Coulomb interactions and the spatial coherence of femtosecond nanometric electron pulses

The transverse coherence of electrons is of utmost importance in high resolution electron microscopes, point-projection microscopes, low-energy electron microscopy and various other applications. Pulsed versions of many of these have recently been realized, mostly relying on femtosecond laser-triggering electron emission from a sharp needle source. We here observe electron interference fringes and measure how the interference visibility becomes reduced as we increase the electron bunch charge. Due to the extremely strong spatio-temporal confinement of the electrons generated here, we observe the visibility reduction already at average electron bunch charges of less than 1 electron per pulse, owing to the stochastic nature of the emission process. We can fully and quantitatively explain the loss of coherence based on model simulations. Via the van Cittert-Zernike theorem we can connect the visibility reduction to an increase of the effective source size. We conclude by discussing emittance, brightness and quantum degeneracy, which have direct ramifications to many setups and devices relying on pulsed coherent electrons

Two-color coherent control in photoemission from gold needle tips

We demonstrate coherent control of photoemission from a gold needle tip using a two-color laser field. The relative phase between a fundamental field and its second harmonic imprints a strong modulation on the emitted photocurrent with up to 96.5 % contrast. The contrast as a function of the second harmonic intensity can be described by three interfering quantum pathways. Increasing the bias voltage applied to the tip reduces the maximum achievable contrast and modifies the weights of the involved pathways. Simulations based on the time-dependent Schr\"odinger equation reproduce the characteristic cooperative signal and its dependence on the second harmonic intensity, which further confirms the involvement of three emission pathways

Quantum-coherent light-electron interaction in an SEM

The last two decades experimentally affirmed the quantum nature of free electron wavepackets by the rapid development of transmission electron microscopes into ultrafast, quantum-coherent systems. In particular, ultrafast electron pulses can be generated and timed to interact with optical near-fields, yielding coherent exchange of the quantized photon energy between the relativistic electron wavepacket and the light field. So far, all experiments have been restricted to the physically-confining bounds of transmission electron microscopes, with their small, millimeter-sized sample chambers. In this work, we show the quantum coherent coupling between electrons and light in a scanning electron microscope, at unprecedentedly low electron energies down to 10.4 keV, so with sub-relativistic electrons. Scanning electron microscopes not only afford the yet-unexplored electron energies from ~0.5 to 30 keV providing optimum light-coupling efficiencies, but they also offer spacious and easily-configurable experimental chambers for extended and cascaded optical set-ups, potentially boasting thousands of photon-electron interaction zones. Our results unleashes the full potential of quantum experiments including electron wavepacket shaping and quantum computing with multiple arithmetic operations and will allow imaging with low-energy electrons and attosecond time resolution

Ponderomotive generation and detection of attosecond free-electron pulse trains

Atomic motion dynamics during structural changes or chemical reactions have been visualized by picosecond and femtosecond pulsed electron beams via ultrafast electron diffraction and microscopy. Imaging the even faster dynamics of electrons in atoms, molecules and solids requires electron pulses with sub-femtosecond durations. We demonstrate here the all-optical generation of trains of attosecond free-electron pulses. The concept is based on the periodic energy modulation of a pulsed electron beam via an inelastic interaction with the ponderomotive potential of an optical travelling wave generated by two femtosecond laser pulses at different frequencies in vacuum. The subsequent dispersive propagation leads to a compression of the electrons and the formation of ultrashort pulses. The longitudinal phase space evolution of the electrons after compression is mapped by a second phase-locked interaction. The comparison of measured and calculated spectrograms reveals the attosecond temporal structure of the compressed electron pulse trains with individual pulse durations of less than 300 as. This technique can be utilized for tailoring and initial characterization of sub-optical cycle free-electron pulses at high repetition rates for stroboscopic time-resolved experiments with sub-femtosecond time resolution

Strong-Field Bloch Electron Interferometry for Band Structure Retrieval

When Bloch electrons in a solid are exposed to a strong optical field, they are coherently driven in their respective bands where they acquire a quantum phase as the imprint of the band shape. If an electron approaches an avoided crossing formed by two bands, it may be split by undergoing a Landau-Zener transition. We here employ subsequent Landau-Zener transitions to realize strong-field Bloch electron interferometry (SFBEI), allowing us to reveal band structure information. In particular, we measure the Fermi velocity (band slope) of graphene in the vicinity of the K points as (1.07$\pm$0.04) nm fs$^{-1}$. We expect SFBEI for band structure retrieval to apply to a wide range of material systems and experimental conditions, making it suitable for studying transient changes in band structure with femtosecond temporal resolution at ambient conditions

Boosting the Efficiency of Smith–Purcell Radiators Using Nanophotonic Inverse Design

The generation of radiation from free electrons passing a grating, known as Smith–Purcell radiation, finds various applications, including nondestructive beam diagnostics and tunable light sources, ranging from terahertz toward X-rays. So far, the gratings used for this purpose have been designed manually, based on human intuition and simple geometric shapes. Here we apply the computer-based technique of nanophotonic inverse design to build a 1400 nm Smith–Purcell radiator for subrelativistic 30 keV electrons. We demonstrate that the resulting silicon nanostructure radiates with a 3× higher efficiency and 2.2× higher overall power than previously used rectangular gratings. With better fabrication accuracy and for the same electron–structure distance, simulations suggest a superiority by a factor of 96 in peak efficiency. While increasing the efficiency is a key step needed for practical applications of free-electron radiators, inverse design also allows to shape the spectral and spatial emission in ways inaccessible with the human mind

Boosting the Efficiency of Smith–Purcell Radiators Using Nanophotonic Inverse Design

The generation of radiation from free electrons passing a grating, known as Smith–Purcell radiation, finds various applications, including nondestructive beam diagnostics and tunable light sources, ranging from terahertz toward X-rays. So far, the gratings used for this purpose have been designed manually, based on human intuition and simple geometric shapes. Here we apply the computer-based technique of nanophotonic inverse design to build a 1400 nm Smith–Purcell radiator for subrelativistic 30 keV electrons. We demonstrate that the resulting silicon nanostructure radiates with a 3× higher efficiency and 2.2× higher overall power than previously used rectangular gratings. With better fabrication accuracy and for the same electron–structure distance, simulations suggest a superiority by a factor of 96 in peak efficiency. While increasing the efficiency is a key step needed for practical applications of free-electron radiators, inverse design also allows to shape the spectral and spatial emission in ways inaccessible with the human mind

Boosting the efficiency of Smith-Purcell radiators using nanophotonic inverse design

The generation of radiation from free electrons passing a grating, known as Smith-Purcell radiation, finds various applications including non-destructive beam diagnostics and tunable light sources, ranging from terahertz towards X-rays. So far, the gratings used for this purpose have been designed manually, based on human intuition and simple geometric shapes. Here we apply the computer-based technique of nanophotonic inverse design to build a 1400nm Smith-Purcell radiator for sub-relativistic 30 keV electrons. We demonstrate that the resulting silicon nanostructure radiates with a 3-times-higher efficiency and 2.2-times-higher overall power than previously used rectangular gratings. With better fabrication accuracy and for the same electron-structure distance, simulations suggest a superiority by a factor of 96 in peak efficiency. While increasing the efficiency is a key step needed for practical applications of free-electron radiators, inverse design also allows to shape the spectral and spatial emission in ways inaccessible with the human mind

Quantum interference visibility spectroscopy in two-color photoemission from tungsten needle tips

When two-color femtosecond laser pulses interact with matter, electrons can be emitted through various multiphoton excitation pathways. Quantum interference between these pathways gives rise to a strong oscillation of the photoemitted electron current, experimentally characterized by its visibility. In this work, we demonstrate two-color visibility spectroscopy of multi-photon photoemission from a solid-state nanoemitter. We investigate the quantum pathway interference visibility over an almost octave-spanning wavelength range of the fundamental femtosecond laser pulses and their second-harmonic. The photoemission shows a high visibility of 90% +/- 5%, with a remarkably constant distribution. Furthermore, by varying the relative intensity ratio of the two colors, we find that we can vary the visibility between 0 and close to 100%. A simple but highly insightful theoretical model allows us to explain all observations, with excellent quantitative agreements. We expect this work to be universal to all kinds of photo-driven quantum interference, including quantum control in physics, chemistry and quantum engineering

Inelastic ponderomotive scattering of electrons at a high-intensity optical travelling wave in vacuum

In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter off the optical intensity grating formed by two counter-propagating light waves [1]. This interaction, driven by the ponderomotive potential of the optical standing wave, was both studied theoretically and demonstrated experimentally for atoms [2] and electrons [3-5]. In the original version of the experiment [1,5], only the transverse momentum of particles was varied, but their energy and longitudinal momentum remained unchanged after the interaction. Here, we report on the generalization of the Kapitza-Dirac effect. We demonstrate that the energy of sub-relativistic electrons is strongly modulated on the few-femtosecond time scale via the interaction with a travelling wave created in vacuum by two colliding laser pulses at different frequencies. This effect extends the possibilities of temporal control of freely propagating particles with coherent light and can serve the attosecond ballistic bunching of electrons [6], or for the acceleration of neutral atoms or molecules by light