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Electronic wavefunctions probed by all-optical attosecond interferometry

Nature Photonics volume 13, pages 54–59 (2019)Cite this article

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Abstract

In photoelectron spectroscopy, the ionized electron wavefunction carries information about the structure of the bound orbital and the ionic potential as well as about the photoionization dynamics. However, retrieving the quantum phase information has been a long-standing challenge. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photoionization—photo-recombination—in attosecond pulse generation. We demonstrate all-optical interferometry of two independent phase-locked attosecond light sources. This measurement enables us to directly determine the phase shift associated with electron scattering in simple quantum systems such as helium and neon, over a large energy range. Moreover, the strong-field nature of attosecond pulse generation resolves the dipole phase around the Cooper minimum in argon through a single scattering angle. This method may enable the probing of complex orbital phases in molecular systems as well as electron correlations through resonances subject to strong laser fields.

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Fig. 1: Phase measurement scheme using XUV–XUV interferometry.
Fig. 2: XUV–XUV interferometry.
Fig. 3: Differential phase measurements of neon and helium.
Fig. 4: Differential phase measurements of argon and neon.

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

    Article  Google Scholar 

  2. Motoki, S. et al. Complete photoionization experiment in the region of the 2σg → σu shape resonance of the N2 molecule. J. Phys. B 35, 3801–3819 (2002).

    Article  ADS  Google Scholar 

  3. Marceau, C. et al. Molecular frame reconstruction using time-domain photoionization interferometry. Phys. Rev. Lett. 119, 083401 (2017).

    Article  ADS  Google Scholar 

  4. Villeneuve, D. M., Hockett, P., Vrakking, M. J. J. & Niikura, H. Coherent imaging of an attosecond electron wave packet. Science 356, 1150–1153 (2017).

    Article  Google Scholar 

  5. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).

    Article  ADS  Google Scholar 

  6. Mairesse, Y. et al. Attosecond synchronization of high-harmonic soft X-rays. Science 302, 1540–1543 (2003).

    Article  ADS  Google Scholar 

  7. Schultze, M. et al. Delay in photoemission. Science 328, 1658–1662 (2010).

    Article  ADS  Google Scholar 

  8. Klünder, K. et al. Probing single-photon ionization on the attosecond time scale. Phys. Rev. Lett. 106, 143002 (2011).

    Article  ADS  Google Scholar 

  9. Månsson, E. P. et al. Double ionization probed on the attosecond timescale. Nat. Phys. 10, 207–211 (2014).

    Article  Google Scholar 

  10. Guénot, D. et al. Measurements of relative photoemission time delays in noble gas atoms. J. Phys. B 47, 245602 (2014).

    Article  ADS  Google Scholar 

  11. Sabbar, M. et al. Resonance effects in photoemission time delays. Phys. Rev. Lett. 115, 133001 (2015).

    Article  ADS  Google Scholar 

  12. Haessler, S. et al. Phase-resolved attosecond near-threshold photoionization of molecular nitrogen. Phys. Rev. A 80, 011404 (2009).

    Article  ADS  Google Scholar 

  13. Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007).

    Article  ADS  Google Scholar 

  14. Wigner, E. P. Lower limit for the energy derivative of the scattering phase shift. Phys. Rev. 98, 145–147 (1955).

    Article  ADS  MathSciNet  Google Scholar 

  15. Dahlström, J. M., L'Huillier, A. & Maquet, A. Introduction to attosecond delays in photoionization. J. Phys. B 45, 183001 (2012).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Young, L. et al. X-ray microprobe of orbital alignment in strong-field ionized atoms. Phys. Rev. Lett. 97, 083601 (2006).

    Article  ADS  Google Scholar 

  18. Hockett, P. Angle-resolved RABBITT: theory and numerics. J. Phys. B 50, 154002 (2017).

    Article  ADS  Google Scholar 

  19. Shafir, D., Mairesse, Y., Villeneuve, D. M., Corkum, P. B. & Dudovich, N. Atomic wavefunctions probed through strong-field light–matter interaction. Nat. Phys. 5, 412–416 (2009).

    Article  Google Scholar 

  20. Zerne, R. et al. Phase-locked high-order harmonic sources. Phys. Rev. Lett. 79, 1006–1009 (1997).

    Article  ADS  Google Scholar 

  21. Kovačev, M. et al. Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics. Phys. Rev. Lett. 95, 223903 (2005).

    Article  ADS  Google Scholar 

  22. Corsi, C., Pirri, A., Sali, E., Tortora, A. & Bellini, M. Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation. Phys. Rev. Lett. 97, 023901 (2006).

    Article  ADS  Google Scholar 

  23. Bertrand, J. B., Wörner, H. J., Salières, P., Villeneuve, D. M. & Corkum, P. B. Linked attosecond phase interferometry for molecular frame measurements. Nat. Phys. 9, 174–178 (2013).

    Article  Google Scholar 

  24. Kanai, T., Takahashi, E. J., Nabekawa, Y. & Midorikawa, K. Destructive interference during high harmonic generation in mixed gases. Phys. Rev. Lett. 98, 153904 (2007).

    Article  ADS  Google Scholar 

  25. Jansen, G. S. M., Rudolf, D., Freisem, L., Eikema, K. S. E. & Witte, S. Spatially resolved Fourier transform spectroscopy in the extreme ultraviolet. Optica 3, 1122–1125 (2016).

    Article  Google Scholar 

  26. Ott, C. et al. Reconstruction and control of a time-dependent two-electron wave packet. Nature 516, 374–378 (2014).

    Article  ADS  Google Scholar 

  27. Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).

    Article  ADS  Google Scholar 

  28. Varjú, K. et al. Frequency chirp of harmonic and attosecond pulses. J. Mod. Opt. 52, 379–394 (2005).

    Article  ADS  Google Scholar 

  29. Shafir, D. et al. Resolving the time when an electron exits a tunnelling barrier. Nature 485, 343–346 (2012).

    Article  ADS  Google Scholar 

  30. Le, A.-T., Morishita, T. & Lin, C. D. Extraction of the species-dependent dipole amplitude and phase from high-order harmonic spectra in rare-gas atoms. Phys. Rev. A 78, 023814 (2008).

    Article  ADS  Google Scholar 

  31. Jin, C., Le, A.-T. & Lin, C. D. Medium propagation effects in high-order harmonic generation of Ar and N2. Phys. Rev. A 83, 023411 (2011).

    Article  ADS  Google Scholar 

  32. Frolov, M. V., Manakov, N. L., Sarantseva, T. S. & Starace, A. F. Analytic confirmation that the factorized formula for harmonic generation involves the exact photorecombination cross section. Phys. Rev. A 83, 043416 (2011).

    Article  ADS  Google Scholar 

  33. Ammosov, M., Delone, N. & Krainov, V. Tunnel ionization of complex atoms and atomic ions in an electromagnetic field. Sov. Phys. JETP 64, 1191–1194 (1986).

    Google Scholar 

  34. Bransden, B. H. & Joachain, C. J. Physics of Atoms and Molecules 2nd edn (Prentice-Hall, Harlow, UK, 2003).

  35. Fano, U. Propensity rules: an analytical approach. Phys. Rev. A. 32, 617–618 (1985).

    Article  ADS  Google Scholar 

  36. Cooper, J. W. Photoionization from outer atomic subshells. A model study. Phys. Rev. 128, 681–693 (1962).

    Article  ADS  Google Scholar 

  37. Wörner, H. J., Niikura, H., Bertrand, J. B., Corkum, P. B. & Villeneuve, D. M. Observation of electronic structure minima in high-harmonic generation. Phys. Rev. Lett. 102, 103901 (2009).

    Article  ADS  Google Scholar 

  38. Higuet, J. et al. High-order harmonic spectroscopy of the Cooper minimum in argon: experimental and theoretical study. Phys. Rev. A 83, 053401 (2011).

    Article  ADS  Google Scholar 

  39. Kheifets, A. S. Time delay in valence-shell photoionization of noble-gas atoms. Phys. Rev. A 87, 063404 (2013).

    Article  ADS  Google Scholar 

  40. Schoun, S. B. et al. Attosecond pulse shaping around a Cooper minimum. Phys. Rev. Lett. 112, 153001 (2014).

    Article  ADS  Google Scholar 

  41. Beutler, H. Über Absorptionsserien von Argon, Krypton und Xenon, zu Termen zwischen den beiden Ionisierungsgrenzen 2 P 3 2/0 und 2 P 1 2/0. Z. Phys. 93, 177–196 (1935).

    Article  ADS  Google Scholar 

  42. Kotur, M. et al. Spectral phase measurement of a Fano resonance using tunable attosecond pulses. Nat. Commun. 7, 10566 (2016).

    Article  ADS  Google Scholar 

  43. Cirelli, C. et al. Anisotropic photoemission time delays close to a Fano resonance. Nat. Commun. 9, 955 (2018).

    Article  ADS  Google Scholar 

  44. Wang, H. et al. Attosecond time-resolved autoionization of argon. Phys. Rev. Lett. 105, 143002 (2010).

    Article  ADS  Google Scholar 

  45. Kaldun, A. et al. Observing the ultrafast buildup of a Fano resonance in the time domain. Science 354, 738–741 (2016).

    Article  ADS  Google Scholar 

  46. Langer, B. et al. Angular distribution of the Ne 2s → np autoionization resonances: experimental and theoretical study. J. Phys. B 30, 593–607 (1997).

    Article  ADS  Google Scholar 

  47. Berrah, N. et al. Angular-distribution parameters and R-matrix calculations of Ar 3s−1→np resonances. J. Phys. B 29, 5351–5365 (1996).

    Article  ADS  Google Scholar 

  48. X-ray Form Factor, Attenuation, and Scattering Tables (NIST, 2016); https://www.nist.gov/pml/x-ray-form-factor-attenuation-and-scattering-tables

  49. Pabst, S. & Santra, R. Spin-orbit effects in atomic high-harmonic generation. J. Phys. B 47, 124026 (2014).

    Article  ADS  Google Scholar 

  50. Torlina, L. & Smirnova, O. Coulomb time delays in high harmonic generation. New J. Phys. 19, 023012 (2017).

    Article  ADS  Google Scholar 

  51. Schmidt, M. W. et al. General atomic and molecular electronic structure system. J. Comput. Chem. 14, 1347–1363 (1993).

    Article  Google Scholar 

  52. Dunning, T. H. Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989).

    Article  ADS  Google Scholar 

  53. Slater, J. C. & Johnson, K. H. Self-consistent-field xα cluster method for polyatomic molecules and solids. Phys. Rev. B 5, 844–853 (1972).

    Article  ADS  Google Scholar 

  54. Schwarz, K. Optimization of the statistical exchange parameter σ for the free atoms H through Nb. Phys. Rev. B 5, 2466–2468 (1972).

    Article  ADS  Google Scholar 

  55. Latter, R. Atomic energy levels for the Thomas-Fermi and Thomas-Fermi-Dirac potential. Phys. Rev. 99, 510–519 (1955).

    Article  ADS  Google Scholar 

  56. Abramowitz, M. & Stegun, I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (US Government Printing Office, Washington, D.C., 1964).

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Acknowledgements

We thank S. Patchkovskii, C. Ott and A. Harth for discussions. N.D. is the incumbent of the Robin Chemers Neustein Professorial Chair. N.D. acknowledges the Minerva Foundation, the Israeli Science Foundation, the Crown Center of Photonics and the European Research Council for financial support. M.K. acknowledges financial support by the Minerva Foundation and the Koshland Foundation. B.P., A.C., B.F. and Y.M. acknowledge financial support from the French National Research Agency through grant ANR-14-CE32-0014 MISFITS.

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Authors and Affiliations

  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel

    Doron Azoury, Omer Kneller, Shaked Rozen, Barry D. Bruner, Nirit Dudovich & Michael Krüger

  2. Université de Bordeaux - CNRS - CEA, CELIA, UMR5107, Talence, France

    Alex Clergerie, Yann Mairesse, Baptiste Fabre & Bernard Pons

  3. Université de Bordeaux - CNRS, ISM, UMR5255, Talence, France

    Alex Clergerie

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Contributions

N.D. and M.K. supervised the study. D.A. and M.K. designed and built the experimental setup. D.A., M.K. and O.K. carried out the measurements and analysed the data. B.P., A.C. and B.F. conceived and performed the theoretical calculations. D.A., M.K., N.D., B.P., B.F. and Y.M. interpreted the experimental and theoretical results. B.D.B. supported the operation of the laser system. All authors discussed the results and contributed to the final manuscript.

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Correspondence to Nirit Dudovich.

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Azoury, D., Kneller, O., Rozen, S. et al. Electronic wavefunctions probed by all-optical attosecond interferometry. Nature Photon 13, 54–59 (2019). https://doi.org/10.1038/s41566-018-0303-4

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