Orbital angular momentum carried by an optical field can be imprinted onto a propagating electron wave.

Photons have fixed spin and unbounded orbital angular momentum (OAM). While the former is manifested in the polarization of light, the latter corresponds to the spatial phase distribution of its wavefront. The distinctive way in which the photon spin dictates the electron motion upon light–matter interaction is the basis for numerous well-established spectroscopies. By contrast, imprinting OAM on a matter wave, specifically on a propagating electron, is generally considered very challenging and the anticipated effect undetectable. Here, we seek to observe an OAM-dependent dichroic photoelectric effect, using a sample of He atoms. Surprisingly, we find that the OAM of an optical field can be imprinted coherently onto a propagating electron wave. 
In the experiment we carried out at the LDM end-station of the FERMI FEL, He atoms are ionized by extreme ultraviolet (XUV) radiation, generated by a free-electron laser (FEL), in the presence of an intense infrared laser field (Fig. 1a). The FEL beam is in a fixed (right-handed) circular polarization state, σFEL=+1. What happens if the infrared field has a vortex phase profile carrying OAM? This would be surprising: the atomic wave function is extremely localized on the scale of the OAM beam’s waist (Fig. 1b). Off-axis atoms experience the infrared laser field as an ordinary Gaussian beam and atoms close to the optical axis, where the OAM is well defined, experience a vanishingly small field. Besides, the fraction of near-axis atoms is small. To investigate the possibility of observing a vortex-dependent dichroic effect on randomly distributed electrons, we used an infrared laser with adjustable right- or left-handed circular polarization (σIR=±1), and variable amount mOAMℏ of OAM, where mOAM is a signed integer, called topological charge. The two light beams are focused and overlapped with a gas jet of He atoms in a vacuum chamber equipped with a velocity map imaging (VMI) spectrometer.
The velocity distribution of electrons produced in the interaction volume is projected onto a two-dimensional (2D) imaging detector. For sufficiently high infrared intensities, the resulting photoelectron spectra (Fig. 1c,d) show a main band, corresponding to direct (XUV-induced) photoemission, together with a series of weaker rings, called sidebands, whose radius increment (decrement) represents the energy acquired (lost) by the photo-emitted electrons upon absorption (emission) of one or more infrared photons. All bands depend on the polar angle at which photoelectrons are emitted. They reflect the interplay between XUV and optical fields during the photoionization process, providing information on the transfer of light properties, for example, angular momentum, to matter. The two VMI spectra shown in Fig. 1c,d were obtained for fixed infrared polarization (σIR=±1) and alternate OAM (+ℏ and -­ℏ, respectively), with all other experimental conditions kept unchanged. The images demonstrate that different topological charges result in qualitatively different photoelectron spectra, attesting to a clear OAM-dependent dichroic effect. This is a proof of the possibility to imprint virtually unbounded photon OAM on the matter wave of a propagating electron.


Figure 1.    Experimental set-up and first evidence of OAM-dependent dichroism. a, Schematic representation of the experimental set-up. The XUV light pulse is generated using a FEL.  It has a fixed (right-handed) circular polarization, a spot size of ~10 μm and power density (at sample position) of the order of 1018 Wm−2. The infrared laser beam has a spot size of ~60 μm and a power density in the range 0.5–4×1018Wm−2. It provides variable circular (right- and left-handed) polarization and can be made to carry a topological charge (mOAM=±1). Helium gas is injected into the experimental chamber (at room temperature) via a gas jet system. A VMI spectrometer is used to determine the angular distribution of the signal generated by the photo-emitted electrons. b, Real-size XUV-FEL (blue) and infrared (red) spatial profiles at the waist position. Helium atoms are also represented as dots with exaggerated dimensions. c, VMI image obtained for high infrared intensity (~3 × 1017W m−2), right-handed infrared polarization and positive topological charge (mOAM=+1). d, As in c, but with negative topological charge (mOAM=−1).

To clarify the underlying physics of OAM-dependent dichroism, we developed a first-principle theoretical model that amounts to a numerical solution of the 3D time-dependent Schrödinger equation for the laser-driven atom, The projection of the solution of the Schrödinger equation on above-threshold continuum states yields the differential cross-sections (DCSs) for a given electron kinetic energy.
Figure 2 shows the experimental and theoretical DCSs for different combinations of OAM and spin carried by the IR beam, together with the OAM-dependent dichroism as a function of the polar angle. The agreement between experiment and theory is good: in both cases there is a clear OAM-dependent dichroic effect. 
Summarizing, we confirm that the spatial distribution of an optical field with vortex phase profile can be imprinted coherently on a photoelectron wave packet that recedes from atoms distributed randomly over the laser spot. Our results explore new aspects of light–matter interaction and point to qualitatively novel analytical tools, which can be used to study, for example, the electronic structure of intrinsic chiral organic molecules.


Figure 2.    Experimental versus theoretical photoelectron spectra and DCSs for different combinations of infrared spin and OAM.a, Experimental VMI spectrum for the combination σIR=+1,mOAM=−1. b, Theoretical VMI spectrum for the same combination as in a. c, Continuous curves: experimental DCSs for the combinations σIR=+1 (labelled CR), mOAM=+1 and σIR=+1,mOAM=−1. Dashed curve: corresponding dichroic contrast. d, Theoretical DCSs and dichroic contrast for the same combination as in c. e, Experimental DCSs and dichroic contrast for the combinations σIR=+1, mOAM=+1 and σIR=−1 (labelled CL), mOAM=−1. f, Theoretical DCSs and dichroic contrast for the same combination as in e. g, Experimental DCSs and dichroic contrast for the combinations σIR=+1, mOAM=+1 and σIR=−1,mOAM=+1. h, Theoretical DCSs and dichroic contrast for the same combination as in g. 


This research was conducted by the following research team:

Giovanni De Ninno1,2, Jonas Wätzel3, Primož Rebernik Ribič2,1, Enrico Allaria2, Marcello Coreno4,2, Miltcho B. Danailov2, Christian David5, Alexander Demidovich2, Michele Di Fraia2, Luca Giannessi2,6, Klavs Hansen7,8, Špela Krušič9, Michele Manfredda2, Michael Meyer10, Andrej Mihelič9, Najmeh Mirian2,Oksana Plekan2, Barbara Ressel1, Benedikt Rösner5, Alberto Simoncig2, Simone Spampinati2, Matija Stupar1, Matjaž Žitnik9, Marco Zangrando2,11, Carlo Callegari2, Jamal Berakdar3


Elettra-Sincrotrone Trieste S.C.p.A., Trieste, Italy
University of Nova Gorica, Nova Gorica, Slovenia
Institut für Physik, Martin-Luther Universität Halle-Wittenberg, Halle (Saale), Germany
ISM-CNR, in Basovizza Area Science Park, Trieste, Italy
Paul Scherrer Institut, Villigen, Switzerland
INFN-LNF, Frascati (Rome), Italy
Center for  Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin, China
Dept. of Physics, Gothenburg University, Gothenburg, Sweden
J. Stefan Institute, Ljubljana, Slovenia
10 European XFEL GmbH Schenefeld, Germany
11 Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste, Italy.

Contact persons:

Giovanni De Ninno, email:



G. De Ninno, J. Wätzel, P. Rebernik Ribič, E. Allaria, M. Coreno, M. B. Danailov, C. David, A. Demidovich, M. Di Fraia, L. Giannessi, K. Hansen, Š. Krušič, M. Manfredda, M. Meyer, A. Mihelič, N. Mirian, O. Plekan, B. Ressel, B. Rösner, A. Simoncig, S. Spampinati, M. Stupar, M. Žitnik, M. Zangrando, C. Callegari, J. Berakdar, "Photoelectric effect with a twist", Nature Photonics 14, 554 (2020). DOI: 10.1038/s41566-020-0669-y

Last Updated on Monday, 19 October 2020 16:32