**Measuring Angle-Resolved Phases in Photoemission**

Photoionization is one of the earliest observations whose explanation led to the establishment of quantum mechanics. The process is fully described by few mathematical quantities—the probability amplitudes—that are of central interest in understanding the electronic structure of matter and its theoretical foundations. Probability amplitudes are complex numbers, which are described by a magnitude and a phase. Phase information (which can be equivalently expressed as a time, i.e., a fraction of the period of the light wave causing ionization) is lost in most measurements.

An international research team from Japan, Germany, Russia, Austria, Hungary, and the local team at the FERMI free-electron laser, combined two-color XUV photoelectron spectroscopy with real-time ab initio simulations to measure phase differences with a precision of few attoseconds. The measurements, in excellent agreement with calculations, revealed a significant anisotropy with the angle of observation of the outgoing photoelectron, particularly when the frequency of the light is nearly resonant with a transition in the atom.

“In atomic and molecular physics, the phase of probability amplitudes can reveal important information about phenomena such as the concerted motion of electrons (electron correlation) in chemical reactions” says Prof. Kevin Prince from Elettra – Sincrotrone Trieste “and our work provides a new tool for attosecond science, i.e., the observation in real time of the motion of electrons inside matter.”

Read more on the ELETTRA website

**Image:** Scheme of the experiment: Bichromatic, linearly polarized light (red and blue waves), with momentum **k**_{g} and electric vector **E**_{g}, ionizes neon in the reaction volume. The electron wave packets (yellow and magenta waves) are emitted with electron momentum **k**. The averaged phase difference between wave packets created by one- and two-photon ionization depends on the emission angle. The photoelectron angular distribution depends on the relative (optical) w‑2w phase f. Lower figures: Polar plots of photoelectron intensity at E_{k}=16.6 eV for coherent harmonics (asymmetric, colored plot) and incoherent harmonics (symmetric, gray plot).

*Credit: Reproduced from You et al., Phys. Rev. X, ***10,** 031070 (2020) doi: 10.1103/PhysRevX.10.031070; copyright 2020 by the Authors. The original figure has been published under a Creative Commons Attribution 4.0 International license (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/