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Springer series on atomic, optical, and plasma physics

Scattering of Photons by Many-Electron Systems

A. N. Hopersky, Victor A. Yavna

Published Nov 2, 2009• 14 citations
Publisher
DOI
10.1007/978-3-642-04256-0

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A Stokes parameter representation for two-photon systems is developed to calculate cross sections for both entangled and classically correlated mixed states scattering off unpolarized and polarized Compton electrons. The cross section of Compton scattering for pairs of maximally entangled annihilation photons, generated by the disintegration of para-positronium, is compared with classical analogs. An analysis of the symmetrical properties and basis independence of these systems is conducted to elucidate the observed differences. We propose a method to establish an upper bound for identifying correlations influenced by entanglement. Furthermore, we calculate the cross section for Compton scattering of annihilation photons from spin-polarized electrons. A qualitative analysis reveals a contradiction to the contemporary assumption that Compton scattering acts as an entanglement kill switch. These findings contribute to a broader understanding of photon systems and their behavior in various scattering scenarios. Although the primary focus of this article is on Compton scattering, the formalism can be adapted to other interactions, provided that the Mueller matrix representation of the interaction is available. Published by the American Physical Society 2024

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Nonrelativistic Kapitza-Dirac scattering of electrons from counterpropagating bichromatic laser waves is studied in the resonant Bragg regime, taking the electron spin into account. We show that the intrinsic field-induced detuning, which arises in the Rabi oscillation dynamics between initial and scattering state of the electron, can be compensated by a suitable adjustment of its incident momentum. Analytical formulas of the optimized electron momentum for spin-dependent three-photon and spin-independent four-photon Kapitza-Dirac scattering are obtained from simplified model systems in reduced dimensionality, which preserve the characteristic properties of the process.
Electron beams are an exceptional tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled nanoscale [2,3] and attosecond phase-resolved mapping of optical near-fields [4] by stimulated inelastic scattering between electrons and light. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [5]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promoting single-particle-based scattering experiments [6]. Here, we demonstrate the generation of nonclassical multiphoton states via coherent cathodoluminescence (CL) from an optical waveguide, approaching near-unity coupling in electron spectroscopy of nanophotonic systems [7]. To this end, we scatter swift electrons at the optical mode of a custom silicon nitride photonic chip. Specifically, inside of a transmission electron microscope, a beam of free electrons (100-keV kinetic energy) passes parallel to the waveguide surface in an aloof geometry (cf. Fig. 1a). The electrons can inelastically scatter with the evanescent tail of the guided optical mode, generating photons at a wavelength around 1400 nm in the fundamental quasi-TM mode, while the electrons lose multiples N of the corresponding photon energy of 0.88 eV (cf. Fig. 1b). The photons are then coupled via optical fibers to a balanced beam splitter and two single-photon avalanche diodes (SPADs), implementing a Hanbury Brown and Twiss (HBT) setup (cf. Fig. 1c). Probing the ensemble average using the 2nd-order correlation function g(2), we observe Poissonian photon statistics in accordance with the underlying coherent scattering mechanism (Fig. 1d, top). A parallel single-particle-resolved measurement using an event-based electron camera (Timepix3 ASIC) coupled to an EEL spectrometer provides information on both electron energy and arrival time. This allows us to further investigate the photon statistics of the generated light as a function of the electron energy. Using this electron-heralded HBT setup, we verify the generation of single photons following an energy loss of E = ℏω (Fig. 1d, bot), and photon pairs for double scattering events. Characterizing the electron-driven photon generation using established metrics for heralded single-photon sources, such as spontaneous parametric down-conversion (SPDC), we find an intrinsic single-photon heralding efficiency of 10% and a coincidence-to-accidental ratio > 30. This establishes a new source for electron-heralded quantum light, which may find its applications in quantum photonics. Practically, efficient electron-photon coupling and event-based detention, offers a new pathway for coincidence-enhanced electron spectroscopy of photonic materials [8]. Besides eliminating undesired and formerly unrecoverable averaging, access to the full scattering distribution of the involved particles can strongly suppress noise in ultrafast electron experiments [6]. Furthermore, for systems that can be directly pumped by single electrons, ultrafast dynamics can be studied using continuous electron beams, achieving sub-nanosecond resolution, only limited by the employed detector technology. Finally, this work represent an essential step toward quantum-enhanced electron imaging and enables the heralding of individual electrons for dose-sensitive applications. a) Electrons are scattered at an extended waveguide, generating light by coherent cathodoluminescence. b) Electron energy loss into discrete sidebands is observed, spaced by the photon energy ℏω. c) Event-based coincidence spectroscopy enables electron-heralded detection of photon number states. d) The discrete 2nd-order correlation function g(2)[q] shows Poissonian statistics for unheralded photon detection, while conditioning on an ℏω energy loss produces high-contrast single-photon states.
A Stokes parameter representation for two-photon systems is developed to calculate cross sections for both entangled and classically correlated mixed states scattering off unpolarized and polarized Compton electrons. The cross section of Compton scattering for pairs of maximally entangled annihilation photons, generated by the disintegration of para-positronium, is compared with classical analogs. An analysis of the symmetrical properties and basis independence of these systems is conducted to elucidate the observed differences. We propose a method to establish an upper bound for identifying correlations influenced by entanglement. Furthermore, we calculate the cross section for Compton scattering of annihilation photons from spin-polarized electrons. A qualitative analysis reveals a contradiction to the contemporary assumption that Compton scattering acts as an entanglement kill switch. These findings contribute to a broader understanding of photon systems and their behavior in various scattering scenarios. Although the primary focus of this article is on Compton scattering, the formalism can be adapted to other interactions, provided that the Mueller matrix representation of the interaction is available. Published by the American Physical Society 2024