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Complete reconstruction of bound and unbound electronic wavefunctions in two-photon double ionization

Nature Physics volume 15, pages 170–177 (2019)Cite this article

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Abstract

To be complete, the characterization of the photoionization process of atoms and molecules requires the extraction of all quantum-mechanical phases and amplitudes. So far, complete experiments have accessed only the ionization process of neutral atoms and molecules. Here we report the quantum-mechanically complete characterization of the single and double ionization of neon to yield doubly charged ions. The first ionization step by intense, polarized extreme ultraviolet light from a free-electron laser leaves the ion in a polarized state (that is, one in which the angular momentum of the ion is aligned in space). By controlling the polarization of the light, we determine the bound and continuum components of the system in the first and second ionization steps leading to the formation of doubly charged neon ions. We test the validity of our approach by characterizing the influence of autoionizing ionic states on the two-photon double-ionization mechanism. Our results are important for understanding the physics of the interaction of extreme ultraviolet radiation with ions.

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Fig. 1: Energy-level diagram and photoelectron spectrum for the two-photon double ionization of neon.
Fig. 2: Two-photon double ionization of neon in the spectral range 44.0–62.0 eV.
Fig. 3: Two-photon double ionization of neon in the region of autoionizing states 2s2p53p.
Fig. 4: Complete experiment on photoionization of Ne+ 2p5 2P to the Ne2+ 2p4 3P state at the photon energy 53 eV.
Fig. 5: Complete experiment on photoionization of Ne+ 2p5 2P to the Ne2+ 2p4 3P state at the photon energies close to the region of autoionizing resonances.
Fig. 6: Reconstruction of bound and unbound electronic density distributions.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Böhme, D. K. Multiply-charged ions and interstellar chemistry. Phys. Chem. Chem. Phys. 13, 18253–18263 (2011).

    Article  ADS  Google Scholar 

  2. Thissen, R. et al. Doubly-charged ions in the planetary ionosphere: a review. Phys. Chem. Chem. Phys. 13, 18264–18287 (2011).

    Article  Google Scholar 

  3. Gillaspy, J. D., Pomeroy, J. M., Perrella, A. C. & Grube, H. The potential of highly charged ions: possible future applications. J. Phys. Conf. Ser. 58, 451–456 (2007).

    Article  ADS  Google Scholar 

  4. McNeil, B. W. J. & Thompson, N. R. X-ray free-electron lasers. Nat. Photon. 4, 814–821 (2010).

    Article  ADS  Google Scholar 

  5. Wabnitz, H. et al. Multiple ionisation of atom clusters by intense soft X-rays from a free-electron laser. Nature 420, 482–485 (2002).

    Article  ADS  Google Scholar 

  6. Young, L. et al. Femtosecond electronic response of atoms to ultra-intense X-rays. Nature 466, 56–61 (2010).

    Article  ADS  Google Scholar 

  7. Kollath, K. J. Theory for laser photoionisation of excited atoms: n2 P1/2,3/2 states of Cs. J. Phys. B 13, 2901–2919 (1980).

    Article  ADS  Google Scholar 

  8. Becker, U. Complete photoionisation experiments. J. Electr. Spectrosc. Relat. Phenom. 96, 105–115 (1998).

    Article  ADS  Google Scholar 

  9. Bederson, B. The ‘perfect’ scattering experiment. I. Comm. Atom. Mol. Phys. 1, 41–44 (1969).

    Google Scholar 

  10. Kleinpoppen, H. Analysis of scattering amplitudes in polarized-electron-atom collisions. I. Elastic scattering on one-electron atoms and the excitation process 2S1/2→2P1/2,3/2. Phys. Rev. A 3, 2015–2027 (1971).

    Article  ADS  Google Scholar 

  11. Duncanson, J. A. Jr., Strand, M. P., Lindgård, A. & Berry, R. S. Angular distributions of electrons from resonant two-photon ionization of sodium. Phys. Rev. Lett. 37, 987–990 (1976).

    Article  ADS  Google Scholar 

  12. Cherepkov, N. A. Spin polarization of photoelectrons ejected from unpolarized atoms. J. Phys. B 12, 1279–1296 (1979).

    Article  ADS  Google Scholar 

  13. Heinzmann, U. Experimental determination of the phase differences of continuum wavefunctions describing the photoionisation process of xenon atoms: I. Measurements of the spin polarisations of photoelectrons and their comparison with theoretical results. J. Phys. B 13, 4353–4366 (1980).

    Article  ADS  Google Scholar 

  14. Heinzmann, U. Experimental determination of the phase differences of continuum wavefunctions describing the photoionisation process of xenon atoms: II. Evaluation of the matrix elements and the phase differences and their comparison with data in the discrete spectral range in application of the multichannel quantum defect theory. J. Phys. B 13, 4367–4381 (1980).

    Article  ADS  Google Scholar 

  15. Kessler, J. The ‘perfect’ photoionization experiment. Comm. Atom. Mol. Phys. 10, 47–55 (1981).

    Google Scholar 

  16. Reid, K. L., Leahy, D. H. & Zare, R. N. Complete description of molecular photoionization from circular dichroism of rotationally resolved photoelectron angular distributions. Phys. Rev. Lett. 68, 3527–3530 (1992).

    Article  ADS  Google Scholar 

  17. Cherepkov, N. A. et al. K-shell photoionization of CO: II. Determination of dipole matrix elements and phase differences. J. Phys. B 33, 4213–4236 (2000).

    Article  ADS  Google Scholar 

  18. Geßner, O. et al. 4σ −1 inner valence photoionization dynamics of NO derived from photoelectron–photoion angular correlations. Phys. Rev. Lett. 88, 193002 (2002).

    Article  ADS  Google Scholar 

  19. Kabachnik, N. M. & Sazhina, I. P. On the problem of a complete experimental characterisation of Auger decay. J. Phys. B 23, L353–L357 (1990).

    Article  ADS  Google Scholar 

  20. Grum-Grzhimailo, A. N., Dorn, A. & Mehlhorn, W. On complete experiments for Auger decay. Comm. Atom. Mol. Phy. Comm. Mod. Phys. D 1, 29–39 (1999).

    Google Scholar 

  21. West, J. B., Ross, K. J., Ueda, K. & Beyer, H. J. Angular correlation measurement between the photo-excited autoionized electron and subsequent polarized fluorescent photon at an autoionization resonance of Sr. J. Phys. B 31, L647–L654 (1998).

    Article  ADS  Google Scholar 

  22. Hergenhahn, U. et al. Dynamically induced spin polarization of resonant Auger electrons. Phys. Rev. Lett. 82, 5020–5023 (1999).

    Article  ADS  Google Scholar 

  23. Becker, U. & Crowe, A. (eds) Complete Scattering Experiments (Kluwer Academic/Plenum, New York, 2001).

  24. Kleinpoppen, H., Lohmann, B. & Grum-Grzhimailo, A. N. Perfect/Complete Scattering Experiments (Springer, Berlin, 2013).

  25. Allaria, E. et al. Control of the polarization of a vacuum-ultraviolet, high-gain, free-electron laser. Phys. Rev. X 4, 041040 (2014).

    Google Scholar 

  26. Flügge, S., Mehlhorn, W. & Schmidt, V. Angular distribution of Auger electrons following photoionization. Phys. Rev. Lett. 29, 7–9 (1972).

    Article  ADS  Google Scholar 

  27. Jacobs, V. L. Theory of atomic photoionization measurements. J. Phys. B 5, 2257–2271 (1972).

    Article  ADS  Google Scholar 

  28. Caldwell, C. D. & Zare, R. N. Alignment of Cd atoms by photoionization. Phys. Rev. A 16, 255–262 (1977).

    Article  ADS  Google Scholar 

  29. Greene, C. H. & Zare, R. N. Photofragment alignment and orientation. Ann. Rev. Phys. Chem. 33, 119–150 (1982).

    Article  ADS  Google Scholar 

  30. Allaria, E. et al. Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nat. Photon. 6, 699–704 (2012).

    Article  ADS  Google Scholar 

  31. Lyamayev, V. et al. A modular end-station for atomic, molecular, and cluster science at the low density matter beamline of FERMI@Elettra. J. Phys. B 46, 164007 (2013).

    Article  ADS  Google Scholar 

  32. Covington, A. M. et al. Photoionization of Ne+ using synchrotron radiation. Phys. Rev. A 66, 062710 (2002).

    Article  ADS  Google Scholar 

  33. Fritzsche, S., Grum-Grzhimailo, A. N., Gryzlova, E. V. & Kabachnik, N. M. Angular distributions and angular correlations in sequential two-photon double ionization of atoms. J. Phys. B 41, 165601 (2008).

    Article  ADS  Google Scholar 

  34. Peshkin, M. in Advances in Chemical Physics Vol. 18 (eds Prigogine, I. & Rice, S. A.) 1–14 (Interscience, New York, 2007).

  35. Gryzlova, E. V., Grum-Grzhimailo, A. N., Fritzsche, S. & Kabachnik, N. M. Angular correlations between two electrons emitted in the sequential two-photon double ionization of atoms. J. Phys. B 43, 225602 (2010).

    Article  ADS  Google Scholar 

  36. Nikolopoulos, L. A. A. Time-dependent theory of angular correlations in sequential double ionization. Phys. Rev. Lett. 111, 093001 (2013).

    Article  ADS  Google Scholar 

  37. Kaneyasu, T. et al. Autoionization of the Ne+ Rydberg states formed via valence photoemission. J. Phys. B 40, 4047–4060 (2007).

    Article  ADS  Google Scholar 

  38. Faye, M. et al. Modified orbital atomic theory calculations of high lying Rydberg series in the photoionization spectra of Ne+. Chin. J. Phys. 53, 100401 (2015).

    Google Scholar 

  39. Edwards, A. K. & Roud, M. E. Excitation of auto-ionizing levels in neon by ion impact. Phys. Rev. 170, 140–144 (1968).

    Article  ADS  Google Scholar 

  40. Morgenstern, R., Niehaus, A. & Zimmermann, G. Autoionizing states formed by electron capture in collisions of multiply charged Ne ions with He, H2 and Xe. J. Phys. B 13, 4811–4831 (1980).

    Article  ADS  Google Scholar 

  41. Braune, M. et al. Electron angular distributions of noble gases in sequential two-photon double ionization. J. Mod. Optics 63, 324–333 (2016).

    Article  ADS  Google Scholar 

  42. Cooper, J. & Zare, R. N. Angular distribution of photoelectrons. J. Chem. Phys. 48, 942–943 (1968).

    Article  ADS  Google Scholar 

  43. Cooper, J. W. & Zare, R. N. in Lectures in Theoretical Physics Vol XI-C (eds Geltman, S. et al.) 317 (Gordon and Breach, New York, 1969).

  44. Grum-Grzhimailo, A. N., Gryzlova, E. V., Fritzsche, S. & Kabachnik, N. M. Photoelectron angular distributions and correlations in sequential double and triple atomic ionization by free electron lasers. J. Mod. Optics 63, 334–357 (2016).

    Article  ADS  Google Scholar 

  45. Gómez de Castro, A. I. & Wamsteker, W. (eds) Fundamental Questions in Astrophysics: Guidelines for Future UV Observatories (Springer, Dordrecht, 2006).

  46. Svetina, C. et al. The Low Density Matter (LDM) beamline at FERMI: optical layout and first commissioning. J. Synchrotron Radiat. 22, 538–543 (2015).

    Article  Google Scholar 

  47. Balashov, V., Grum-Grzhimailo, A. & Kabachnik, N. Polarization and Correlation Phenomena in Atomic Collisions: A Practical Theory Course (Plenum, New York, 2000).

    Chapter  Google Scholar 

  48. Kabachnik, N. & Sazhina, I. Angular distribution and polarization of photoelectrons in the region of resonances. J. Phys. B 9, 1681–1697 (1976).

    Article  ADS  Google Scholar 

  49. Baier, S., Grum-Grzhimailo, A. & Kabachnik, N. Angular distribution of photoelectrons in resonant photoionization of polarized atoms. J. Phys. B 27, 3363–3388 (1994).

    Article  ADS  Google Scholar 

  50. Cowan, R. D. The Theory of Atomic Structure and Spectra (Univ. California Press, Berkeley, 1981).

    Google Scholar 

Download references

Acknowledgements

Financial support by the Italian Ministry of Research (project FIRB no. RBID08CRXK) is gratefully acknowledged. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 641789 MEDEA. D.F and M.N. acknowledge support from the European Research Council Starting Research Grant UDYNI (grant agreement no. 307964). K.U. acknowledges support by the X-ray Free Electron Laser Utilization Research Project and the X-ray Free Electron Laser Priority Strategy Program of the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), by the Cooperative Research Program of ‘Network Joint Research Center for Materials and Devices: Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials’, by the bilateral project CNR-JSPS ‘Ultrafast science with extreme ultraviolet Free Electron Lasers’ and by the IMRAM project for the international co-operation. M.M. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) under grant no. SFB 925.

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Author notes

  1. These authors contributed equally: P. A. Carpeggiani, E. V. Gryzlova

Authors and Affiliations

  1. Dipartimento di Fisica, Politecnico di Milano, Milan, Italy

    P. A. Carpeggiani, M. Reduzzi, A. Dubrouil, D. Faccialá & M. Negro

  2. IFN-CNR Politecnico, Milan, Italy

    P. A. Carpeggiani, M. Reduzzi, D. Faccialá & M. Negro

  3. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

    E. V. Gryzlova & A. N. Grum-Grzhimailo

  4. Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan

    K. Ueda

  5. Pacific National University, Khabarovsk, Russia

    S. M. Burkov

  6. IFN-CNR, Padua, Italy

    F. Frassetto

  7. Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

    F. Stienkemeier & G. Sansone

  8. Institut für Optik und Atomare Physik, TU Berlin, Berlin, Germany

    Y. Ovcharenko

  9. European XFEL, Schenefeld, Germany

    Y. Ovcharenko & M. Meyer

  10. Elettra-Sincrotrone Trieste, Basovizza, Trieste, Italy

    O. Plekan, P. Finetti, K. C. Prince & C. Callegari

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Contributions

K.U., G.S. and A.N.G.-G. conceived the present study. M.R., D.F., M.N., K.U., F.F., F.S., Y.O., M.M., O.P., P.F., K.C.P., C.C. and G.S. conducted the experiment. P.A.C. analysed the experimental data. A.D. contributed to the development of the analysis programmes. E.V.G., S.M.B. and A.N.G.-G. developed the theoretical background and performed the numerical simulations. E.V.G., A.N.G.-G. and G.S. drafted the manuscript. All authors discussed the experimental results and the final version of the manuscript.

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Correspondence to A. N. Grum-Grzhimailo or G. Sansone.

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Carpeggiani, P.A., Gryzlova, E.V., Reduzzi, M. et al. Complete reconstruction of bound and unbound electronic wavefunctions in two-photon double ionization. Nature Phys 15, 170–177 (2019). https://doi.org/10.1038/s41567-018-0340-4

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