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Molecular photoelectron interference effects by intense circularly polarized attosecond x-ray pulses

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Abstract

We present photoelectron interference effects in molecular photoionization by intense circularly polarized attosecond X-ray laser pulses. Simulations are performed on single electron molecular systems, H\(_{2}^{+}\), HeH2+, and H\(_{3}^{2+}\), by numerically solving the corresponding three-dimensional time dependent Schrödinger equations. Photoelectron spectra show that both momentum ring and stripe patterns are obtained, arising respectively from the interference of the direct ionized and scattered electron wave packets. Multi-center electron interference models in molecular ultrafast photoionization are used to describe the ionized electron dynamics. The interference patterns are shown to be dependent on molecular orbital symmetry, thus offering tools for attosecond imaging molecular structure at different molecular geometries.

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References

  1. Brabec T, Krausz F (2000) Intense few-cycle laser fields: frontiers of nonlinear optics. Rev Mod Phys 72:545–591

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  3. Huang L, Massa L, Karle J (1999) Quantum crystallography applied to crystalline maleic anhydride. Int J Quantum Chem 73:439–450

    Article  CAS  Google Scholar 

  4. Huang L, Massa L, Karle J (1999) Quantum crystallography. J Mol Struct 474:9–12

    Article  Google Scholar 

  5. Huang L, Massa L, Karle J (2002) Form factors for core electrons useful for the application of quantum crystallography (QCr) to organic molecules. Acta Cryst. A 58:410–411

    Google Scholar 

  6. Huang L, Matta C, Massa L (2015) The kernel energy method (KEM) delivers fast and accurate QTAIM electrostatic charge for atoms in large molecules. Struct Chem 26:1433–1442

    Article  CAS  Google Scholar 

  7. Bandrauk A D, Chelkowski S, Nguyen H S (2004) Attosecond localization of electrons in molecules. Int J Quantum Chem 100:834–844

    Article  CAS  Google Scholar 

  8. Kraus P M, Mignolet B, Baykusheva D, Rupenyan A, Horný L, Penka E F, Grassi G, Tolstikhin O I, Schneider J, Jensen F, Madsen L B, Bandrauk A D, Remacle F, Wörner H J (2015) Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science 350:790–795

    Article  CAS  Google Scholar 

  9. Shao H C, Starace A F (2010) Detecting electron motion in atoms and molecules. Phys Rev Lett 105:263201

    Article  Google Scholar 

  10. Yudin G L, Bandrauk A D, Corkum P B (2006) Chirped attosecond photoelectron spectroscopy. Phys Rev Lett 96:063002

    Article  CAS  Google Scholar 

  11. Chelkowski S, Yudin G L, Bandrauk A D (2006) Observing electron motion in molecules. J Phys B 39:S409–S417

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  13. Yurchenko S N, Patchkovskii S, Litvinyuk I V, Corkum P B, Yudin G L (2004) Laser-induced interference, focusing, and diffraction of rescattering molecular photoelectrons. Phys Rev Lett 93 :223003

    Article  CAS  Google Scholar 

  14. Bian X B, Bandrauk A D (2012) Attosecond time-resolved imaging of molecular structure by photoelectron holography. Phys Rev Lett 108:263003

    Article  Google Scholar 

  15. Pullen M G, Wolter B, Le A T, Baudisch M, Hemmer M, Senftleben A, Schröter C D, Ullrich J, Moshammer R, Lin C D, Biegert J (2015) Imaging an aligned polyatomic molecule with laser-induced electron diffraction. Nature Commun 6 :7262

    Article  CAS  Google Scholar 

  16. Meckel M, Comtois D, Zeidler D, Staudte A, Pavičić D, Bandulet HC, Pépin H, Kieffer JC, Dörner R, Villeneuve DM, Corkum PB (2008) Laser-induced electron tunneling and diffraction. Science 320:1478–1482

    Article  CAS  Google Scholar 

  17. Peters M, Nguyen-Dang T T, Cornaggia C, Saugout S, Charron E, Keller A, Atabek O (2011) Ultrafast molecular imaging by laser-induced electron diffraction. Phys Rev A 83:051403

    Article  Google Scholar 

  18. Puthumpally-Joseph R, Viau-Trudel J, Peters M, Nguyen-Dang T T, Atabek O, Charron E (2016) Inversion of strong-field photoelectron spectra for molecular orbital imaging. Phys Rev A 94:023421

    Article  Google Scholar 

  19. Matta C F, Boyd R J (2007) The quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley-VCH, Weinheim

    Book  Google Scholar 

  20. Vrakking M J J (2014) Attosecond imaging. Phys Chem Chem Phys 16:2775–2789

    Article  CAS  Google Scholar 

  21. Cohen H D, Fano U (1966) Interference in the photo-ionization of molecules. Phys Rev 150:30–33

    Article  CAS  Google Scholar 

  22. Kaplan I G, Markin A P (1969) Interference phenomena in photoionization of molecules. Sov Phys Dokl 14:36

    Google Scholar 

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

    Article  CAS  Google Scholar 

  24. Bandrauk A D, Chelkowski S, Goudreau S (2005) Control of harmonic generation using two-colour femtosecond-Cattosecond laser fields: quantum and classical perspectives. J Mod Opt 52:411–428

    Article  CAS  Google Scholar 

  25. Bandrauk A D, Chelkowski S, Yu H, Constant E (1997) Enhanced harmonic generation in extended molecular systems by two-color excitation. Phys Rev A 56:R2537–R2540

    Article  CAS  Google Scholar 

  26. Bandrauk A D, Barmaki S, Kamta G L (2007) Laser phase control of high-order harmonic generation at large internuclear distance: The H+-\(\mathrm {H}^{+}_{2}\) system. Phys Rev Lett 98:013001

    Article  Google Scholar 

  27. Zuo T, Bandrauk A D (1995) High-order harmonic generation in intense laser and magnetic fields. J Nonlinear Opt Phys Mater 4:533–546

    Article  CAS  Google Scholar 

  28. Long S, Becker W, McIver J K (1995) Model calculations of polarization-dependent two-color high-harmonic generation. Phys Rev A 52:2262–2278

    Article  CAS  Google Scholar 

  29. Barth I, Manz J (2006) Periodic electron circulation induced by circularly polarized laser pulses: quantum model simulations for Mg-porphyrin. Angew Chem Int Ed 45:2962–2965

    Article  CAS  Google Scholar 

  30. Akagi H, Otobe T, Staudte A, Shiner A, Turner F, Döner R, Villeneuve D M, Corkum P B (2009) Laser tunnel ionization from multiple orbitals in HCl. Science 325:1364–1367

    Article  CAS  Google Scholar 

  31. Chen C, Tao Z, Hernández-García C, Matyba P, Carr A, Knut R, Kfir O, Zusin D, Gentry C, Grychtol P, Cohen O, Plaja L, Becker A, Jaron-Becker A, Kapteyn H, Murnane M (2016) Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology. Sci Adv 2:e1501333

    Article  Google Scholar 

  32. Sáchez-Barriga J, Varykhalov A, Braun J, Xu S Y, Alidoust N, Kornilov O, Miná J, Hummer K, Springholz G, Bauer G, Schumann R, Yashina L V, Ebert H, Hasan M Z, Rader O (2014) Photoemission of Bi2Se3 with circularly polarized light: probe of spin polarization or means for spin manipulation?. Phys Rev X 4:011046

    Google Scholar 

  33. Mauger F, Chandre C, Uzer T (2010) From recollisions to the knee: a road map for double ionization in intense laser fields. Phys Rev Lett 104:043005

    Article  CAS  Google Scholar 

  34. Mauger F, Chandre C, Uzer T (2010) Recollisions and correlated double ionization with circularly polarized light. Phys Rev Lett 105:083002

    Article  CAS  Google Scholar 

  35. Bandrauk A D, Lu H Z (2003) Controlling harmonic generation in molecules with intense laser and static magnetic fields: orientation effects. Phys Rev A 68:043408

    Article  Google Scholar 

  36. Hadas I, Bahabad A (2014) Macroscopic manipulation of high-order-harmonic generation through bound-state coherent control. Phys Rev Lett 113:253902

    Article  Google Scholar 

  37. Chelkowski S, Bredtmann T, Bandrauk A D (2013) High-harmonic generation from a coherent superposition of electronic states: controlling interference patterns via short and long quantum orbits. Phys Rev A 88:033423

    Article  Google Scholar 

  38. Milošević D, Becker W, Kopold R (2000) Generation of circularly polarized high-order harmonics by two-color coplanar field mixing. Phys Rev A 61:063403

    Article  Google Scholar 

  39. Mauger F, Bandrauk AD, Uzer T (2016) Circularly polarized molecular high harmonic generation using a bicircular laser. J Phys B 49:10LT01

    Article  Google Scholar 

  40. Bandrauk AD, Mauger F, Yuan KJ (2016) Circularly polarized harmonic generation by intense bicircular laser pulses: electron recollision dynamics and frequency dependent helicity. J Phys B 49:23LT01

    Article  Google Scholar 

  41. Milošević D (2015) Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in thepstate: a tool for exploring chirality-sensitive processes. Phys Rev A 92:043827

    Article  Google Scholar 

  42. Reich D M, Madsen L B (2016) Illuminating molecular symmetries with bicircular high-order-harmonic generation. Phys Rev Lett 117:133902

    Article  Google Scholar 

  43. Kfir O, Grychtol P, Turgut E, Knut R, Zusin D, Popmintchev D, Popmintchev T, Nembach H, Shaw J M, Fleischer A, Kapteyn H, Murnane M, Cohen O (2014) Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics. Nature Photon 9:99–105

    Article  Google Scholar 

  44. Fan T, Grychtol P, Knut R, Hernández-García C, Hickstein D D, Zusin D, Gentry C, Dollar F J, Mancuso C A, Hogle C W, Kfir O, Legut D, Carva K, Ellis J L, Dorney K M, Chen C, Shpyrko O G, Fullerton E E, Cohen O, Oppeneer P, Milošević D, Becker A, Jaroń-Becker AA, Popmintchev T, Murnane MM, Kapteyn HC (2015) Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism. Proc Natl Acad Sci USA 112:14206–14211

    Article  CAS  Google Scholar 

  45. Baykusheva D, Ahsan M S, Lin N, Wörner H J (2016) Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules. Phys Rev Lett 116:123001

    Article  Google Scholar 

  46. Liu X, Zhu X, Li L, Li Y, Zhang Q, Lan P, Lu P (2016) Selection rules of high-order-harmonic generation: symmetries of molecules and laser fields. Phys Rev A 94:033410

    Article  Google Scholar 

  47. Yuan K J, Bandrauk A D (2011) Circularly polarized molecular high-order harmonic generation in \(\mathrm {H}_{2}^{+}\) with intense laser pulses and static fields. Phys Rev A 83:063422

    Article  Google Scholar 

  48. Yuan K J, Bandrauk A D (2012) Circularly polarized attosecond pulses from molecular high-order harmonic generation by ultrashort intense bichromatic circularly and linearly polarized laser pulses. J Phys B 45:074001

    Article  Google Scholar 

  49. Yuan K J, Bandrauk A D (2013) Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media. Phys Rev Lett 110:023003

    Article  Google Scholar 

  50. Horner D A, Miyabe S, Rescigno T N, McCurdy C W, Morales F, Martín F (2008) Classical two-slit interference effects in double photoionization of molecular hydrogen at high energies. Phys Rev Lett 101:183002

    Article  CAS  Google Scholar 

  51. Yuan K J, Lu H Z, Bandrauk A D (2009) Laser-induced electron diffraction in H2 with linear and circular polarization ultrashort XUV laser pulses. Phys Rev A 80:061403(R)

    Article  Google Scholar 

  52. Yuan K J, Lu H Z, Bandrauk A D (2011) Linear- and circular-polarization photoionization angular distributions in H2 and \(\mathrm {H}_{2}^{+}\) by attosecond xuv laser pulses. Phys Rev A 83:043418

    Article  Google Scholar 

  53. Huang C, Zhou Y, Liao Q, Lu P (2012) Imaging molecular structures with high-energy photoelectrons produced by extreme ultraviolet pulses. J Opt Soc Am B 29:734–737

    Article  Google Scholar 

  54. Yuan K J, Lu H Z, Bandrauk A D (2013) Electron interference in molecular photoionization by attosecond laser pulses. ChemPhysChem 14:1496–1501

    Article  CAS  Google Scholar 

  55. Ngoko Djiokap J M, Hu S X, Madsen L B, Manakov N L, Meremianin A V, Starace A F (2015) Electron vortices in photoionization by circularly polarized attosecond pulses. Phys Rev Lett 115:113004

    Article  CAS  Google Scholar 

  56. Ngoko Djiokap J M, Meremianin A V, Manakov N L, Hu S X, Madsen L B, Starace A F (2016) Multistart spiral electron vortices in ionization by circularly polarized UV pulses. Phys Rev A 94:013408

    Article  Google Scholar 

  57. Yuan K J, Chelkowski S, Bandrauk A D (2016) Photoelectron momentum distributions of molecules in bichromatic circularly polarized attosecond UV laser fields. Phys Rev A 93 :053425

    Article  Google Scholar 

  58. Barth I, Manz J, Shigeta Y, Yagi K (2006) Unidirectional electronic ring current driven by a few cycle circularly polarized laser pulse: quantum model simulations for Mg-Porphyrin. J Am Chem Soc 128:7043–7049

    Article  CAS  Google Scholar 

  59. Barth I, Manz J (2007) Electric ring currents in atomic orbitals and magnetic fields induced by short intense circularly polarized laser pulses. Phys Rev A 75:012510

    Article  Google Scholar 

  60. Yuan K J, Bandrauk A D (2013) Attosecond-magnetic-field-pulse generation by intense few-cycle circularly polarized UV laser pulses. Phys Rev A 88:013417

    Article  Google Scholar 

  61. Yuan K J, Bandrauk A D (2015) Attosecond-magnetic-field-pulse generation by electronic currents in bichromatic circularly polarized UV laser fields. Phys Rev A 92:063401

    Article  Google Scholar 

  62. Chelkowski S, Bandrauk A D (2002) Measuring molecular wave functions using laser Coulomb explosion imaging with ultraviolet lasers. Appl Phys B 74:s113–s120

    Article  CAS  Google Scholar 

  63. Bandrauk A D, Fillion-Gourdeau F, Lorin E (2013) Atoms and molecules in intense laser fields: gauge invariance of theory and models. J Phys B 46:153001

    Article  Google Scholar 

  64. Bandrauk A D, Shen H (1993) Exponential split operator methods for solving coupled time-dependent Schrödinger equations. J Chem Phys 99:1185–1193

    Article  CAS  Google Scholar 

  65. Bandrauk A D, Lu H Z (2013) Exponential propagators (integrators) for the time-dependent Schrödinger equation. J Theor Comput Chem 12:1340001–1340017

    Article  Google Scholar 

  66. Lee K F, Villeneuve D M, Corkum P B, Stolow A, Underwood JG (2006) Field-free three-dimensional alignment of polyatomic molecules. Phys Rev Lett 97:173001

    Article  Google Scholar 

  67. Girardeau M D, Kim K G, Widmayer C C (1992) Theory of atomic excitation and ionization by ultrashort laser pulses. Phys Rev A 46:5932–5937

    Article  CAS  Google Scholar 

  68. Yuan K J, Bandrauk A D (2015) Molecular alignment dependent electron interference in attosecond ultraviolet photoionization. Struct Dyn 2:014101

    Article  Google Scholar 

  69. Becker U (2011) Molecular physics: matter-wave interference made clear. Nature 474(586):587

    Google Scholar 

  70. Baltenkov A S, Becker U, Manson S T, Msezane A (2012) Nondipole effects in the photoabsorption of electrons in two-centre zero-range potentials. J Phys B 45:035202

    Article  Google Scholar 

  71. Yuan K J, Bandrauk A D (2012) Photoelectron angular distributions of \(\mathrm {H}_{2}^{+}\) and HHe2+ by intense circularly polarized extreme ultraviolet laser pulses. J Phys B 45:105601

    Article  Google Scholar 

  72. McCarroll R, Moiseiwitsch B L (1957) Approximate molecular orbitals: VI - the 2p σ state of HeH2+. Proc Phys Soc A 70:507–511

    Article  Google Scholar 

  73. Guan X, Secor E B, DuToit R C, Bartschat K (2012) Diffraction patterns in the ionization of the heteronuclear HeH2+ ion by attosecond x-ray radiation. Phys Rev A 86:053425

    Article  Google Scholar 

  74. Lefebvre C, Lu H Z, Chelkowski S, Bandrauk A D (2014) Electron-nuclear dynamics of the one-electron nonlinear polyatomic molecule \(\mathrm {H}_{3}^{2+}\) in ultrashort intense laser pulses. Phys Rev A 89:023403

    Article  Google Scholar 

  75. Lötstedt E, Midorikawa K (2014) Carrier-envelope phase control of electron motion in laser-driven \(\mathrm {H}_{3}^{2+}\). J Phys B 47 :204018

    Article  Google Scholar 

  76. Barty A, Küpper J, Chapman H N (2013) Molecular imaging using X-ray free-electron lasers. Annu Rev Phys Chem 64:415– 435

    Article  CAS  Google Scholar 

  77. Miao J, Ishikawa T, Robinson I K, Murnane M M (2015) Beyond crystallography: diffractive imaging using coherent x-ray light sources. Science 348:530–535

    Article  CAS  Google Scholar 

  78. Karle J, Huang L, Massa L (1999) Quantum crystal-lography: features and application. In: Tsoucaris G. (ed) Current challenges on large supramolecular assemblies. NATO science series C: mathematical and physical sciences, vol 519, pp 1–5

  79. Yuan K J, Bandrauk A D (2016) Monitoring coherent electron wave packet excitation dynamics by two-color attosecond laser pulses. J Chem Phys 145:194304

    Article  Google Scholar 

  80. Lefebvre C, Nguyen-Dang T T, Dion F, Vrakking M J J, Serov V N, Atabek O (2014) Attosecond pump-probe transition-state spectroscopy of laser-induced molecular dissociative ionization: Adiabatic versus nonadiabatic dressed-state dynamics. Phys Rev A 88:053416

    Article  Google Scholar 

  81. Yang J, Guehr M, Shen X, Li R, Vecchione T, Coffee R, Corbett J, Fry A, Hartmann N, Hast C, Hegazy K, Jobe K, Makasyuk I, Robinson J, Robinson M S, Vetter S, Weathersby S, Yoneda C, Wang X, Centurion M (2016) Diffractive imaging of coherent nuclear motion in isolated molecules. Phys Rev Lett 117:153002

    Article  Google Scholar 

  82. Glownia J M, Natan A, Cryan J P, Hartsock R, Kozina M, Minitti M P, Nelson S, Robinson J, Sato T, van Driel T, Welch G, Weninger C, Zhu D, Bucksbaum P H (2016) Self-referenced coherent diffraction X-ray movie of Ångstrom- and femtosecond-scale atomic motion. Phys Rev Lett 117:153003

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Acknowledgements

The authors thank RQCHP and Compute Canada for access to massively parallel computer clusters.

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  1. Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada

    Kai-Jun Yuan, Huizhong Lu & André D. Bandrauk

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  1. Kai-Jun Yuan
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  2. Huizhong Lu
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Correspondence to Kai-Jun Yuan.

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This paper is dedicated to Professor Lou Massa on the occasion of his 75th anniversary

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Yuan, KJ., Lu, H. & Bandrauk, A.D. Molecular photoelectron interference effects by intense circularly polarized attosecond x-ray pulses. Struct Chem 28, 1297–1309 (2017). https://doi.org/10.1007/s11224-017-0964-5

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