The use of electron beams is ubiquitous; electron microscopy, scanning tunneling microscopy, electron lithography, and electron diffractometry all use well-collimated and focused beams. On the other hand, quantum degenerate electron beams do currently not exist. The realization of such beams may impact all electron beam technologies and are interesting to pursue. Past attempts to reach degeneracy were hampered by the low degeneracy of continuously emitting electron sources. With the recent advent of ultra-short electron pulses, high degeneracy is expected. Coulomb repulsion and low quantum coherence are hurdles that need to be overcome. A quantum analysis of the electron degeneracy for partially coherent pulsed electron sources is presented. Two-particle coincidence spectra are obtained for source parameters that are currently available. The conclusive demonstration of the fermionic Hanbury-Brown Twiss (HBT) effect for free electrons is shown to be within reach, and our results support the claim that femto-second nanotip electron sources, both polarized and unpolarized, can manifest partial to complete quantum degeneracy with appreciable signal-to-noise-ratios for free electron pulses notwithstanding their small particle numbers.
The use of electron beams is ubiquitous; electron microscopy, scanning tunneling microscopy, electron lithography, and electron diffractometry all use well-collimated and focused beams. On the other hand, quantum degenerate electron beams do currently not exist. The realization of such beams may impact all electron beam technologies and are interesting to pursue. Past attempts to reach degeneracy were hampered by the low degeneracy of continuously emitting electron sources. With the recent advent of ultra-short electron pulses, high degeneracy is expected. Coulomb repulsion and low quantum coherence are hurdles that need to be overcome. A quantum analysis of the electron degeneracy for partially coherent pulsed electron sources is presented. Two-particle coincidence spectra are obtained for source parameters that are currently available. The conclusive demonstration of the fermionic Hanbury-Brown Twiss (HBT) effect for free electrons is shown to be within reach, and our results support the claim that femto-second nanotip electron sources, both polarized and unpolarized, can manifest partial to complete quantum degeneracy with appreciable signal-to-noise-ratios for free electron pulses notwithstanding their small particle numbers.
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements, and chip-based applications rely on intensive, tunable, coherent sources for free low-energy electron-matter waves. In most cases, the electrons get field emitted from a metal nanotip, where its radius and geometry toward a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter-wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 6.4 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy, and sensor technology.
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements and chip based applications rely on intensive, tunable, coherent sources for free low energy electron matter waves. In most cases, the electrons get field emitted from a metal nanotip where its radius and geometry towards a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 33 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy and sensor technology
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (λ/2), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
Understanding how fermionic exchange and Coulomb repulsion jointly shape two-electron correlations is essential for identifying genuine quantum signatures in multi-electron interference experiments. To address this interplay, we investigate Hanbury Brown and Twiss interference of two electrons generated by two independent needle-tip emitters within a full quantum-mechanical framework. In the absence of Coulomb interaction, the approach reproduces the results previously obtained within a quantum path formalism. For Coulomb-interacting electrons, we predict characteristic features absent in a semiclassical description: a pronounced Coulomb-dominated suppression region as well as Coulomb-induced phase offsets and fringe shifts. At the same time, outside of the Coulomb-dominated region, the spatial oscillation frequency is essentially governed by fermionic exchange symmetry. Our results establish quantitative parameter regimes for disentangling Coulomb interaction from fermionic exchange symmetry in such experiments.
Electron microscopy and diffraction have long been used to study the structure of materials. A recent development is the achievement of ultrafast time resolution using high-repetition rate single electron sources and single-shot many-electron sources. Achieving large coherence lengths under these conditions is challenging due to intrinsic heating mechanisms including inter-particle Coulombic forces. Near-threshold, pulsed photoionization of atoms trapped and cooled with lasers is being investigated as a means to produce intense electron pulses with large intrinsic coherence length due to a low electron temperature. Photo-ionizaton sources are, of course, not an entirely new idea but recent implementations using trapped atoms offer new possibilities. Several properties of electron beams extracted from such ultracold sources have already been investigated, showing in particular that temperatures of a few Kelvin and emittances in the nanometer-radian range can be achieved with tens of thousands electrons per pulse for nanosecond pulse lengths. This can be combined with delicate shaping of the charge distribution to counteract emittance growth due to non-linear self fields. Using ultrafast lasers for the ionization step, shorter electron pulses can be achieved, but an interesting question is whether the concomitant spread in photon energy still allows for low electron temperature. Recent experiments have shown that few-Kelvin temperatures combined with picosecond pulse lengths are indeed possible. It turns out that this can be understood with a classical model for electron trajectories resulting from photoionization. In addition, experimentally observed polarization effects are in general agreement with model results. --------------------------------------------------------------------------------