time and space. Phys Rev Lett, 2007, 98: 083201

    Article  ADS  Google Scholar 

  5. Geppert D, von den Hoff P, de Vivie-Riedle R. Electron dynamics in molecules: A new combination of nuclear quantum dynamics and electronic structure theory. J Phys B, 2008, 41: 074006

    Article  ADS  Google Scholar 

  6. Bandrauk A D, Chelkowski S, Corkum P B, et al. Attosecond photoionization of a coherent superposition of bound and dissociative molecular states: Effect of nuclear motion. J Phys B, 2009, 42: 134001

    Article  ADS  Google Scholar 

  7. Bandrauk A D, Manz J, Vrakking M. Attosecond molecular dynamics, preface. Chem Phys, 2009, 366: 1

    Article  ADS  Google Scholar 

  8. Baum P, Zewail A H. 4D attosecond imaging with free electrons: Diffraction methods and potential applications. Chem Phys, 2009, 366: 2–8

    Article  ADS  Google Scholar 

  9. Farrell J P, McFarland B K, Gühr M, et al. Relation of high harmonic spectra to electronic structure in N2. Chem Phys, 2009, 366: 15–21

    Article  ADS  Google Scholar 

  10. Lock R M, Zhou X, Lia W, et al. Measuring the intensity and phase of high-order harmonic emission from aligned molecules. Chem Phys, 2009, 366: 22–32

    Article  ADS  Google Scholar 

  11. Trallero-Herrero C, Schmidt B E, Shiner A D, et al. High harmonic generation in ethylene with infrared pulses. Chem Phys, 2009, 366: 33–36

    Article  ADS  Google Scholar 

  12. Sukiasyan S, McDonald C, Van Vlack C, et al. Correlated few-electron dynamics in intense laser fields. Chem Phys, 2009, 366: 37–45

    Article  ADS  Google Scholar 

  13. Kato T, Kono H. Time-dependent multiconfiguration theory for ultrafast electronic dynamics of molecules in an intense laser field: Electron correlation and energy redistribution among natural orbitals. Chem Phys, 2009, 366: 46–53

    Article  ADS  Google Scholar 

  14. Chirilă C C, Lein M. High-order harmonic generation in vibrating twoelectron molecules. Chem Phys, 2009, 366: 54–57

    Article  ADS  Google Scholar 

  15. Morales F, Pérez-Torres J F, Sanz-Vicario J L, et al. Probing H2 quantum autoionization dynamics with XUV atto and femtosecond laser pulses. Chem Phys, 2009, 366: 58–63

    Article  ADS  Google Scholar 

  16. Nguyen-Dang T T, Peters M, Wang S M, et al. Toward ab-initio simulations of multiple ionization processes in intense laser field. Chem Phys, 2009, 366: 71–84

    Article  ADS  Google Scholar 

  17. Milošević D B, Busuladžić M, Gazibegović-Busuladžić A, et al. Strongfield approximation for high-order above-threshold ionization of randomly oriented diatomic molecules. Chem Phys, 2009, 366: 85–90

    Article  Google Scholar 

  18. Son S K, Chu S I. Theoretical study of orientation-dependent multiphoton ionization of polyatomic molecules in intense ultrashort laser fields: A new time-dependent Voronoi-cell finite difference method. Chem Phys, 2009, 366: 91–102

    Article  ADS  Google Scholar 

  19. Yonehara T, Takatsuka K. Characterization of electron-deficient chemical bonding of diborane with attosecond electron wavepacket dynamics and laser response. Chem Phys, 2009, 366: 115–128

    Article  ADS  Google Scholar 

  20. Periyasamy G, Levine R D, Remacle F. Electronic wave packet motion in water dimer cation: A many electron description. Chem Phys, 2009, 366: 129–138

    Article  ADS  Google Scholar 

  21. von den Hoff P, Znakovskaya I, Kling M F, et al. Attosecond control of the dissociative ionization via electron localization: A comparison between D2 and CO. Chem Phys, 2009, 366: 139–147

    Article  ADS  Google Scholar 

  22. Zewail A H. 4D ultrafast electron diffraction, crystallography, and microscopy. Annu Rev Phys Chem, 2006, 57: 65–103

    Article  ADS  Google Scholar 

  23. Gedik N, Yang D S, Logvenov G, et al. Nonequilibrium phase transitions in cuprates observed by ultrafast electron crystallography. Science 2007, 316: 425–429

    Article  ADS  Google Scholar 

  24. Carbone F, Baum P, Rudolf P, et al. Structural preablation dynamics of graphite observed by ultrafast electron crystallography. Phys Rev Lett, 2008, 100: 035501

    Article  ADS  Google Scholar 

  25. Yang D S, Lao C, Zewail A H. 4D electron diffraction reveals correlated unidirectional behavior in zinc oxide nanowires. Science 2008, 321: 1660–1664

    Article  ADS  Google Scholar 

  26. Ruan C Y, Murooka Y, Raman R K, et al. Dynamics of size-selected gold nanoparticles studied by ultrafast electron nanocrystallography. Nano Lett, 2007, 7: 1290–1296

    Article  ADS  Google Scholar 

  27. Chen S, Seidel M T, Zewail A H. Atomic-scale dynamical structures of fatty acid bilayers observed by ultrafast electron crystallography. Proc Natl Acad Sci USA, 2005, 102: 8854–8859

    Article  ADS  Google Scholar 

  28. Gahlmann A, Park S T, Zewail A H. Structure of isolated biomolecules by electron diffraction-laser desorption: Uracil and guanine. J Am Chem Soc, 2009, 131: 2806–2809

    Article  Google Scholar 

  29. Siwick B J, Dwyer J R, Jordan R E, et al. An atomic-level view of melting using femtosecond electron diffraction. Science 2003, 302: 1382–1385

    Article  ADS  Google Scholar 

  30. Harb M, Ernstorfer R, Hebeisen C T, et al. Electronically driven structure changes of Si captured by femtosecond electron diffraction. Phys Rev Lett, 2008, 100: 155504

    Article  ADS  Google Scholar 

  31. Wang X, Nie S H, Li J J, et al. Electronic Grüneisen parameter and thermal expansion in ferromagnetic transition metal. Appl Phys Lett, 2008, 92: 121918

    Article  ADS  Google Scholar 

  32. Reckenthaeler P, Centurion M, Fuß W, et al. Time-resolved electron diffraction from selectively aligned molecules. Phys Rev Lett, 2009, 102: 213001

    Article  ADS  Google Scholar 

  33. Zewail A H, Thomas J M. 4D Electron Microscopy. London: Imperial College Press, 2009

    Book  Google Scholar 

  34. Park H S, Kwon O H, Baskin J S, et al. Direct observation of martensitic phase-transformation dynamics in Iron by 4D single-pulse electron microscopy. Nano Lett, 2009, 9: 3954–3962

    Article  Google Scholar 

  35. Barwick B, Park H S, Kwon O H, et al. 4D imaging of transient structures and morphologies in ultrafast electron microscopy. Science, 2008, 322: 1227–1231

    Article  ADS  Google Scholar 

  36. Yurtsever A, Zewail A H. 4D nanoscale diffraction observed by convergent-beam ultrafast electron microscopy. Science, 2009, 326: 708–712

    Article  ADS  Google Scholar 

  37. Carbone F, Kwon O H, Zewail A H. Dynamics of chemical bonding mapped by energy-resolved 4D electron microscopy. Science, 2009, 325: 181–184

    Article  ADS  Google Scholar 

  38. Breidbach J, Cederbaum L S. Universal attosecond response to the removal of an electron. Phys Rev Lett, 2005, 94: 033901

    Article  ADS  Google Scholar 

  39. Baum P, Zewail A H. Attosecond electron pulses for 4D diffraction and microscopy. Proc Natl Acad Sci USA, 2007, 104: 18409–18414

    Article  ADS  Google Scholar 

  40. Hilbert S A, Uiterwaal C, Barwick B, et al. Temporal lenses for attosecond and femtosecond electron pulses. Proc Natl Acad Sci USA, 2009, 106: 10558–10563

    Article  ADS  Google Scholar 

  41. Krausz F, Ivanov M. Attosecond physics. Rev Mod Phys, 2009, 81: 163–234

    Article  ADS  Google Scholar 

  42. Corkum P B, Krausz F. Attosecond science. Nature Phys, 2007, 3: 381–387

    Article  ADS  Google Scholar 

  43. Illenberger E, Momigny J. Gaseous Molecular Ions. An Introduction to Elementary Processes Induced by Ionization. New York: Springer, 1992

    Google Scholar 

  44. Gertitschke P L, Domcke W. Time-dependent wave-packet description of dissociative electron attachment. Phys Rev A, 1993, 47: 1031–1044

    Article  ADS  Google Scholar 

  45. Lehr L, Manz J, Miller WH. A classical approach to resonant low energy electron scattering off molecules: Application to the a1-shape resonance of CF3Cl. Chem Phys, 1997, 214: 301–312

    Article  Google Scholar 

  46. Harvey A G, Tennyson J. Electron re-scattering from H2 and CO2 using R-matrix techniques. J Mod Opt, 2007, 54: 1099–1106

    Article  ADS  Google Scholar 

  47. Harvey A G, Tennyson J. Electron re-scattering from aligned linear molecules using the R-matrix method. J Phys B-A Mol Opt Phys, 2009, 42: 095101

    Article  ADS  Google Scholar 

  48. Burke P G, Tennyson J. R-matrix theory of electron molecule scattering. Mol Phys, 2005, 103: 2537–2548

    Article  ADS  Google Scholar 

  49. Gorfinkiel J D, Faure A, Taioli S, et al. Electron-molecule collisions at low and intermediate energies using the R-matrix method. Eur Phys J D, 2005, 35: 231–237

    Article  ADS  Google Scholar 

  50. Blanco F, Garcia G. Screening corrections for calculation of electron scattering differential cross sections from polyatomic molecules. Phys Lett A, 2004, 330: 230–237

    Article  MATH  ADS  Google Scholar 

  51. Iga I, Lee M T, Bonham R A. Role of the intramolecular multiple scattering on electron diffraction from nitrogen molecule in the intermediate energy range. J Mol Struc: Theochem, 1999, 468: 241–251

    Article  Google Scholar 

  52. Zuo T, Bandrauk A D, Corkum P B. Laser-induced electron diffraction: A new tool for probing ultrafast molecular dynamics. Chem Phys Lett, 1996, 259: 313–320

    Article  ADS  Google Scholar 

  53. Spanner M, Smirnova O, Corkum P B, et al. Reading diffraction images in strong field ionization of diatomic molecules. J Phys B, 2004, 37: L243–L250

    Article  ADS  Google Scholar 

  54. Yurchenko S N, Patchkovskii S, Litvinyuk I V, et al. Laser-induced interference, focusing, and diffraction of rescattering molecular photoelectrons. Phys Rev Lett, 2004, 93: 223003

    Article  ADS  Google Scholar 

  55. Hu S X, Collins L A. Imaging molecular structures by electron diffraction using an intense few-cycle pulse. Phys Rev Lett, 2005, 94: 073004

    Article  ADS  Google Scholar 

  56. Meckel M, Comtois D, Zeidler D, et al. Laser-induced electron tunneling and diffraction. Science, 2008, 320: 1478–1482

    Article  ADS  Google Scholar 

  57. Morishita T, Okunishi M, Shimada K, et al. Retrieval of experimental differential electron-ion elastic scattering cross sections from high-energy ATI spectra of rare gas atoms by infrared lasers. J Phys B: At Mol Opt Phys, 2009, 42: 105205

    Article  ADS  Google Scholar 

  58. Bandrauk A D, Chelkowski S, Diestler D J, et al. Quantum-mechanical models for photo-ionization: Uni-directional electron re-scattering by a laser pulse. Int J Mass Spec, 2008, 277: 189–196

    Article  Google Scholar 

  59. Bandrauk A D, Manz J, Yuan K J. Electron wavepacket phases in ionization and rescattering processes by intense laser pulses. Laser Phys, 2009, 19: 1559–1573

    Article  ADS  Google Scholar 

  60. Corkum P B. Plasma perspective on strong field multiphoton ionization. Phys Rev Lett, 1993, 71: 1994–1997

    Article  ADS  Google Scholar 

  61. Bandrauk A D, Lu H. Laser-induced electron recollision in H2 and electron correlation. Phys Rev A, 2005, 72: 023408

    Article  ADS  Google Scholar 

  62. Bandrauk A D, Chelkowski S, Kawai S, et al. Effect of nuclear motion on molecular high-order harmonics and on generation of attosecond pulses in intense laser pulses. Phys Rev Lett, 2008, 101: 153901

    Article  ADS  Google Scholar 

  63. Walters Z B, Tonzanic S, Greene C H. Vibrational interference of Raman and high harmonic generation pathways. Chem Phys, 2009, 366: 103–114

    Article  ADS  Google Scholar 

  64. Smirnova O, Mairesse Y, Patchkovskii S, et al. High harmonic interferometry of multi-electron dynamics in molecules. Nature, 2009, 460: 972–977

    Article  ADS  Google Scholar 

  65. Morishita T, Le A T, Chen Z, et al. Accurate retrieval of structural information from laser-induced photoelectron and high-order harmonic spectra by few-cycle laser pulses. Phys Rev Lett, 2008, 100: 013903

    Article  ADS  Google Scholar 

  66. Bandrauk A D, Chelkowski S, Diestler D J, et al. Quantum simulation of high-order harmonic spectra of the hydrogen atom. Phys Rev A, 2009, 79: 023403

    Article  ADS  Google Scholar 

  67. Hu S X, Collins L A, Schneider B I. Attosecond photoelectron microscopy of H +2 . Phys Rev A, 2009, 80: 023426

    Article  ADS  Google Scholar 

  68. Yuan K J, Lu H, Bandrauk A D. LIED — Laser induced electron diffraction in H2 with linear and circular polarization ultrashort XUV laser pulses. Phys Rev A, 2009, 80: 061403

    Article  ADS  Google Scholar 

  69. Dörner R, Bräuning H, Jagutzki O, et al. Double photoionization of spatially aligned D2. Phys Rev Lett, 1998, 81: 5776–5779

    Article  ADS  Google Scholar 

  70. Fernández J, Yip F L, Rescigno T N, et al. Two-center effects in onephoton single ionization of H +2 , H2, and Li +2 with circularly polarized light. Phys Rev A, 2009, 79: 043409

    Article  ADS  Google Scholar 

  71. Barth I, Manz J, Paramonov G K. Time-dependent extension of Koopmans’ picture for ionisation by a laser pulse: Application to H(B 1Σ +u ). Mol Phys, 2008, 106: 467–483

    Article  ADS  Google Scholar 

  72. Taylor J R. Scattering Theory—The Quantum Theory of Nonrelativistic Collisions. New York: John Wiley & Sons, 1972

    Google Scholar 

  73. Glaeser R M. Review: Electron crystallography: Present excitement, a nod to the past, anticipating the future. J Struct Biol, 1999, 128: 3–14

    Article  Google Scholar 

  74. Peng L M. Electron atomic scattering factors and scattering potentials of crystals. Micron, 1999, 30: 625–649

    Article  Google Scholar 

  75. Stapelfeldt H, Seideman T. Colloquium: Aligning molecules with strong laser pulses. Rev Mod Phys, 2003, 75: 543–557

    Article  ADS  Google Scholar 

  76. Filsinger F, Küpper J, Meijer G, et al. Quantum-state selection, alignment, and orientation of large molecules using static electric and laser fields. J Chem Phys, 2009, 131: 064309

    Article  ADS  Google Scholar 

  77. Heller E J, Manz J. Dissociation of symmetry-adapted local modes studied by FFT-propagation of bond-adapted wavefunctions. Z Phys D, 1989, 13: 281–288

    Article  ADS  Google Scholar 

  78. Peek J M. Eigenparameters of the 1s σg and 2p σu orbitals of H +2 . J Chem Phys, 1965, 43: 3004

    Article  ADS  Google Scholar 

  79. Tannor D J. Introduction to Quantum Mechanics—A Time Dependent Perspective. USA: University Science Books, 2007

    Google Scholar 

  80. Bisseling R H, Kosloff R, Manz J. Dynamics of hyperspherical and local mode resonance decay studied by time dependent wave packet propagation. J Chem Phys, 1985, 83: 993–1004

    Article  ADS  Google Scholar 

  81. Feit M D, Fleck Jr J A, Steiger A. Solution of the Schrödinger equation by a spectral method. J Comp Phys, 1982, 47: 412–433

    Article  MATH  MathSciNet  ADS  Google Scholar 

  82. Feit M D, Fleck Jr J A. Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules. J Chem Phys, 1983, 78: 301–308

    Article  ADS  Google Scholar 

  83. Leforestier C, Bisseling R, Cerjan C, et al. A comparison of different propagation schemes for the time dependent Schrödinger equation. J Comput Phys, 1991, 94: 59–80

    Article  MATH  MathSciNet  ADS  Google Scholar 

  84. Schmidt B, Lorenz U. WavePacket 4.6 (/4.7): A program package for quantum-mechanical wavepacket propagation and time-dependent spectroscopy. Available via http://wavepacket.sourceforge.net (2009)

  85. Gonzalez-Lezana T, Rackham E J, Manolopoulos D E. Quantum reactive scattering with a transmission-free absorbing potential. J Chem Phys, 2004, 120: 2247–2254

    Article  ADS  Google Scholar 

  86. Press W H, Teukolsky S A, Vetterling W T, et al. Numerical Recipes in Fortran 90. USA: Cambridge University Press, 1996

    Google Scholar 

  87. Okuyama M, Takatsuka K. Electron flux in molecules induced by nuclear motion. Chem Phys Lett, 2009, 476: 109–115

    Article  ADS  Google Scholar 

  88. Barth I, Hege H C, Ikeda H, et al. Concerted quantum effects of electronic and nuclear fluxes in molecules. Chem Phys Lett, 2009, 481: 118–123

    Article  ADS  Google Scholar 

  89. Inokuti M. Inelastic collisions of fast charged particles with atoms and molecules—The Bethe theory revisited. Rev Mod Phys, 1971, 43: 297–347

    Article  ADS  Google Scholar 

  90. Jablonski A, Tanuma S, Powell C J. Modified predictive formula for the electron stopping power. J Appl Phys, 2008, 103: 063708

    Article  ADS  Google Scholar 

  91. Caprez A, Barwick B, Batelaan H. Macroscopic test of the Aharonov-Bohm effect. Phys Rev Lett, 2007, 99: 210401

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute of Quantum Optics, and Ludwig-Maximilians-Universität München, Am Coulombwall 1, Garching, 85748, Germany

    Peter Baum

  2. Freie Universität Berlin, Institut für Chemie und Biochemie, Takustr. 3, Berlin, 14195, Germany

    Jörn Manz & Axel Schild

Authors
  1. Peter Baum
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jörn Manz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Axel Schild
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jörn Manz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baum, P., Manz, J. & Schild, A. Quantum model simulations of attosecond electron diffraction. Sci. China Phys. Mech. Astron. 53, 987–1004 (2010). https://doi.org/10.1007/s11433-010-4017-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-010-4017-y

Keywords

Search

Navigation