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.