Electron Vortex Research Articles

Multislice method based full-space analysis on mechanical interaction of electron vortex beam with a crystalline particle

A full-space analysis based on the multislice method is presented and has been applied to the simulation of mechanical interaction of electron vortex beam with a nanoparticle. The moment acting on the particle is calculated and presented as a moment map. We have calculated the total torque and compared it with the result from orbital angular momentum analysis. The thickness dependent torque and angular momentum are derived and discussed for different incident energies, convergence angles and angular momenta of the incident electron vortex beam. For different incident beams, the enhanced torque caused by diffraction enhancement is discussed. The oscillation behavior of the torque and angular momentum on depth is explained by a channeling theory. A comparison of thickness dependent angular momentum between the proposed analysis and conventional orbital angular momentum analysis in both the multislice method and the Bloch wave method is presented and discussed.

Kinetic‐Size Magnetic Holes in the Terrestrial Foreshock Region

AbstractKinetic‐size magnetic holes (KSMHs) can accelerate and heat the particles, resulting the energy dissipation in space plasmas. KSMHs in the terrestrial foreshock region are statistically investigated based on the Magnetospheric Multiscale data from October 2015 to December 2019. A total of 98 KSMHs are successfully selected, and most of them are accompanied by electron vortices. The fluxes of electrons at ∼90° of pitch angle enhance inside the magnetic holes, where the perpendicular and total electron temperature increase, and the parallel electron temperature slightly decreases inside these magnetic holes. Moreover, we reveal a novel phenomenon that a lot of the observed KSMHs are probably moving toward the Sun in the plasma flow frame. Such sunward propagating KSMHs are detected for the first time in the foreshock region. We propose that these observed KSMHs are probably generated in the foreshock region and then propagate to the Sun.

Dynamical Control of Nuclear Isomer Depletion via Electron Vortex Beams.

Some nuclear isomers are known to store a large amount of energy over long periods of time, with a very high energy-to-mass ratio. Here, we describe a protocol to achieve the external control of the isomeric nuclear decay by using electron vortex beams whose wave function has been especially designed and reshaped on demand. Recombination of these electrons into the isomer's atomic shell can lead to the controlled release of the stored nuclear energy. On the example of ^{93m}Mo, we show theoretically that the use of tailored electron vortex beams increases the depletion by 4 orders of magnitude compared to the spontaneous nuclear decay of the isomer. Furthermore, specific orbitals can sustain an enhancement of the recombination cross section for vortex electron beams by as much as 6 orders of magnitude, providing a handle for manipulating the capture mechanism. These findings open new prospects for controlling the interplay between atomic and nuclear degrees of freedom, with potential energy-related and high-energy radiation source applications.

Electrostatic shock waves driven by electron vortices in laser–plasma interactions

Nonlinear structures such as shock waves and vortices widely exist in nature and the Universe. They have also been separately observed in laser–plasma interactions. We show for the first time that two perpendicularly propagated collisionless electrostatic shock waves (CESs) can be excited by a moving electron vortex (EV). The latter is driven by an ultrashort intense laser pulse propagating through a sandwich nonuniform underdense plasma slab and is found to move perpendicularly to the density gradient. Two CESs are observed on both sides of the passing route of the EVs. The left-side CES is induced by a high-density electron layer, which originates from the vortex front and is compressed and accelerated during the EV motion. The right-side CES is induced by supersonic ions accelerated by the EVs directly. Ion acceleration by such CESs along the directions perpendicular to the vortex propagation is also observed. This study reveals the transformation of nonlinear structures and provides new routes for laser energy dissipation in plasmas.

Comment on “Nonlinear quantum effects in electromagnetic radiation of a vortex electron”

This comment on the paper by Karlovets and Pupasov-Maksimov [Phys. Rev. A 103, 012214 (2021)] addresses their criticism of the combined experimental and theoretical study by Remez et al. [Phys. Rev. Lett. 123, 060401 (2019)]. We show, by means of simple optical arguments as well as numerical simulations, that the arguments raised by Karlovets and Pupasov-Maksimov do not hold in the experimental regime reported by Remez et al. Further, we discuss a clarification for the theoretical derivations presented by Karlovets and Pupasov-Maksimov, as they hold only when the final state of the emitting electron is observed in coincidence with the emitted photon. Although this scenario is feasible and may stimulate new experimental regimes that do correspond to the predictions reported by Karlovets and Pupasov-Maksimov, it is not the common scenario in cathodoluminescence, where only the light is measured. Upon lifting the concerns regarding the experimental regime reported by Remez et al., and explicitly clarifying the electron postselection, we believe that the paper by Karlovets and Pupasov-Maksimov may constitute a valuable contribution to the problem of spontaneous emission by shaped electron wave functions, as it presents new expressions for the emission rates beyond the ubiquitous paraxial approximation.

Reply to “Comment on ‘Nonlinear quantum effects in electromagnetic radiation of a vortex electron' ”

We argue that although the experiment of Remez et al. [Phys. Rev. Lett. 123, 060401 (2019)] is interesting, and its conclusions may well be correct, the observed lack of dependence of the measured angular distributions on the electron's transverse coherence length could have been expected for the parameters chosen. This is because for Smith-Purcell radiation it is the coherence length of a virtual photon ${\ensuremath{\sigma}}_{\ensuremath{\perp}}^{(\ensuremath{\gamma})}\ensuremath{\approx}\ensuremath{\beta}\ensuremath{\gamma}\ensuremath{\lambda}\ensuremath{\lesssim}\ensuremath{\lambda}$ that plays a role of the radiation formation width and not the entire electron's coherence length that can well be orders of magnitude larger than the former. This is a common feature for all the radiation processes in which a photon is emitted not directly by the electron packet, which can be delocalized in space, but rather by a much better localized atom or a conduction electron on a surface. Therefore, in our opinion the results of Remez et al. cannot rule out the alternative hypothesis of the delocalized charge. The question, mainly addressed in the Comment by Karnieli et al., of whether the measurements were performed in the wave zone or not is interesting but somewhat secondary. We emphasize that the measured azimuthal distributions are unusually wide and there exists a family of classical effects that could also have resulted in the measured distributions. Such alternative classical hypotheses include: (i) effects of the beam sizes, of its angular divergence, of the temporal coherence of the radiation process, which is also related to how the wave zone is defined, and (ii) influence of the grating shape and of its material---the effects that are known to be of crucial importance for Smith-Purcell radiation from nonrelativistic electrons. Finally, we propose to repeat the experiment and to measure diffraction radiation from a thin metallic semiplane (or a strip) in which case the aforementioned classical effects play a much smaller role.

Floquet vortex states induced by light carrying an orbital angular momentum

We propose a scheme to create an electronic Floquet vortex state by irradiating a two-dimensional semiconductor with the laser light carrying non-zero orbital angular momentum. We analytically and numerically study the properties of the Floquet vortex states, with the methods analogous to the ones previously applied to the analysis of superconducting vortex states. We show that such Floquet vortex states are similar to the superconducting vortex states, and they exhibit a wide range of tunability. To illustrate the potential utility of such tunability, we show how such states could be used for quantum state engineering.

Theoretical and practical aspects of the design and production of synthetic holograms for transmission electron microscopy

Beam shaping—the ability to engineer the phase and the amplitude of massive and massless particles—has long interested scientists working on communication, imaging, and the foundations of quantum mechanics. In light optics, the shaping of electromagnetic waves (photons) can be achieved using techniques that include, but are not limited to, direct manipulation of the beam source (as in x-ray free electron lasers and synchrotrons), deformable mirrors, spatial light modulators, mode converters, and holograms. The recent introduction of holographic masks for electrons provides new possibilities for electron beam shaping. Their fabrication has been made possible by advances in micrometric and nanometric device production using lithography and focused on ion beam patterning. This article provides a tutorial on the generation, production, and analysis of synthetic holograms for transmission electron microscopy. It begins with an introduction to synthetic holograms, outlining why they are useful for beam shaping to study material properties. It then focuses on the fabrication of the required devices from theoretical and experimental perspectives, with examples taken from both simulations and experimental results. Applications of synthetic electron holograms as aberration correctors, electron vortex generators, and spatial mode sorters are then presented.

Electron vortices in spin-orbit coupling system

There exists an electron vortex solution with orbital angular momentum quantum in a non-spin-orbit coupling system which has nonconservative orbital angular momentum. We discuss the system with spin-orbit coupling and nonconservative orbital angular momentum, and we can find that the electrons with the total angular momentum numbers also have vortex beam solutions. And the vortex beam is expressed as an entangled wave function of the spin wave function and the vortex wave function. Taking the electrons in the central force field for example, in this paper constructed is a spinor vortex structure which is caused by the propagation of electrons carrying a fixed quantum number of total angular momentum along the <i>z</i>-axis. The spinor vortex structure is under the condition that the orbital angular momentum caused by spin-orbit coupling is non-conserved but the total angular momentum is conserved. The corresponding electron vortex beams in spin-vortex entanglement are solved by perturbation method, and the Foldy-Wouthuysen transformation is utilized to show that the vortex solution of the four-component spinor does exist in the case of relativity, when the electron with a fixed total angular momentum quantum number propagates along the <i>z</i>-axis in the central force field. The spinor provides theoretical support for the existence of the vortex structure for the system where the orbital angular momentum is not conserved but the total angular momentum is conserved due to spin-orbit coupling.

Post-solitons and electron vortices generated by femtosecond intense laser interacting with uniform near-critical-density plasmas

Generation of nonlinear structures, such as stimulated Raman side scattering waves, post-solitons and electron vortices, during ultra-short intense laser pulse transportation in near-critical-density (NCD) plasmas is studied by using multi-dimensional particle-in-cell (PIC) simulations. In two-dimensional geometries, both P- and S-polarized laser pulses are used to drive these nonlinear structures and to check the polarization effects on them. In the S-polarized case, the scattered waves can be captured by surrounding plasmas leading to the generation of post-solitons, while the main pulse excites convective electric currents leading to the formation of electron vortices through Kelvin–Helmholtz instability (KHI). In the P-polarized case, the scattered waves dissipate their energy by heating surrounding plasmas. Electron vortices are excited due to the hosing instability of the drive laser. These polarization dependent physical processes are reproduced in two different planes perpendicular to the laser propagation direction in three-dimensional simulation with linearly polarized laser driver. The current work provides inspiration for future experiments of laser–NCD plasma interactions.

Electron spectra for twisted electron collisions

Ionization collisions have important consequences in many physical phenomena, and the mechanism that leads to ionization is not universal. Double differential cross sections (DDCSs) are often used to identify ionization mechanisms because they exhibit features that distinguish close collisions from grazing collisions. In the angular DDCS, a sharp peak indicates ionization through a close binary collision, while a broad angular distribution points to a grazing collision. In the DDCS energy spectrum, electrons ejected through a binary encounter collision result in a peak at an energy predicted from momentum conservation. These insights into ionization processes are well-established for plane wave projectiles. However, the recent development of sculpted particle wave packets reopens the question of how ionization occurs for these new particle wave forms. We present theoretical DDCSs for (e, 2e) ionization of atomic hydrogen for electron vortex projectiles. Our results predict that the ionization mechanism for vortex projectiles is similar to that of non-vortex projectiles, but that the projectile’s momentum uncertainty causes noticeable changes to the shape and magnitude of the vortex DDCSs. Specifically, there is a broadening and splitting of the angular DDCS peak for vortex projectiles, and an increase in the cross section for high energy ejected electrons.

Investigation of vortex arms in electron vortices by counter-rotating elliptically polarized attosecond laser pulses

We theoretically investigate the vortex patterns in photoelectron momentum distributions of He+ driven by counter-rotating elliptically polarized, time delayed attosecond laser pulses by numerically solving the two-dimensional time-dependent Schrödinger equation. It is found that the number of vortex arms is extremely sensitive to the ellipticity and wavelength of counter-rotating elliptically polarized laser pulses, which is illustrated by the attosecond perturbation ionization models. In addition, the effect of different time delays between two pulses on the interference patterns is also investigated and the corresponding physical mechanism is demonstrated. Since the wavelength, ellipticity and time delay have a significant effect on the vortex interference patterns, this may be a new method for laser field detection.

In Situ Detection of Kinetic-size Magnetic Holes in the Martian Magnetosheath

Abstract Depression in magnetic field strength with a scale below one proton gyroradius is referred to as a kinetic-size magnetic hole (KSMH). KSMHs are frequently observed near Earth’s space environments and are thought to play an important role in electron energization and energy dissipation in space plasmas. Recently, KSMHs have been evidenced in the Venusian magnetosheath. However, observations of KSMHs in other planetary environments are still lacking. In this study, we present the in situ detection of KSMHs in the Martian magnetosheath using Mars Atmosphere and Volatile EvolutioN (MAVEN) for the first time. The distribution of KSMHs is asymmetry in the southern–northern hemisphere and no obvious asymmetry in the dawn–dusk hemisphere. The observed KSMHs are accompanied by increases in the electron fluxes in the perpendicular direction, indicating the cues of trapped electrons and the formation of electron vortices inside KSMHs. These features are similar to the observations in the Earth’s magnetosheath and magnetotail plasma sheet and the Venusian magnetosheath. This implies that KSMHs are a universal magnetic structure in space.

Hydrodynamic theory of vorticity-induced spin transport

Electron spin transport in a disordered metal is theoretically studied from the hydrodynamic viewpoint focusing on the role of electron vorticity. The spin-resolved momentum flux density of electrons is calculated taking account of the spin-orbit interaction and uniform magnetization, and the expression for the spin motive force is obtained as the linear response to a driving electric field. It is shown that the spin-resolved momentum flux density and motive force are characterized by troidal moments expressed as vector products of the applied external electric field and the spin polarization and/or magnetization. The spin-vorticity and magnetization-vorticity couplings studied recently are shown to arise from the toridal moments contribution to the momentum flux density. Spin motive force turns out to have a nonconservative contribution besides the conventional conservative one due to the spin-vorticity coupling. Spin accumulation induced by an electric field is calculated to demonstrate the direct relation between vorticity and induced spin, and the spin Hall effect is interpreted as due to the spin-vorticity coupling. The spin-vorticity coupling is shown to give rise to a vorticity-induced torque and a spin relaxation. The vorticity-induced torque is a linear effect of the spin-orbit interaction and is expected to be larger than the second-order torques such as nonadiabatic ($\beta$) current-induced torque due to magnetization structure. The intrinsic inverse spin Hall effect is argued to correspond to the antisymmetric components of the momentum flux density in the hydrodynamic context.

Statistical Properties of Electron-scale Magnetic Peaks in the Solar Wind at 1 au

Abstract Energy cascade from magnetohydrodynamic to kinetic scales can create many coherent structures in the turbulent astrophysical plasma environment, such as magnetic holes and magnetic peaks. Knowing the properties of each coherent structure is critical to better understand the process of the energy cascade. Recently, electron-scale magnetic peaks (ESMPs) are revealed to exist in the solar wind at 1 au. Here, we investigate the properties of the ESMPs upstream of the terrestrial bow shock based on observations of the Magnetospheric Multiscale spacecraft. We regard an isolated ESMP or a train of ESMPs as an ESMP event, and 204 ESMPs or 32 ESMP events are found. Both the durations and cross-section sizes of the ESMPs obey log-normal distributions. The median duration and cross-section size are ∼0.25 s and ∼0.33 ion gyroradius, respectively. The ESMP event with an average occurrence rate of ∼8.8 events per day tends to occur during the weak interplanetary magnetic field strength or the slow solar wind. We also find that the ion foreshock is an important source of the ESMP events, and a small part of the ESMP events originates from the upstream pristine solar wind. Although only 12 out of 204 ESMPs have bipolar electron velocities, we suggest that the electron vortex is an essential feature for the stable ESMP. The generation mechanism of the ESMPs is unclear; nevertheless, finding out the origin of the electron vortex in the ion foreshock might help to reveal their generation mechanism.

Collimated electron sheet driven by an intense Laguerre–Gaussian pulse

A collimated electron sheet is generated by using an intense circularly polarized (CP) Laguerre–Gaussian (LG) laser to irradiate the plasma in three-dimensional particle-in-cell simulations. It is found that the CP LGpl(p=0, l=1, σz=1) laser provides a more stable vortex force to ensure the concentrated transport of electrons as compared to a linearly polarized LG laser. Herein, the effects of the laser intensity, target density, and preplasma on collimated sheet formation are discussed in detail. Such collimated electron sheets may be potentially used in various applications such as the generation of vortex radiation sources and electron microscopy.

Multichromatic Polarization-Controlled Pulse Sequences for Coherent Control of Multiphoton Ionization

In this review, we report on recent progress in the generation and application of multichromatic polarization-tailored pulse sequences for the coherent control of multiphoton ionization (MPI) dynamics and present unpublished experimental results that complement our previous findings. Specifically, we utilize single-color, bichromatic, and trichromatic polarization-controlled pulse sequences generated by spectral amplitude, phase and polarization modulation of a carrier-envelope phase (CEP)-stable white light supercontinuum for MPI. The analysis of the number of ionization pathways and the number of distinct final free electron states shows that both increase significantly, but scale differently with the number of absorbed photons and the number of pulses in the sequence. In our experiments, ultrafast polarization shaping is combined with high-resolution photoelectron tomography to generate, control, and reconstruct three-dimensional photoelectron momentum distributions from atomic and molecular MPI. We discuss the use of polarization-controlled single-color and bichromatic pulse sequences in perturbative and non-perturbative coherent control of coupled electron-nuclear dynamics in molecules, atomic spin-orbit wave packet dynamics and the directional photoemission from atoms and chiral molecules. We compare the coherent control of CEP-insensitive intraband multipath interference in the MPI with a fixed number of photons with CEP-sensitive interband multipath interference in the ionization with a different number of photons. The generation and control of free electron vortices with even-numbered rotational symmetry by MPI with single-color pulse sequences is contrasted with the bichromatic control of CEP-sensitive electron vortices with odd-numbered rotational symmetry. To illustrate the potential of multichromatic pulse sequences for coherent control, we present a trichromatic scheme for shaper-based quantum state holography.

Coherent control mechanisms in bichromatic multiphoton ionization

Free electron vortices (FEVs) generated by multiphoton ionization (MPI) with ultrashort laser pulses have attracted significant attention due to their varied symmetries and unusual topological properties. We study two physical mechanisms of coherent control in atomic MPI with bichromatic polarization-shaped femtosecond laser pulses which give rise to the rich variety of FEVs. In the experiments, we combine pulse shaping of a carrier-envelope phase-stable supercontinuum with photoelectron tomography to generate and reconstruct three-dimensional photoelectron momentum distributions (PMDs). Simultaneous measurements of energetically separated photoelectrons from intraband and interband interference in a single PMD allow us to compare phase and polarization control of the angular distributions by both mechanisms. We investigate phase control in three scenarios: first, counterrotating circularly polarized pulses are employed to contrast the phase-insensitive angular momentum eigenstate created by intraband interference via frequency mixing with the phase-sensitive c 7 rotationally symmetric FEV from pure interband interference of two single-color ionization pathways. In the second scenario, we use orthogonal linearly polarized pulses to compare the phase control properties of a six-lobed angular momentum wave packet from intraband interference to those of a complex shaped interband PMD in the presence of phase fluctuations. Finally, we demonstrate phase control of a photoelectron hologram from mixed interband interference. In a (3 + 1) resonance enhanced MPI scheme, the red pump pulse induces a bound electron wave packet probed by the time-delayed blue pulse. The latter simultaneously creates a reference wave packet by three-photon ionization to form the photoelectron hologram. Rotation of the hologram with c 1 or c 5 rotational symmetry maps the time evolution of the bound wave packet. To analyze our results, we develop analytical expressions for the wave functions of intraband and interband interference in perturbative non-resonant MPI. The experiments are complemented with two-dimensional TDSE simulations to follow the FEV formation dynamics and to validate the physical pictures.

Single and double scattering mechanisms in ionization of helium by electron vortex projectiles

Triple differential cross sections (TDCSs) for electron vortex projectile ionization of helium into the azimuthal plane are calculated using the distorted wave Born approximation. In this collision geometry, the TDCSs at low and intermediate energies exhibit unique qualitative features that can be used to identify single and double scattering mechanisms. In general, our results predict that the ionization dynamics for vortex projectiles are similar to those of their non-vortex counterparts. However, some key differences are observed. For non-vortex projectiles, a double scattering mechanism is required to emit electrons into the azimuthal plane, and this mechanism becomes more important with increasing energy. Our results demonstrate that for vortex projectiles, emission into the azimuthal plane does not require a double scattering mechanism, although this process still significantly influences the shape of the TDCS at higher energies. At low projectile energies, non-vortex ionization proceeds primarily through single binary collisions. The same is generally true for vortex projectiles, although our results indicate that double scattering is also important, even at low energy. Vortex projectiles have an inherent uncertainty in their incident momentum, which causes a broadening of the binary peak at all energies and results in a splitting of the binary peak at higher energies. The results presented here lead to several predictions that can be experimentally tested.

Lower-hybrid drift waves and their interaction with plasmas in a 3D symmetric reconnection simulation with zero guide field

We investigate lower-hybrid drift waves (LHDW) in symmetric magnetic reconnection with zero guide field using three-dimensional particle-in-cell simulations. The long-wavelength mode with kρiρe∼1 develops in the bifurcated electron current layer around the X-line within the width of the electron meandering motion from the mid-plane, where ρi(e) is the ion (electron) gyroradius. The short-wavelength mode with kρe∼1 develops in the separatrix region downstream of the electron outflow jet, producing electron vortices in the background flow frame. Electrons follow the E × B drift with corrections from the diamagnetic drift and are heated inside the vortices with diverging electric fields. In the vortices, ions have comparable E × B and inertia drifts, which together mostly cancel the diamagnetic drift. Toward the center of diverging field vortices, ions are decelerated, leading to a decrease in the perpendicular temperature, while the loss of low-energy ions results in an increase in the parallel temperature. Parallel electric fields exist as a combination of the LHDW wave field projected to the magnetic field direction and the penetration of whistler waves that are mainly outside of the LHDW layer. The magnetic flux tube is twisted in the vortices. The twist may potentially lead to slippage reconnection, as indicated by the non-uniform parallel potential variation across field lines, while the periodic variations of the twisting directions are a limiting factor.