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New Method for Measuring Angle-Resolved Phases in Photoemission

Photoionization, i.e, the emission of an electron by an atom, a molecule, or a solid, when irradiated with short-wavelength light, such as UV or x-rays, is one of the earliest observations that led to the hypotheses upon which quantum mechanics was built a century ago. Meanwhile, we know that the process is fully described by few mathematical quantities, the probability amplitudes, that are related to the transition between the initial (ground state) and the final (continuum state) of the system. The measurement of these quantities, and the comparison with theoretical calculations, has thus been 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; the former is easier to measure, whereas information on the latter is lost in most measurements, unless one uses sophisticated interferometric techniques. In everyday experience, this loss is well exemplified by the difference between a photograph and a hologram; in atomic and molecular physics, the phase of probability amplitudes (which can be equivalently expressed as a time, i.e., a fraction of the period of the light wave) can reveal important information about phenomena such as the concerted motion of electrons (electron correlation) in chemical reactions.
Using two-color extreme ultraviolet (XUV) photoelectron spectroscopy at the LDM beamline of the FERMI free-electron laser (FEL) an international collaboration led by Professors Kiyoshi Ueda from Tohoku University (Japan) and Kevin C. Prince from Elettra – Sincrotrone Trieste developed a new kind of interferometric spectroscopy, and succeeded in measuring phase differences with a precision of few attoseconds (1 attosecond = 10-18 seconds, or a billionth of a billionth of a second). The measurements revealed that this phase difference is not isotropic: it varies significantly with the angle of observation of the outgoing electron, particularly when the frequency of the light is nearly resonant with a transition in the atom. The measurements were in excellent agreement with state-of-the-art quantum mechanical calculations performed by the teams of Professors Alexei N. Grum-Grzhimailo from Lomonosov Moscow State University (Russia) and Kenichi L. Ishikawa from Tokyo State University (Japan). This work provides a new tool for attosecond science, i.e., the observation in real time of the motion of electrons inside matter.

Figure 1.  Scheme of the experiment: Bichromatic, linearly polarized light (red and blue waves), with momentum kγ and electric vector Eγ, ionizes neon in the reaction volume. The electron wave packets (yellow and magenta waves) are emitted with electron momentum k. The m-averaged phase difference Δη between wave packets created by one- and two-photon ionization depends on the emission angle. The photoelectron angular distribution depends on the relative (optical )ω‑2ω phase Φ Lower figures: Polar plots of photoelectron intensity at Ek=16.6 eV for coherent harmonics (asymmetric, colored plot) and incoherent harmonics (symmetric, gray plot).


Figure 2.  Upper: Typical photoelectron yields I(θ;ϕ) as a function of optical phase ϕ at intervals of polar angles θ. The signal is integrated over the 5 intervals shown on the right. The photoelectron kinetic energy is 7.0 eV. Circles are experimental results; lines are sinusoidal fits of the experimental results. Lower: Extracted phase shift differences as a function of the polar angles, for four datasets and three photoelectron kinetic energies: left (c), 7.0 eV; middle (d), 10.2 eV; right (e), 16.6 eV. Circles are experimental results; shaded areas show their uncertainties. Dashed lines, perturbation theory; solid lines, real-time ab initio theory. Note that the curves in (a) and (b) oscillate in antiphase, because they correspond to emission directions on opposite sides of the photon propagation direction.


This research was conducted by the following research team:

Daehyun You1, Kiyoshi Ueda1, Elena V. Gryzlova2, Alexei N. Grum-Grzhimailo2, Maria M. Popova2,3, Ekaterina I. Staroselskaya3, Oyunbileg Tugs4, Yuki Orimo4, Takeshi Sato4,5,6, Kenichi L. Ishikawa4,5,6, Paolo Antonio Carpeggiani7, Tamás Csizmadia8, Miklós Füle8, Giuseppe Sansone9, Praveen Kumar Maroju9, Alessandro D’Elia10,11, Tommaso Mazza12, Michael Meyer12, Carlo Callegari13, Michele Di Fraia13, Oksana Plekan13, Robert Richter13, Luca Giannessi13,14, Enrico Allaria13, Giovanni De Ninno13,15, Mauro Trovò13, Laura Badano13, Bruno Diviacco13, Giulio Gaio13, David Gauthier13, Najmeh Mirian13, Giuseppe Penco13, Primož Rebernik Ribič13,15, Simone Spampinati13, Carlo Spezzani13, and Kevin C. Prince13,16


Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Institut für Photonik, Technische Universität Wien, 1040 Vienna, Austria
ELI-ALPS, ELI-HU Non-Profit Limited, Dugonics tér 13, H-6720 Szeged, Hungary
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79106 Freiburg, Germany
10 University of Trieste, Department of Physics, 34127 Trieste, Italy
11 IOM-CNR, Laboratorio Nazionale TASC, 34149 Basovizza, Trieste, Italy
12 European X-Ray Free Electron Laser Facility GmbH, Holzkoppel 4, 22869 Schenefeld, Germany
13 Elettra-Sincrotrone Trieste S.C.p.A., 34149 Basovizza, Trieste, Italy
14 INFN-Laboratori Nazionali di Frascati, 00044 Frascati, Rome, Italy
15 Laboratory of Quantum Optics, University of Nova Gorica, Nova Gorica 5001, Slovenia
16 Centre for Translational Atomaterials, Swinburne University of Technology, 3122 Melbourne, Australia

Contact persons:

Kevin C. Prince, email:


D. You, K. Ueda, E. V. Gryzlova, A. N. Grum-Grzhimailo, M. M. Popova, E. I. Staroselskaya, O. Tugs, Y. Orimo, T. Sato, K. L. Ishikawa, P. A. Carpeggiani, T. Csizmadia, M. Füle, G. Sansone, P. K. Maroju, A. D’Elia, T. Mazza, M. Meyer, C. Callegari, M. Di Fraia, O. Plekan, R. Richter, L. Giannessi, E. Allaria, G. De Ninno, M. Trovò, L. Badano, B. Diviacco, G. Gaio, D. Gauthier, N. Mirian, G. Penco, P. Rebernik Ribič, S. Spampinati, C. Spezzani, K. C. Prince, “New Method for Measuring Angle-Resolved Phases in Photoemission”, Phys. Rev. X 10, 031070 (2020), DOI: 10.1103/PhysRevX.10.031070.

Last Updated on Wednesday, 25 November 2020 11:08