Photoelectron spectroscopy is a powerful method that provides insight into the quantum mechanical properties of a wide range of systems. The ionized electron wavefunction carries information on the structure of the bound orbital, the ionic potential as well as the photo-ionization dynamics itself. While photoelectron spectroscopy resolves the absolute amplitude of the wavefunction, retrieving the spectral phase information has been a long-standing challenge. Established photo-ionization spectroscopy methods, such as reconstruction of attosecond beating by interference of two-photon transitions (RABBITT), are able to access only the first derivative of the spectral phase, the group delay, due to their nonlinear nature [1,2]. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photo-ionization– photo-recombination – in high-harmonic generation (HHG). The extreme-ultraviolet attosecond pulses produced in HHG carry the full information of the light-matter interaction, including the electronic structure of the system under scrutiny. Their spectral phase directly encodes the photo-ionization dipole phase due to the final step of HHG – photo-recombination of a well-defined electron wavepacket into the ion. In this work, we access this phase using interferometry, which is highly challenging in the XUV spectral domain due to the absence of efficient optics.

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