Tomographic imaging of molecular orbitals in length and velocity form

Recently Itatani et al. [Nature 432, 876 (2004)] introduced the new concept of molecular orbital tomography, where high harmonic generation (HHG) is used to image electronic wave functions. We describe an alternative reconstruction form, using momentum instead of dipole matrix elements for the electron recombination step in HHG. We show that using this velocity-form reconstruction, one obtains better results than using the original length-form reconstruction. We provide numerical evidence for our claim that one has to resort to extremely short pulses to perform the reconstruction for an orbital with arbitrary symmetry. The numerical evidence is based on the exact solution of the time-dependent Schrödinger equation for 2D model systems to simulate the experiment. Furthermore we show that in the case of cylindrically symmetric orbitals, such as the N2 orbital that was reconstructed in the original work, one can obtain the full 3D wave function and not only a 2D projection of it. Vor kurzem führten Itatani et al. [Nature 432, 876 (2004)] das Konzept der Molelkülorbital-Tomographie ein. Hierbei wird die Erzeugung hoher Harmonischer verwendet, um Bilder von elektronischen Wellenfunktionen zu gewinnen. Wir beschreiben eine alternative Form der Rekonstruktion, die auf Impuls- statt Dipol-Matrixelementen für den Rekombinationsschritt bei der Erzeugung der Harmonischen basiert. Wir zeigen, dass diese "Geschwindigkeitsform" der Rekonstruktion bessere Ergebnisse als die ursprüngliche "Längenform" liefert. Wir zeigen numerische Beweise für unsere Behauptung, dass man zu extrem kurzen Laserpulsen gehen muss, um Orbitale mit beliebiger Symmetrie zu rekonstruieren. Diese Ergebnisse basieren auf der exakten Lösung der zeitabhängigen Schrödingergleichung für 2D-Modellsysteme. Wir zeigen ferner, dass für zylindersymmetrische Orbitale wie das N2-Orbital, welches in der oben zitierten Arbeit rekonstruiert wurde, das volle 3D-Orbital rekonstruiert werden kann, nicht nur seine 2D-Projektion.

Spatio-temporal resolution studies on a highly compact ultrafast electron diffractometer

Time-resolved diffraction with femtosecond electron pulses has become a promising technique to directly provide insights into photo induced primary dynamics at the atomic level in molecules and solids. Ultrashort pulse duration as well as extensive spatial coherence are desired, however, space charge effects complicate the bunching of multiple electrons in a single pulse.Weexperimentally investigate the interplay between spatial and temporal aspects of resolution limits in ultrafast electron diffraction (UED) on our highly compact transmission electron diffractometer. To that end, the initial source size and charge density of electron bunches are systematically manipulated and the resulting bunch properties at the sample position are fully characterized in terms of lateral coherence, temporal width and diffracted intensity.Weobtain a so far not reported measured overall temporal resolution of 130 fs (full width at half maximum) corresponding to 60 fs (root mean square) and transversal coherence lengths up to 20 nm. Instrumental impacts on the effective signal yield in diffraction and electron pulse brightness are discussed as well. The performance of our compactUEDsetup at selected electron pulse conditions is finally demonstrated in a time-resolved study of lattice heating in multilayer graphene after optical excitation.