# 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 k_{γ} 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 You^{1}, Kiyoshi Ueda^{1}, Elena V. Gryzlova^{2}, Alexei N. Grum-Grzhimailo^{2}, Maria M. Popova^{2,3}, Ekaterina I. Staroselskaya^{3}, Oyunbileg Tugs^{4}, Yuki Orimo^{4}, Takeshi Sato^{4,5,6}, Kenichi L. Ishikawa^{4,5,6}, Paolo Antonio Carpeggiani^{7}, Tamás Csizmadia^{8}, Miklós Füle^{8}, Giuseppe Sansone^{9}, Praveen Kumar Maroju^{9}, Alessandro D’Elia^{10,11}, Tommaso Mazza^{12}, Michael Meyer^{12}, Carlo Callegari^{13}, Michele Di Fraia^{13}, Oksana Plekan^{13}, Robert Richter^{13}, Luca Giannessi^{13,14}, Enrico Allaria^{13}, Giovanni De Ninno^{13,15}, Mauro Trovò^{13}, Laura Badano^{13}, Bruno Diviacco^{13}, Giulio Gaio^{13}, David Gauthier^{13}, Najmeh Mirian^{13}, Giuseppe Penco^{13}, Primož Rebernik Ribič^{13,15}, Simone Spampinati^{13}, Carlo Spezzani^{13}, and Kevin C. Prince^{13,16}

^{1 }Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

^{2 }Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

^{3 }Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

^{4 }Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

^{5 }Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

^{6 }Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

^{7 }Institut für Photonik, Technische Universität Wien, 1040 Vienna, Austria

^{8 }ELI-ALPS, ELI-HU Non-Profit Limited, Dugonics tér 13, H-6720 Szeged, Hungary

^{9 }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:**

### Reference

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, |