Strong Interaction of Slow Electrons with Near-Field Light Visited from First Principles

Nahid Talebi

Phys. Rev. Lett. 125, 080401 – Published 18 August 2020

Abstract

Strong interaction between light and matter waves, such as electron beams in electron microscopes, has recently emerged as a new tool for manipulating the electron wave packets. Here, we systematically investigate electron-light interactions from first principles. We show that enhanced coupling can be achieved for systems involving slow electron wave packets interacting with plasmonic nanoparticles, due to simultaneous classical recoil and quantum mechanical photon absorption and emission processes. For slow electrons with longitudinal broadenings longer than the dimensions of nanoparticles, phase matching between slow electrons and plasmonic oscillations is manifested as an additional degree of freedom to control the strength of coupling. Our findings pave the way toward a systematic and realistic understanding of electron-light interactions beyond adiabatic approximations, and lay the ground for the realization of matter-wave interferometry and boson-sampling devices involving light and matter waves.

Received 1 April 2020
Revised 31 May 2020
Accepted 7 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.080401

Physics Subject Headings (PhySH)

Electron beams & optics Light-matter interaction Ultrafast phenomena

Atomic, Molecular & Optical

Authors & Affiliations

Nahid Talebi ^*

Institute for Experimental and Applied Physics, Christian Albrechts University, Leibnizstrasse 19, 24118 Kiel, Germany

^*talebi@physik.uni-kiel.de

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 125, Iss. 8 — 21 August 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Weak and strong electron-light interactions. (a) Interaction of an electron wave packet with laser-induced dipolar plasmon oscillations in a gold nanorod with the radius of 15 nm, with the impact parameter $y_{0} = 15 nm$ . Demonstrated is the amplitude of the electron wave function before and after the interaction, and the electromagnetic scalar potential. Electron has the kinetic energy of 200 eV ( $β = 0.028$ ), and its initial longitudinal and transverse broadenings are 20 and 2 nm, respectively. Laser field amplitude, wavelength, and temporal broadening are $E_{0} = 2 \times 10^{9} V m^{- 1}$ , 800 nm, and 16 fs, respectively. (b)–(d) PINEM spectra for an electron wave packet with the same specifications as above, but a different kinetic energy of 400 eV ( $β = 0.0395$ ), interacting with the same system as stated above, excited at different laser field amplitudes of (b) $E_{0} = 5 \times 10^{8} V m^{- 1}$ , (c) $E_{0} = 1 \times 10^{9} V m^{- 1}$ , and (d) $E_{0} = 5 \times 10^{9} V m^{- 1}$ , specifying an increasing coupling strength and therefore photon absorption and emission orders.
Reuse & Permissions
Figure 2
Weak interactions between an electron and photon-induced plasmon oscillations in a gold nanorod with an elliptical cross section. The electron has a kinetic energy of 400 eV ( $β = 0.0395$ ) and initial longitudinal and transverse broadenings of 20 and 2 nm, respectively. Laser electric-field-amplitude, wavelength, and temporal broadening are $E_{0} = 5 \times 10^{9} V m^{- 1}$ , 800 nm, and 21 fs, respectively. (a) Angle-resolved differential expectation value of energy and (b) PINEM spectrum. Inset demonstrates the amplitude of the electron wave packet after its interaction with the system.
Reuse & Permissions
Figure 3
Strong interaction for an electron at the kinetic energy of $U = 400 eV$ ( $β = 0.0395$ ), interacting with the laser-induced localized plasmon oscillations in a gold nanorod with the radius of 15 nm. Electron has initial broadenings of 2 and 20 nm at the transverse and longitudinal directions. The laser electric-field amplitude is $E_{0} = 5 \times 10^{9} V m^{- 1}$ and its wavelength and temporal broadening are 800 nm and 16 fs, respectively. Amplitude of the electron wave packet at the (a) spatial and (b) momentum space. (c) Single ( $A$ ), ( $B$ ) and two-photon ( $C$ ) processes, leading to electron acceleration, deceleration, and diffraction, respectively. (d) Map of the angle-resolved differential expectation value of energy, demonstrating the effect of diffraction and energy loss and gain processes on the electron wave packet (see Supplemental Material movie [19]).
Reuse & Permissions
Figure 4
Controlling coupling strength by means of phase matching (synchronicity) between electron and light oscillations. (a),(c,),(e) amplitude of the electron wave packet and (b),(d),(f) PINEM spectra, after the interaction with a gold nanorod excited with an $x$ -polarized laser pulse at the wavelength of 800 nm, electric-field amplitude of $E_{0} = 5 \times 10^{9} V m^{- 1}$ , and temporal broadening of 16 fs. (a),(b) $U = 359 eV$ ( $β = 0.0375$ ) and $r = 15 nm$ , (c),(d) $U = 1436 eV$ ( $β = 0.0748$ ) and $r = 15 nm$ , (e),(f) $U = 359 eV$ ( $β = 0.0375$ ) and $r = 50 nm$ .
Reuse & Permissions

Physical Review Letters