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 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.

Electric interactions have a strong impact on the structure and dynamics of biomolecules in their native water environment. Given the variety of water arrangements in hydration shells and the femto- to subnanosecond time range of structural fluctuations, there is a strong quest for sensitive noninvasive probes of local electric fields. The stretching vibrations of phosphate groups, in particular the asymmetric (PO 2 ) − stretching vibration ν AS (PO 2 ) − , allow for a quantitative mapping of dynamic electric fields in aqueous environments via a field-induced redshift of their transition frequencies and concomitant changes of vibrational line shapes. We present a systematic study of ν AS (PO 2 ) − excitations in molecular systems of increasing complexity, including dimethyl phosphate (DMP), short DNA and RNA duplex structures, and transfer RNA (tRNA) in water. A combination of linear infrared absorption, two-dimensional infrared (2D-IR) spectroscopy, and molecular dynamics (MD) simulations gives quantitative insight in electric-field tuning rates of vibrational frequencies, electric field and fluctuation amplitudes, and molecular interaction geometries. Beyond neat water environments, the formation of contact ion pairs of phosphate groups with Mg 2+ ions is demonstrated via frequency upshifts of the ν AS (PO 2 ) − vibration, resulting in a distinct vibrational band. The frequency positions of contact geometries are determined by an interplay of attractive electric and repulsive exchange interactions.

The interaction of phosphate groups with ions in an aqueous environment has a strong impact on the structure and folding processes of DNA and RNA. The dynamic variety of ionic arrangements, including both contact pairs and water separated ions, and the molecular coupling mechanisms are far from being understood. In a combined experimental and theoretical approach, we address the properties of contact ion pairs of the prototypical system dimethyl-phosphate with Na + , Ca 2+ , and Mg 2+ ions in water. Linear and femtosecond twodimensional infrared (2D-IR) spectroscopy of the asymmetric (PO2)stretching vibration separates and characterizes the different species via their blue-shifted vibrational signatures and 2D-IR lineshapes. Phosphate-magnesium contact pairs stand out as the most compact geometry while the contact pairs with Ca 2+ and Na + display a wider structural variation.Microscopic density functional theory simulations rationalize the observed frequency shifts and reveal distinct differences between the contact geometries. TOC Graphic

Electric interactions between ions and ionic molecular groups in aqueous solution play a fundamental role in chemistry and biology. While Mg 2+ ions are known to strongly affect the structure and folding dynamics of biomolecules, the relevance of different solvation geometries and the underlying interactions are mainly unresolved. We study dynamics and couplings between the hydrated Mg 2+ and the dimethylphosphate anion, an established model system for the DNA and RNA backbone. The asymmetric (PO 2 − ) stretching vibration serves as a sensitive noninvasive probe of phosphate−ion interactions. Femtosecond two-dimensional infrared (2D-IR) spectroscopy directly maps Mg 2+ ions in contact with the phosphate groups via a distinct blue-shifted signature in the 2D spectrum. Data for different Mg 2+ concentrations are analyzed by microscopic density functional theory modeling of cluster geometries and associated spectroscopic features, providing spatial assignments of the observed 2D-IR signatures. Phosphate−ion interactions arising from electrostatic Coulomb forces and exchange repulsion are the predominant origin of the observed frequency shifts.