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Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams

Amir H. Tavabi1, Paolo Rosi2, Enzo Rotunno3,*, Alberto Roncaglia4, Luca Belsito4, Stefano Frabboni2,3, Giulio Pozzi1,5, Gian Carlo Gazzadi3, Peng-Han Lu1,6 et al.

Robert Nijland7, Moumita Ghosh7, Peter Tiemeijer7, Ebrahim Karimi8, Rafal E. Dunin-Borkowski1, and Vincenzo Grillo3,†

  • 1Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
  • 2Dipartimento FIM, Universitá di Modena e Reggio Emilia, 41125 Modena, Italy
  • 3Centro S3, Istituto di Nanoscienze—CNR, 41125 Modena, Italy
  • 4Istituto per la Microelettronica e i Microsistemi-CNR, 40129 Bologna, Italy
  • 5Department of Physics and Astronomy, University of Bologna, 40127 Bologna, Italy
  • 6RWTH Aachen University, 52074 Aachen, Germany
  • 7Thermo Fisher Scientific, PO Box 80066, 5600 KA Eindhoven, Netherlands
  • 8Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

  • *Corresponding author. enzo.rotunno@cnr.it
  • †Corresponding author. vincenzo.grillo@cnr.it

Phys. Rev. Lett. 126, 094802 – Published 5 March, 2021

DOI: https://doi.org/10.1103/PhysRevLett.126.094802

Abstract

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50 nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

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References (58)

  1. E. Ruska, Das entstehen des elektronenmikroskops und der elektronenmikroskopie (Nobel-Vortrag), Angew. Chem. 99, 611 (1987).
  2. R. Courtland, The microscope revolution that’s sweeping through materials science, Nature (London) 563, 462 (2018).
  3. Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, Electron ptychography of 2D materials to deep sub-Ångström resolution, Nature (London) 559, 343 (2018).
  4. L. Jin, J. Barthel, C.-L. Jia, and K. W. Urban, Atomic resolution imaging of YAlO3: Ce in the chromatic and spherical aberration corrected PICO electron microscope, Ultramicroscopy 176, 99 (2017).
  5. E. Yücelen, I. Lazić, and E. G. T. Bosch, Phase contrast scanning transmission electron microscopy imaging of light and heavy atoms at the limit of contrast and resolution, Sci. Rep. 8, 2676 (2018).
  6. S. de Graaf, J. Momand, C. Mitterbauer, S. Lazar, and B. J. Kooi, Resolving hydrogen atoms at metal-metal hydride interfaces, Sci. Adv. 6, eaay4312 (2020).
  7. P. A. Midgley and R. E. Dunin-Borkowski, Electron tomography and holography in materials science, Nat. Mater. 8, 271 (2009).
  8. S. Lopatin, B. Cheng, W.-T. Liu, M.-L. Tsai, J.-H. He, and A. Chuvilin, Optimization of monochromated TEM for ultimate resolution imaging and ultrahigh resolution electron energy loss spectroscopy, Ultramicroscopy 184, 109 (2018).
  9. D. Rossouw and G. A. Botton, Plasmonic Response of Bent Silver Nanowires for Nanophotonic Subwavelength Waveguiding, Phys. Rev. Lett. 110, 066801 (2013).
  10. R. Henderson, The potential and limitations of neutrons, electrons and x-rays for atomic resolution microscopy of unstained biological molecules, Q. Rev. Biophys. 28, 171 (1995).
  11. R. Henderson, Avoiding the pitfalls of single particle cryo-electron microscopy: Einstein from noise, Proc. Natl. Acad. Sci. U.S.A. 110, 18037 (2013).
  12. M. Haider, S. Uhlemann, E. Schwan, H. Rose, B. Kabius, and K. Urban, Electron microscopy image enhanced, Nature (London) 392, 768 (1998).
  13. O. L. Krivanek, N. Dellby, and A. R. Lupini, Towards sub-Å electron beams, Ultramicroscopy 78, 1 (1999).
  14. H. H. Rose, Historical aspects of aberration correction, J. Electron Microsc. 58, 77 (2009).
  15. K. Y. Bliokh, Y. P. Bliokh, S. Savel’ev, and F. Nori, Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices, Phys. Rev. Lett. 99, 190404 (2007).
  16. M. Uchida and A. Tonomura, Generation of electron beams carrying orbital angular momentum, Nature (London) 464, 737 (2010).
  17. J. Verbeeck, H. Tian, and P. Schattschneider, Production and application of electron vortex beams, Nature (London) 467, 301 (2010).
  18. B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, Electron vortex beams with high quanta of orbital angular momentum, Science 331, 192 (2011).
  19. J. Harris, V. Grillo, E. Mafakheri, G. C. Gazzadi, S. Frabboni, R. W. Boyd, and E. Karimi, Structured quantum waves, Nat. Phys. 11, 629 (2015).
  20. B. J. McMorran, A. Agrawal, P. A. Ercius, V. Grillo, A. A. Herzing, T. R. Harvey, M. Linck, and J. S. Pierce, Origins and demonstrations of electrons with orbital angular momentum, Phil. Trans. R. Soc. A 375, 20150434 (2017).
  21. K. Y. Bliokh, I. P. Ivanov, G. Guzzinati, L. Clark, R. Van Boxem, A. Béché, R. Juchtmans, M. A. Alonso, P. Schattschneider, F. Nori, and J. Verbeeck, Theory and applications of free-electron vortex states, Phys. Rep. 690, 1 (2017).
  22. S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, Electron vortices: Beams with orbital angular momentum, Rev. Mod. Phys. 89, 035004 (2017).
  23. D. Pohl, S. Schneider, P. Zeiger, J. Rusz, P. Tiemeijer, S. Lazar, K. Nielsch, and B. Rellinghaus, Atom size electron vortex beams with selectable orbital angular momentum, Sci. Rep. 7, 934 (2017).
  24. H. Larocque, I. Kaminer, V. Grillo, G. Leuchs, M. J. Padgett, R. W. Boyd, M. Segev, and E. Karimi, ‘Twisted’ electrons, Contemp. Phys. 59, 126 (2018).
  25. V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, Generation of Nondiffracting Electron Bessel Beams, Phys. Rev. X 4, 011013 (2014).
  26. N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Generation of electron Airy beams, Nature (London) 494, 331 (2013).
  27. V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, Measuring the orbital angular momentum spectrum of an electron beam, Nat. Commun. 8, 15536 (2017).
  28. V. Grillo, T. R. Harvey, F. Venturi, J. S. Pierce, R. Balboni, F. Bouchard, G. Carlo Gazzadi, S. Frabboni, A. H. Tavabi, Z.-A. Li, R. E. Dunin-Borkowski, R. W. Boyd, B. J. McMorran, and E. Karimi, Observation of nanoscale magnetic fields using twisted electron beams, Nat. Commun. 8, 689 (2017).
  29. G. Guzzinati, A. Béché, D. McGrouther, and J. Verbeeck, Prospects for out-of-plane magnetic field measurements through interference of electron vortex modes in the TEM, J. Opt. 21, 124002 (2019).
  30. B. J. McMorran, T. R. Harvey, and M. P. J. Lavery, Efficient sorting of free electron orbital angular momentum, New J. Phys. 19, 023053 (2017).
  31. G. Pozzi, V. Grillo, P.-H. Lu, A. H. Tavabi, E. Karimi, and R. E. Dunin-Borkowski, Design of electrostatic phase elements for sorting the orbital angular momentum of electrons, Ultramicroscopy 208, 112861 (2020).
  32. A. H. Tavabi, M. Beleggia, V. Migunov, A. Savenko, O. Öktem, R. E. Dunin-Borkowski, and G. Pozzi, Tunable ampere phase plate for low dose imaging of biomolecular complexes, Sci. Rep. 8, 5592 (2018).
  33. M. Zanfrognini, E. Rotunno, S. Frabboni, A. Sit, E. Karimi, U. Hohenester, and V. Grillo, Orbital angular momentum and energy loss characterization of plasmonic excitations in metallic nanostructures in TEM, ACS Photonics 6, 620 (2019).
  34. E. Rotunno, M. Zanfrognini, S. Frabboni, J. Rusz, R. E. Dunin Borkowski, E. Karimi, and V. Grillo, Orbital angular momentum resolved electron magnetic chiral dichroism, Phys. Rev. B 100, 224409 (2019).
  35. M. Zanfrognini, E. Rotunno, J. Rusz, R. E. D. Borkowski, E. Karimi, S. Frabboni, and V. Grillo, Sum rules in zone axis STEM-orbital angular momentum resolved electron magnetic chiral dichroism, Phys. Rev. B 102, 184420 (2020).
  36. F. S. Hage, R. J. Nicholls, J. R. Yates, D. G. McCulloch, T. C. Lovejoy, N. Dellby, O. L. Krivanek, K. Refson, and Q. M. Ramasse, Nanoscale momentum-resolved vibrational spectroscopy, Sci. Adv. 4, eaar7495 (2018).
  37. R. Senga, K. Suenaga, P. Barone, S. Morishita, F. Mauri, and T. Pichler, Position and momentum mapping of vibrations in graphene nanostructures, Nature (London) 573, 247 (2019).
  38. C. A. Guido, E. Rotunno, M. Zanfrognini, S. Corni, and V. Grillo, Exploring the azimuthal symmetries of electronic transitions in molecular and biomolecular systems by swift electrons, arXiv:2005.07440.
  39. G. Bertoni, E. Rotunno, A. Tavabi, M. Zanfrognini, P. Rosi, S. Frabboni, E. Karimi, R. Dunin-Borkowski, and V. Grillo, Combination of electron energy-loss spectroscopy and orbital angular momentum spectroscopy. Applications to electron magnetic chiral dichroism, plasmon-loss, and core-loss, Microsc. Microanal. 26, 1752 (2020).
  40. K. X. Nguyen, Y. Jiang, M. C. Cao, P. Purohit, A. K. Yadav, P. García-Fernández, M. W. Tate, C. S. Chang, P. Aguado-Puente, J. Íñiguez, F. Gomez-Ortiz, S. M. Gruner, J. Junquera, L. W. Martin, R. Ramesh, and D. A. Muller, Transferring orbital angular momentum to an electron beam reveals toroidal and chiral order, arXiv:2012.04134.
  41. F. Troiani, E. Rotunno, S. Frabboni, R. B. G. Ravelli, P. J. Peters, E. Karimi, and V. Grillo, Efficient molecule discrimination in electron microscopy through an optimized orbital angular momentum sorter, Phys. Rev. A 102, 043510 (2020).
  42. K. Saitoh, Y. Hasegawa, K. Hirakawa, N. Tanaka, and M. Uchida, Measuring the Orbital Angular Momentum of Electron Vortex Beams Using a Forked Grating, Phys. Rev. Lett. 111, 074801 (2013).
  43. G. Guzzinati, L. Clark, A. Béché, and J. Verbeeck, Measuring the orbital angular momentum of electron beams, Phys. Rev. A 89, 025803 (2014).
  44. L. Clark, A. Béché, G. Guzzinati, and J. Verbeeck, Quantitative measurement of orbital angular momentum in electron microscopy, Phys. Rev. A 89, 053818 (2014).
  45. R. Shiloh, Y. Tsur, R. Remez, Y. Lereah, B. A. Malomed, V. Shvedov, C. Hnatovsky, W. Krolikowski, and A. Arie, Unveiling the Orbital Angular Momentum and Acceleration of Electron Beams, Phys. Rev. Lett. 114, 096102 (2015).
  46. H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, Nondestructive Measurement of Orbital Angular Momentum for an Electron Beam, Phys. Rev. Lett. 117, 154801 (2016).
  47. T. R. Harvey, V. Grillo, and B. J. McMorran, Stern-Gerlach-like approach to electron orbital angular momentum measurement, Phys. Rev. A 95, 021801(R) (2017).
  48. Y. Noguchi, S. Nakayama, T. Ishida, K. Saitoh, and M. Uchida, Efficient Measurement of the Orbital-Angular-Momentum Spectrum of an Electron Beam via a Dammann Vortex Grating, Phys. Rev. Applied 12, 064062 (2019).
  49. A. Lubk, G. Guzzinati, F. Börrnert, and J. Verbeeck, Transport of Intensity Phase Retrieval of Arbitrary Wave Fields Including Vortices, Phys. Rev. Lett. 111, 173902 (2013).
  50. T. Schachinger, S. Löffler, A. Steiger-Thirsfeld, M. Stöger-Pollach, S. Schneider, D. Pohl, B. Rellinghaus, and P. Schattschneider, EMCD with an electron vortex filter: Limitations and possibilities, Ultramicroscopy 179, 15 (2017).
  51. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Efficient Sorting of Orbital Angular Momentum States of Light, Phys. Rev. Lett. 105, 153601 (2010).
  52. G. Ruffato, E. Rotunno, and V. Grillo, A general framework for conformal transformations in electron optics, arXiv:2003.09635.
  53. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.126.094802 for details about formulas, holograms, simulations, for an analytical model of the “mismatch effect” and an independent check of the validity of the OAM decomposition.
  54. V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, Holographic Generation of Highly Twisted Electron Beams, Phys. Rev. Lett. 114, 034801 (2015).
  55. E. Rotunno, A. H. Tavabi, P. Rosi, S. Frabboni, P. Tiemeijer, R. E. Dunin-Borkowski, and V. Grillo, Alignment of electron optical beam shaping elements using a convolutional neural network, arXiv:2101.04358.
  56. J. Y. Wang, Optical resolution through a turbulent medium with adaptive phase compensations, J. Opt. Soc. Am. 67, 383 (1977).
  57. J. Verbeeck, A. Béché, K. Müller-Caspary, G. Guzzinati, M. A. Luong, and M. Den, Hertog, demonstration of a 2×2 programmable phase plate for electrons, Ultramicroscopy 190, 58 (2018).10.1038/s41578-020-00275-8
  58. J. C. Idrobo, A new resolution quest in electron microscopy, Nat. Rev. Mater. 6, 100 (2021).

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