Anomalous Photon-Induced Near-Field Electron Microscopy

Yiming Pan, Bin Zhang, and Avraham Gover

Phys. Rev. Lett. 122, 183204 – Published 10 May 2019

Abstract

We reveal the classical and quantum regimes of free electron interaction with radiation, common to the general variety of radiation sources (e.g., a Smith-Purcell radiation), the dielectric laser accelerator, and photo-induced near-field electron microscopy (PINEM). Modeling the electron with initial conditions of a coherent quantum electron wave packet, its topology in phase space uniquely defines a universal distinction of three interaction regimes: point-particle-like acceleration, a quantum wave function (PINEM), and a newly reported regime of anomalous PINEM (APINEM). The quantum interference beat of APINEM is capable of improving the spectral resolution of postselective electron microscopy. The particle-wave duality transition between regimes reveals the history-dependent nature of quantum electron interaction with light.

Received 12 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.183204

Physics Subject Headings (PhySH)

Free-electron laser acceleration Light-matter interaction Quantum foundations Quantum tomography Quantum-to-classical transition

Electron microscopy

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Yiming Pan^1,3,*, Bin Zhang², and Avraham Gover^3,†

¹Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
²National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
³Department of Electrical Engineering Physical Electronics, Tel Aviv University, Ramat Aviv 69978, Israel

^*Corresponding author. yiming.pan@weizmann.ac.il
^†Corresponding author. gover@eng.tau.ac.il

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Vol. 122, Iss. 18 — 10 May 2019

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Images

Figure 1
Illustrations of PINEM, acceleration, and APINEM processes in phase-space representation before (broken-line ellipses) and after (positive, red and yellow; negative, blue) interaction and their energy (momentum) distributions (EELS). The initial distributions $W^{(00)}$ of the quantum electron wave packets (QEW) of area $h / 2$ are overlaid over a grid of area $h$ (Planck constant) tiles. (a) A universal light-electron interaction scheme. (b),(c) PINEM case, the initial distribution is temporally (or longitudinally) expanded [Eq. (2)], and its energy spread is narrow [Eq. (1)], (b) Unchirped. (c) Prechirped. (d) Particlelike acceleration with net momentum shift for an initially temporally short QEW with well-defined phase. (e) APINEM case. Expanded and strongly prechirped initial QEW, with quantum interference fringes emerging.
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Figure 2
Universal classification of light-matter interaction regimes in terms of the initial parameters of the quantum electron wave function: its minimal axial waist size $σ_{z 0}$ and the preinteraction drift length from this point, $L_{D}$ . Point-particle-like acceleration as in Fig. 1 takes place with the initial parameter regime $Γ < \sqrt{2}$ , or $σ_{z} (t_{D}) < β λ / \sqrt{2} π$ , PINEM interaction [Figs. 1 and 1] takes place in the regime $Γ_{0} = 2 π σ_{z_{0}} / β λ > \sqrt{2}$ , and APINEM interaction takes place in the regime $Γ_{0} < \sqrt{2}$ and $Γ > \sqrt{2}$ . The classical point-particle picture appears at the limit $Γ = 2 π σ_{z} (L_{D}) / β λ \to 0$ . The diagram is drawn for optical wavelength $λ = 0.8 μ m$ .
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Figure 3
Numerical simulations of (a) PINEM (with wave packet entering at its waist; $σ_{z_{0}} = 0.4 μ m$ , $β λ = 0.2 μ m$ ); (b) acceleration (with wave packet entering at its waist; $σ_{z_{0}} = 0.04 μ m$ , $β λ = 1.2 μ m$ ); and (c) APINEM (with $σ_{z} (L_{D}) = 1.5 μ m > β λ$ after preinteraction drift of $L_{D} = 60 cm$ ). The interaction region is represented by the sinusoidal interacting wave component of the near field of a laser illuminated grating. The period of the wave should be compared to the axial extents of the wave packet at entrance. Shown are the features of the quantum electron wave function distributions in phase space before and after interaction, and the momentum distributions in momentum space (right panels).
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Figure 4
The dependence on wavelength of the momentum or energy spectral sideband spacing in PINEM ( $δ p = ℏ ω / v_{0} = 2 π ℏ / β λ$ ) and APINEM [ $δ p ≃ (m^{*} v_{0} / L_{D}) β λ$ ]. The lines (solid and dashed) are based on theory, and in the corresponding data; the points (blue, red, and purple) were computed numerically from Schrödinger equation for different wave packet sizes and drift lengths. The different scaling with $β λ$ of the PINEM energy spectrum sideband separation and the APINEM interference beats distinguishes well the two effects in the experiment.
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