arXiv subjects

Peter Schattschneider

Publications and source records attributed to Peter Schattschneider.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement in Elastic Electron Scattering: Perturbation theory misses fundamental aspects of Bragg scattering

Elastic electron scattering is one of the primary means of investigating materials on the atomic scale. It is usually described in a one-particle approach (the probe electron's evolution in a perturbative static potential), whereas we are dealing here with a two-body interaction between the probe and the sample, both described by separate quantum states, inducing entanglement. In this work, we present a quantum treatment of elastic electron scattering. We find that the entanglement between probe and scatterer can have far-reaching consequences, particularly on coherence and image contrast. As a timely example, we discuss decoherence in Bragg scattering on nanoparticles. We find that conventional scattering theory is recovered in most cases. The situation changes dramatically for freely evolving nano particles as e.g. levitated motional ground states, an active field of research.

quant-ph↗

arXiv2024

A Snapshot of Relativistic Motion: Visualizing the Terrell Effect

We present an experimental visualization of the Terrell effect, an optical phenomenon predicted in 1959 by Roger Penrose and James Terrell, which reveals that the Lorentz contraction of a moving object is not visible in a snapshot photograph. Using fs-laser pulses and a gated intensified camera that allows gating times as short as 300 ps, we achieve a virtual reduction of the speed of light to less than 2 m/s, enabling the visualisation of relativistically moving objects in real time. By capturing light reflected from deliberately Lorentz-contracted objects, our setup effectively reconstructs their visual appearance. This didactic visualization not only commemorates the centennial of Anton Lampa's seminal 1924 paper on relativistic length contraction but also provides the first experimental evidence of the Terrell effect in a laboratory setup. Our results comprise detailed relativistic illustrations, simulations and photographic snapshots of a sphere and a cube, which are animated to velocities close to the speed of light, revealing the apparent rotation effect and the distortion predicted by relativistic theory.

physics.optics↗

arXiv2023

A quantum logic gate for free electrons

The topological charge $m$ of vortex electrons spans an infinite-dimensional Hilbert space. Selecting a two-dimensional subspace spanned by $m=\pm 1$, a beam electron in a transmission electron microscope (TEM) can be considered as a quantum bit (qubit) freely propagating in the column. A combination of electron optical quadrupole lenses can serve as a universal device to manipulate such qubits at the experimenter's discretion. We set up a TEM probe forming lens system as a quantum gate and demonstrate its action numerically and experimentally. High-end TEMs with aberration correctors are a promising platform for such experiments, opening the way to study quantum logic gates in the electron microscope.

quant-ph↗

arXiv2020

The electron microscope as a quantum gate

We propose to use the topological charge instead of the spin variable to span a two-dimensional Hilbert space for beam electrons in a transmission electron microscope (TEM). In this basis, an electron can be considered as a qbit freely floating in vacuum. We show how a combination of magnetic quadrupoles with a magnetic drift tube can serve as a universal device to manipulate such qbits at the experimenter's discretion. High-end TEMs with aberration correctors, high beam coherence and utmost stability are a promising platform for such experiments, allowing the construction of quantum logic gates for single beam electrons in a microscope.

quant-ph↗

arXiv2018

Entanglement and Entropy in Electron-Electron Scattering

Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy. For spinless distinguishable electrons the entropy is sizeable at low energies, indicating strong momentum entanglement, and drops to almost zero at energies of the order of 10 keV when the azimutal degree of freedom is integrated out, i.e. practically no entanglement and almost pure one-electron states. If spin is taken into account, the entropy for electrons with antiparallel spins should be larger than in the parallel-spin case, since it embodies both momentum and spin entanglement. Surprisingly, this difference, as well as the deviation from the spin-less case, is extremely small for the complete scattering state. Strong spin entanglement can however be obtained by post-selecting states at scattering angle pi/2.

quant-ph↗

arXiv2018

$π$/2 Mode Converters and Vortex Generators for Electrons

In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be produced in a setup consisting of two identical cylinder lenses. In electron optics, quadrupole lenses can be used for the same purpose. Here we investigate generalized asymmetric designs of a quadrupole mode converter that may be realized within the constraints of existing electron microscopes and can steer the development of dedicated vortex generators for high brilliance electron vortex probes of atomic scale.

physics.app-ph↗

arXiv2017

Peculiar Rotation of Electron Vortex Beams

Standard electron optics predicts Larmor image rotation in the magnetic lens field of a TEM. Introducing the possibility to produce electron vortex beams with quantized orbital angular momentum brought up the question of their rotational dynamics in the presence of a magnetic field. Recently, it has been shown that electron vortex beams can be prepared as free electron Landau states showing peculiar rotational dynamics, including no and cyclotron (double-Larmor) rotation. Additionally very fast Gouy rotation of electron vortex beams has been observed. In this work a model is developed which reveals that the rotational dynamics of electron vortices are a combination of slow Larmor and fast Gouy rotations and that the Landau states naturally occur in the transition region in between the two regimes. This more general picture is confirmed by experimental data showing an extended set of peculiar rotations, including no, cyclotron, Larmor and rapid Gouy rotations all present in one single convergent electron vortex beam.

physics.class-ph↗

arXiv2017

EMCD with an electron vortex filter: Limitations and possibilities

We discuss the feasibility of detecting spin polarized electronic transitions with a vortex filter. This approach does not rely on the principal condition of the standard energy loss magnetic chiral dichroism (EMCD) technique, the precise alignment of the crystal, and thus paves the way for the application of EMCD to new classes of materials and problems. The dichroic signal strength in the L$_{2,3}$-edge of ferromagnetic cobalt is estimated on theoretical grounds. It is shown that magnetic dichroism can, in principle, be detected. However, as an experimental test shows, count rates are currently too low under standard conditions.

cond-mat.mtrl-sci↗

arXiv2016

Mapping atomic orbitals with the transmission electron microscope: Images of defective graphene predicted from first-principles theory

Transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time. Here, we explore its capabilities by a first principles approach. For the example of defected graphene, exhibiting either an isolated vacancy or a substitutional nitrogen atom, we show that three different kinds of images are to be expected, depending on the orbital character. To judge the feasibility of visualizing orbitals in a real microscope, the effect of the optics aberrations is simulated. We demonstrate that, by making use of energy-filtering, it should indeed be possible to map atomic orbitals in a state-of-the-art transmission electron microscope.

cond-mat.mtrl-sci↗

arXiv2016

Real-space mapping of electronic orbitals

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the Ångström scale in bulk rutile (TiO2) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.

cond-mat.mtrl-sci↗

arXiv2016

Magnetic properties of single nanomagnets: EMCD on FePt nanoparticles

Energy-loss magnetic chiral dichroism (EMCD) allows for the quantification of magnetic properties of materials at the nanometer scale. It is shown that with the support of simulations that help to identify the optimal conditions for a successful experiment and upon implementing measurement routines that effectively reduce the noise floor, EMCD measurements can be pushed towards quantitative magnetic measurements even on individual nanoparticles. With this approach, the ratio of orbital to spin magnetic moments for the Fe atoms in a single L$1_0$ ordered FePt nanoparticle is determined to be ${m_l}/{m_s} = 0.08 \pm 0.02$. This finding is in good quantitative agreement with the results of XMCD ensemble measurements.

cond-mat.mtrl-sci↗

arXiv2015

Spin polarisation with electron Bessel beams

The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized. In the limit of infinitely small detectors on axis, the spin polarisation tends to 100 % . Increasing the detector size, the polarisation decreases rapidly, dropping below 10^-4 for standard settings of medium voltage microscopes. For extremely low voltages, the figure of merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage.

quant-ph↗

arXiv2013

Is magnetic chiral dichroism feasible with electron vortices?

We discuss the feasibility of detecting magnetic transitions with focused electron vortex probes, suggested by selection rules for the magnetic quantum number. We theoretically estimate the dichroic signal strength in the L$_{2,3}$ edge of the ferromagnetic d metals. It is shown that under realistic conditions, the dichroic signal is undetectable for nanoparticles larger than ~1 nm. This is confirmed by a key experiment with nanometer sized vortices.

quant-ph↗

arXiv2013

Comment on "Quantized Orbital Angular Momentum Transfer and Magnetic Dichroism in the Interaction of Electron Vortices with Matter"

It was claimed (Lloyd et al., PRL 108 (2012) 074802) that energy loss magnetic chiral dichroism (EMCD) with electron vortex beams is feasible, and has even advantages over the standard setup with Bragg diffracted waves. In this Comment, we show that Lloyd et al. ignored an important constraint on the proposed selection rule for the transfer of angular momentum in the interaction, namely that it is only valid for an atom located in the very center of the vortex. As an experimental consequence, the EMCD signal will only be strong for extremely small nanoparticles of 1 to 2 nm diameter.

quant-ph↗

arXiv2013

A pure state decomposition approach of the mixed dynamic form factor for mapping atomic orbitals

We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as a quadratic form. This makes it possible to use matrix diagonalization methods to reduce the number of terms that need to be taken into account when calculating the inelastic scattering of electrons in a crystal. It also leads in a natural way to a new basis that helps elucidate the underlying physics. The new method is applied to several cases to show its versatility. In particular, predictions are made for directly imaging atomic orbitals in crystals.

cond-mat.mtrl-sci↗

arXiv2013

Observation of the Larmor and Gouy Rotations with Electron Vortex Beams

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, hen passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behaviour is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.

physics.optics↗

arXiv2012

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.

quant-ph↗

arXiv2012

A novel vortex generator and mode converter for electrons

A mode converter for electron vortex beams is described. Numerical simulations, confirmed by experiment, show that the converter transforms a vortex beam with topological charge $m=\pm 1$ into beams closely resembling Hermite-Gaussian HG$_{10}$ and HG$_{01}$ modes. The converter can be used as a mode discriminator or filter for electron vortex beams. Combining the converter with a phase plate turns a plane wave into modes with topological charge $m=\pm 1$. This combination serves as a generator of electron vortex beams of high brilliance.

quant-ph↗