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Electron beams with a twist It has been possible to produce photon vortex beams — optical beams with spiralling wavefronts — for some time, and they have found widespread application as optical tweezers, in interferometry and in information transfer, for example. The production of vortex beams of electrons was demonstrated earlier this year ( http://go.nature.com/4H2xWR ) in a procedure involving the passage of electrons through a spiral stack of graphite thin films. The ability to generate such beams reproducibly in a conventional electron microscope would enable many new applications. Now Jo Verbeeck and colleagues have taken a step towards that goal. They describe a versatile holographic technique for generating these twisted electron beams, and demonstrate their potential use as probes of a material's magnetic properties. It was demonstrated recently that passing electrons through a spiral stack of graphite thin films generates an electron beam with orbital angular momentum — analogous to the spiralling wavefronts that can be introduced in photon beams and which have found widespread application. Here, a versatile holographic technique for generating these twisted electron beams is described. Moreover, a demonstration is provided of their potential use in probing a material's magnetic properties. Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum 1 , 2 , improving channel capacity in optical 3 and radio-wave 4 information transfer, astrophysics 5 and so on 6 . Very recently, an experimental realization of vortex beams formed of electrons was demonstrated 7 . Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.

Interfacing electrons and light enables ultrafast electron microscopy and quantum control of electrons, as well as new optical elements for high-sensitivity imaging. Here, we demonstrate for the first time programmable transverse electron-beam shaping in free space based on ponderomotive potentials from short intense laser pulses. We can realize both convex and concave electron lenses with a focal length of a few millimeters, comparable to those in state-of-the-art electron microscopes. We further show that we can realize almost arbitrary deflection patterns by shaping the ponderomotive potentials using a spatial light modulator. Our modulator is lossless and programmable, has unity fill factor, and could pave the way to electron wave-front shaping with hundreds of individually addressable pixels.

The synergy between free electrons and light has recently been leveraged to reach an impressive degree of simultaneous spatial and spectral resolution, enabling applications in microscopy and quantum optics. However, the required combination of electron optics and light injection into the spectrally narrow modes of arbitrary specimens remains a challenge. Here, we demonstrate microelectronvolt spectral resolution with a sub-nanometer probe of photonic modes with quality factors as high as 10 4 . We rely on mode matching of a tightly focused laser beam to whispering gallery modes to achieve a 10 8 -fold increase in light-electron coupling efficiency. By adapting the shape and size of free-space optical beams to address specific physical questions, our approach allows us to interrogate any type of photonic structure with unprecedented spectral and spatial detail. The authors present μeV electron spectromicroscopy, a technique that combines free-space light and electron beams to achieve unmatched spatial and spectral resolution. This approach enables detailed investigation of photonic structures, promising advancements in microscopy and quantum optics.

The one-dimensional, chiral edge channels of the quantum Hall effect are a promising platform in which to implement electron quantum optics experiments; however, Coulomb interactions between edge channels are a major source of decoherence and energy relaxation. It is therefore of large interest to understand the range and limitations of the simple quantum electron optics picture. Here we confirm experimentally for the first time the predicted relaxation and revival of electrons injected at finite energy into an edge channel. The observed decay of the injected electrons is reproduced theoretically within a Tomonaga-Luttinger liquid framework, including an important dissipation towards external degrees of freedom. This gives us a quantitative empirical understanding of the strength of the interaction and the dissipation. Quantum Hall phases have chiral edge modes, which could be used to explore and exploit the quantum properties of electrons. Interactions in these edge states lead to relaxation and decoherence, hindering any realistic exploitation. Here the authors observe spectroscopically the decay and revival of the excitation created by injection of an electron into the edge mode. Their results confirm phase-coherent transport and quantify the effect of dissipation-induced decoherence.

We present a quantum switch based on analogous Dirac fermion optics (DFO), in which the angle dependence of Klein tunneling is explicitly utilized to build tunable collimators and reflectors for the quantum wave function of Dirac fermions. We employ a dual-source design with a single flat reflector, which minimizes diffusive edge scattering and suppresses the background incoherent transmission. Our gate-tunable collimator–reflector device design enables the quantitative measurement of the net DFO contribution in the switching device operation. We obtain a full set of transmission coefficients between multiple leads of the device, separating the classical contribution from the coherent transport contribution. The DFO behavior demonstrated in this work requires no explicit energy gap. We demonstrate its robustness against thermal fluctuations up to 230 K and large bias current density up to 10² A/m, over a wide range of carrier densities. The characterizable and tunable optical components (collimator–reflector) coupled with the conjugated source electrodes developed in this work provide essential building blocks toward more advanced DFO circuits such as quantum interferometers. The capability of building optical circuit analogies at a microscopic scale with highly tunable electron wavelength paves a path toward highly integrated and electrically tunable electron-optical components and circuits.

Multimode optical fibers represent the ideal platform for transferring multidimensional light states. However, dispersion degrades the correlations between the light’s degrees of freedom, thus limiting the effective transport of ultrashort pulses between distant nodes of optical networks. Here, we demonstrate that tailoring the spatiotemporal structure of ultrashort light pulses can overcome the physical limitations imposed by both chromatic and modal dispersion in multimode optical fibers. We synthesize these light states with predefined spatial and chromatic dynamics through applying a sequence of transformations to shape the optical field in all its dimensions. Similar methods can also be used to overcome dispersion processes in other physical settings like acoustics and electron optics. Our results will enable advancements in laser-based technologies, including multimode optical communications, imaging, ultrafast light-matter interactions, and high brightness fiber sources. The authors demonstrate mitigation of both chromatic and modal dispersion in multimode optical fibers via spatiotemporal tailoring of ultrashort light pulses. This holds potential for applications such as in multimode imaging, long-distance communications, ultrafast light-matter interactions, optical fiber amplifiers, and multidimensional information encoding.

The observation of oscillations in the conductance characteristics of narrow graphene p–n-junctions confirms their ability to collimate ballistic carriers. Moreover, the phase of these oscillations at low magnetic field suggests the occurrence of the perfect transmission of carriers normal to the junction as a direct result of the Klein effect. The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality 1 , 2 , 3 , 4 . Although electron optics such as lensing 5 and focusing 6 have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge owing to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength 7 . Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions. Analysis of the oscillations confirms that p–n junctions have a collimating effect on ballistically transmitted carriers 8 . The phase shift observed in the conductance fringes at low magnetic fields is a signature of the perfect transmission of carriers normally incident on the junctions 9 and thus constitutes a direct experimental observation of ‘Klein tunnelling’ 10 , 11 , 12 .