arXiv subjects

Stefan Löffler

Publications and source records attributed to Stefan Löffler.

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↗

arXiv2026

Simulating Microwave-Controlled Spin Imaging with Free-Space Electrons

Coherent spin resonance techniques, such as nuclear and electron spin resonance spectroscopy, have revolutionized non-invasive imaging by providing spectrally resolved information about spin dynamics. Motivated by the recent emergence of electron microscopy methods capable of sensing microwave-excitations, we establish a theoretical framework for Spin Resonance Spectroscopy (SRS) in transmission electron microscopy (TEM). This technique combines microwave pump fields with focused electron probe beams to enable state-selective spin imaging at the atomic scale. Using scattering theory, we model the interaction between free-space electrons and electron spin systems, capturing both elastic and inelastic processes. The strongest effect of the spin system on the free electron is a magnetic phase shift. Our simulations demonstrate that phase shifts from individual electron spins are detectable in both image mode and diffraction mode. In principle, differential measurements under microwave control allow the extraction of local resonance frequencies that are influenced by the surrounding spin environment. By evaluating the Classical Fisher Information (CFI), we identify imaging conditions that maximize the signal-to-noise ratio (SNR), showing how defocus and beam width affect the measurement sensitivity. These findings establish a foundation for integrating SRS with high-resolution TEM, bridging spin spectroscopy and atomic-scale imaging, and enabling new capabilities in quantum spin research and nanoscale materials characterization.

quant-ph↗

arXiv2023

Visualising emergent phenomena at oxide interfaces

Knowledge of atomic-level details of structure, chemistry, and electronic states is paramount for a comprehensive understanding of emergent properties at oxide interfaces. We utilise a novel methodology based on atomic-scale electron energy loss spectroscopy (EELS) to spatially map the electronic states tied to the formation of a two-dimensional electron gas (2DEG) at the prototypical non-polar/polar $TiO_2$/$LaAlO_3$ interface. Combined with differential phase contrast analysis we directly visualise the microscopic locations of ions and charge and find that 2DEG states and $Ti^{3+}$ defect states exhibit different spatial distributions. Supported by density functional theory (DFT) and inelastic scattering simulations we examine the role of oxygen vacancies in 2DEG formation. Our work presents a general pathway to directly image emergent phenomena at interfaces using this unique combination of arising microscopy techniques with machine learning assisted data analysis procedures.

cond-mat.mtrl-sci↗

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↗

arXiv2023

Image Difference Metrics for High-Resolution Electron Microscopy

Digital image comparison and matching brings many advantages over the traditional subjective human comparison, including speed and reproducibility. Despite the existence of an abundance of image difference metrics, most of them are not suited for high-resolution transmission electron microscopy (HRTEM) images. In this work we adopt two image difference metrics not widely used for TEM images. We compare them to subjective evaluation and to the mean squared error in regards to their behaviour regarding image noise pollution. Finally, the methods are applied to and tested by the task of determining precipitate sizes of a model material.

cond-mat.mtrl-sci↗

arXiv2023

Optimizing Experimental Parameters for Orbital Mapping

A new material characterization technique is emerging for the transmission electron microscope (TEM). Using electron energy-loss spectroscopy, real space mappings of the underlying electronic transitions in the sample, so called orbital maps, can be produced. Thus, unprecedented insight into the electronic orbitals responsible for most of the electrical, magnetic and optical properties of bulk materials can be gained. However, the incredibly demanding requirements on spatial as well as spectral resolution paired with the low signal-to-noise ratio severely limits the day-to-day use of this new technique. With the use of simulations, we strive to alleviate these challenges as much as possible by identifying optimal experimental parameters. In this manner, we investigate representative examples of a transition metal oxide, a material consisting entirely of light elements, and an interface between two different materials to find and compare acceptable ranges for sample thickness, acceleration voltage and electron dose for a scanning probe as well as for parallel illumination.

cond-mat.mtrl-sci↗

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↗

arXiv2020

Using Cerenkov radiation for measuring the refractive index in thick samples by interferometric cathodoluminescence

Cathodoluminescence (CL) has evolved into a standard analytical technique in (scanning) transmission electron microscopy. CL utilizes light excited due to the interactions between the electron-beam and the sample. In the present study we focus on Cerenkov radiation. We make use of the fact that the electron transparent specimen acts as a Fabry-Pérot interferometer for coherently emitted radiation. From the wavelength dependent interference pattern of thickness dependent measurements we calculate the refractive index of the studied material. We describe the limits of this approach and compare it with the determination of the refractive index by using valence electron energy loss spectrometry (VEELS)

physics.app-ph↗

arXiv2019

Unitary Two-State Quantum Operators Realized By Quadrupole Fields in the Electron Microscope

In this work, a novel method for using a set of electromagnetic quadrupole fields is presented to implement arbitrary unitary operators on a two-state quantum system of electrons. In addition to analytical derivations of the required quadrupole and beam settings which allow an easy direct implementation, numerical simulations of realistic scenarios show the feasibility of the proposed setup. This is expected to pave the way not only for new measurement schemes in electron microscopy and related fields but even one day for the implementation of quantum computing in the electron microscope.

quant-ph↗

arXiv2019

Elastic propagation of fast electron vortices through amorphous materials

In this work, we study the elastic scattering behavior of electron vortices when propagating through amorphous samples. We use a formulation of the multislice approach in cylindrical coordinates to theoretically investigate the redistribution of intensity between different angular momentum components due to scattering. To corroborate and elaborate on our theoretical results, we perform extensive numerical simulations on three model systems (Si$_3$N$_4$, Fe$_{0.8}$B$_{0.2}$, Pt) for a wide variety of experimental parameters to quantify the purity of the vortices, the net angular momentum transfer, and the variability of the results with respect to the random relative position between the electron beam and the scattering atoms. These results will help scientists to further improve the creation of electron vortices and enhance applications involving them.

cond-mat.mtrl-sci↗

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

Convergent-Beam EMCD: Benefits, Pitfalls, and Applications

Energy-loss magnetic chiral dichroism (EMCD) is a versatile method for studying magnetic properties on the nanoscale. However, the classical EMCD technique is notorious for its low signal to noise ratio (SNR). Here, we study the theoretical possibilities of using a convergent beam for EMCD. In particular, we study the influence of detector positioning as well as convergence and collection angles on the detectable EMCD signal. In addition, we analyze the expected SNR and give guidelines for achieving optimal EMCD results.

physics.ins-det↗

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↗