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Electronic wavefunctions probed by all-optical attosecond interferometry


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.

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.


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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.

Author information




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).

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