Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven 'quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.

We introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond pulse trains for electron microscopy. Specifically, we employ phaselocked single-color and two-color optical fields to coherently control the electron wave function along the beam direction. We establish a new variant of quantum state tomography -"SQUIRRELS" -to reconstruct the density matrices of freeelectron ensembles and their attosecond temporal structure. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and the development of new forms of ultrafast electron microscopy and spectroscopy down to the attosecond regime.Optical, electron and x-ray microscopy and spectroscopy reveal specimen properties via spatial and spectral signatures imprinted onto a beam of radiation or electrons. Leaving behind the traditional paradigm of idealized, simple probe beams, advanced optical techniques increasingly harness tailored probes, or even their quantum properties and probe-sample entanglement. The rise of structured illumination microscopy 1 , pulse shaping 2 , and multidimensional 3 and quantum-optical spectroscopy 4 exemplify this development. Similarly, electron microscopy explores the use of shaped electron beams exhibiting particular spatial symmetries 5 or angular momentum 6,7 , and novel measurement schemes involving quantum aspects of electron probes have been proposed 8,9 . Ultrafast imaging and spectroscopy with electrons and x-rays are the basis for an ongoing revolution in the understanding of dynamical processes in matter on atomic scales [10][11][12][13] . The underlying technology heavily rests on laser science for the 2 generation and characterization of ever-shorter femtosecond electron 10,14 and xray [15][16][17] probe pulses, with examples in optical pulse compression 18 and streaking spectroscopy [19][20][21] . The temporal structuring of electron probe beams is facilitated by time-dependent fields in the radio-frequency [22][23][24] , terahertz 18,25 or optical domains. Promising a further leap in temporal resolution, recent findings suggest that ultrafast electron diffraction and microscopy with optically phasecontrolled and sub-cycle, attosecond-structured wave functions may be feasible 8,[26][27][28][29][30] . Specifically, light-field control may translate the temporal resolution of ultrafast transmission electron microscopy (UTEM) 31,32 and electron diffraction (UED) 10,33 , currently at about 200 fs 34 and 20 fs 14,23 , respectively, to the range of attoseconds 26,27,35 . However, such future technologies call for means to both prepare and fully analyze the corresponding quantum states of free electrons.Here, we demonstrate the coherent control and attosecond density modulation of free-electron quantum states using multiple phase-locked optical interactions. Moreover, we introduce quantum state tomography for free electrons, providing crucial e...

We present the development of the first ultrafast transmission electron microscope (UTEM) driven by localized photoemission from a field emitter cathode. We describe the implementation of the instrument, the photoemitter concept and the quantitative electron beam parameters achieved. Establishing a new source for ultrafast TEM, the Göttingen UTEM employs nano-localized linear photoemission from a Schottky emitter, which enables operation with freely tunable temporal structure, from continuous wave to femtosecond pulsed mode. Using this emission mechanism, we achieve record pulse properties in ultrafast electron microscopy of 9Å focused beam diameter, 200fs pulse duration and 0.6eV energy width. We illustrate the possibility to conduct ultrafast imaging, diffraction, holography and spectroscopy with this instrument and also discuss opportunities to harness quantum coherent interactions between intense laser fields and free-electron beams.

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Probing interfaces with electrons When molecules move on surfaces, they behave differently from when inside a solid. But surface layers give off limited signals, so to probe these systems, scientists need to act fast. Gulde et al. developed an ultrafast low-energy electron diffraction technique and used it to study how a polymer moved and melted on a graphene substrate (see the Perspective by Nibbering). After hitting the sample with a laser pulse, energy transferred across the graphene-polymer interface, the polymer film became less orderly, and an amorphous phase appeared. Science , this issue p. 200 ; see also p. 137

Interference between multiple distinct paths is a defining property of quantum physics, 1 where "paths" may involve actual physical trajectories, as in interferometry, 2 or transitions between different internal (e.g. spin) states, 3 or both. 4 A hallmark of quantum coherent evolution is the possibility to interact with a system multiple times in a phasepreserving manner. This principle underpins powerful multi-dimensional optical 5 and nuclear magnetic resonance 3 spectroscopies and related techniques, including Ramsey's method of separated oscillatory fields 6 used in atomic clocks. Previously established for atomic, molecular and quantum dot systems, 7 recent developments in the optical quantum state preparation of free electron beams 8 suggest a transfer of such concepts to the realm of ultrafast electron imaging and spectroscopy.Here, we demonstrate the sequential coherent interaction of free electron states with two spatially separated, phase-controlled optical near-fields. Ultrashort electron pulses are acted upon in a tailored nanostructure featuring two near-field regions with anisotropic polarization response. The amplitude and relative phase of these two near-fields are independently controlled by the incident polarization state, allowing for constructive and destructive quantum interference of the subsequent interactions. Future implementations of such electron-light interferometers may yield unprecedented access to optically phase-resolved electronic dynamics and dephasing mechanisms with attosecond precision.A central objective of attosecond science is the optical control over electron motion in and near atoms, molecules and solids, leading to the generation of attosecond light pulses or the study of static and dynamic properties of bound electronic wavefunctions. 9-13 One of the most elementary forms of optical control is the dressing of free electron states in a periodic field, 14,15 which is observed, for example, in two-color ionization, 16,17 free-free transitions near atoms, 14,18 and in photoemission from surfaces. [19][20][21] Similarly, beams of free electrons can be manipulated by the interaction with standing waves 22,23 or optical near-fields. [24][25][26][27]8 In this process, field localization at nanostructures facilitates the exchange of energy and momentum between free electrons and light. In the past few years, inelastic electron-light scattering 25,26,28 found application in so-called "photon-induced near-field electron microscopy" or PINEM, 24,29,30,8 the characterization of ultrashort electron pulses, 26,27,30 or in work towards optically-driven electron accelerators. 32,33 Very recently, the quantum coherence of such interactions was demonstrated by observing multilevel Rabi-oscillations in the electron populations of the comb of photon sidebands. 8,25 Access to these quantum features, gained by nanoscopic electron sources of high spatial coherence, 34,35 opens up a wide range of possibilities in coherent manipulations, control schemes and interferometry with free electron stat...

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