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.

The equilibrium structure of the RNA sugar-phosphate backbone and its hydration shell is distinctly different from hydrated DNA. Applying femtosecond two-dimensional infrared (2D-IR) spectroscopy in a range from 950 to 1300 cm, we elucidate the character, dynamics, and couplings of backbone modes of a double-stranded RNA A-helix geometry in its aqueous environment. The 2D-IR spectra display a greater number of backbone modes than for DNA, with distinctly different lineshapes of diagonal peaks. Phosphate-ribose interactions and local hydration structures are reflected in the complex coupling pattern of RNA modes. Interactions with the fluctuating water shell give rise to spectral diffusion on a 300 fs time scale, leading to a quasi-homogeneous line shape of the symmetric (PO) stretching mode of the strongly hydrated phosphate groups. The RNA results are benchmarked by 2D-IR spectra of DNA oligomers in water and analyzed by molecular dynamics and quantum mechanical molecular mechanics simulations.

Ions interacting with hydrated RNA play a central role in defining its secondary and tertiary structure. While spatial arrangements of ions, water molecules, and phosphate groups have been inferred from X-ray studies, the role of electrostatic and other noncovalent interactions in stabilizing compact folded RNA structures is not fully understood at the molecular level. Here, we demonstrate that contact ion pairs of magnesium (Mg 2+ ) and phosphate groups embedded in local water shells stabilize the tertiary equilibrium structure of transfer RNA (tRNA). Employing dialyzed tRNA Phe from yeast and tRNA from Escherichia coli , we follow the population of Mg 2+ sites close to phosphate groups of the ribose-phosphodiester backbone step by step, combining linear and nonlinear infrared spectroscopy of phosphate vibrations with molecular dynamics simulations and ab initio vibrational frequency calculations. The formation of up to six Mg 2+ /phosphate contact pairs per tRNA and local field-induced reorientations of water molecules balance the phosphate–phosphate repulsion in nonhelical parts of tRNA, thus stabilizing the folded structure electrostatically. Such geometries display limited sub-picosecond fluctuations in the arrangement of water molecules and ion residence times longer than 1 μs. At higher Mg 2+ excess, the number of contact ion pairs per tRNA saturates around 6 and weakly interacting ions prevail. Our results suggest a predominance of contact ion pairs over long-range coupling of the ion atmosphere and the biomolecule in defining and stabilizing the tertiary structure of tRNA.

The water hydration shell has decisive impact on the structural and functional properties of RNA. Changes of RNA structure upon melting and in biochemical processes are accompanied by a change of hydration patterns, a process which is barely characterized. To discern hydration geometries around the backbone phosphate groups of an RNA double helix at the molecular level, we combine two-dimensional infrared spectroscopy of phosphate vibrations with theoretical simulations. There are three distinct coexisting hydration motifs of the RNA A-helix, an ordered chain-like arrangement of water molecules with links between neighboring phosphate groups, separate local hydration shells of up to six water molecules, and hydrated phosphate/counterion contact pairs. RNA disordering upon melting is connected with a transition from predominant ordered water structures to local hydration shells around phosphate units. Structural fluctuations are dominated by librational water motions occurring on a 300 fs time scale, without exchange between hydration motifs.