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Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description the effect is time-independent. In the present work, we extend the Kapitza-Dirac concept to the time domain. By tracking the spatiotemporal evolution of a pulsed electron wave packet diffracted by a femtosecond (10 15 second) standing wave pulse in a pump-probe scheme, we observe so far unseen time-dependent diffraction patterns. The fringe spacing in the observed pattern differs from that generated by the conventional Kapitza-Dirac effect, moreover it decreases as the pump-probe delay time increases. By exploiting this time-resolved diffraction scheme, we gather access to the time evolution of the previously inaccessible phase properties of a free electron.

Free-electron lasers (FELs) are the world's most brilliant light sources with rapidly evolving technological capabilities in terms of ultrabright and ultrashort pulses over a large range of accessible photon energies. Their revolutionary and innovative developments have opened new fields of science regarding nonlinear light-matter interaction, the investigation of ultrafast processes from specific observer sites, and approaches to imaging matter with atomic resolution. A core aspect of FEL science is the study of isolated and prototypical systems in the gas phase with the possibility of addressing well-defined electronic transitions or particular atomic sites in molecules. Notably for polarization-controlled short-wavelength FELs, the gas phase offers new avenues for investigations of nonlinear and ultrafast phenomena in spin orientated systems, for decoding the function of the chiral building blocks of life as well as steering reactions and particle emission dynamics in otherwise inaccessible ways. This roadmap comprises descriptions of technological capabilities of facilities worldwide, innovative diagnostics and instrumentation, as well as recent scientific highlights, novel methodology and mathematical modeling. The experimental and theoretical landscape of using polarization controllable FELs for dichroic light-matter interaction in the gas phase will be discussed and comprehensively outlined to stimulate and strengthen global collaborative efforts of all disciplines.

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the classical cutoff is found to be vastly different from that below the cutoff. A V-shape structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schr\"odinger equation simulations for different model potentials., Comment: 6 pages, 3 figures

The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules the photoelectron energy does not depend on the electron's emission direction but theoretical studies have questioned this since 1990. Here we provide experimental evidence, that the energies of photoelectrons emitted against the light-propagation direction are shifted towards higher values while those electrons that are emitted along the light-propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution from the interaction of the moving electrons with the incident photons., Comment: 6 pages, 4 figures

We present experimental data on the non-adiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schr\"odinger equation (TDSE). Experiment and TDSE show four above-threshold ionization (ATI) peaks in the electron's energy spectrum. The most probable emission angle (also known as 'attoclock-offset angle' or 'streaking angle') is found to increase with energy, a trend that is opposite to standard predictions based on Coulomb interaction with the ion. We show that this increase of deflection-angle can be explained by a model that includes non-adiabatic corrections of the initial momentum distribution at the tunnel exit and non-adiabatic corrections of the tunnel exit position itself., Comment: 8 pages, 5 figures

If matter absorbs a photon of sufficient energy it emits an electron. The question of the duration of the emission process has intrigued scientists for decades. With the advent of attosecond metrology, experiments addressing such ultrashort intervals became possible. While these types of studies require attosecond experimental precision, we present here a novel measurement approach that avoids those experimental difficulties. We instead extract the emission delay from the interference pattern generated as the emitted photoelectron is diffracted by the parent ion's potential. Targeting core electrons in CO, we measured a 2d map of photoelectron emission delays in the molecular frame over a wide range of electron energies. The measured emission times depend drastically on the emission direction and exhibit characteristic changes along the shape resonance of the molecule. Our approach can be routinely extended to other electron orbitals and more complex molecules.

We present an experimental and theoretical study of core-level ionization of small hetero- and homo-nuclear molecules employing circularly polarized light and address molecular-frame photoelectron angular distributions in the light's polarization plane (CP-MFPADs). We find that the main forward-scattering peaks of CP-MFPADs are slightly tilted with respect to the molecular axis. We show that this tilt angle can be directly connected to the molecular bond length by a simple, universal formula. The extraction of the bond length becomes more accurate as the photoelectron energy is increased. We apply the derived formula to several examples of CP-MFPADs of C 1s and O 1s photoelectrons of CO, which have been measured experimentally or obtained by means of ab initio modeling. The photoelectron kinetic energies range from 70 to 1000~eV and the extracted bond lengths agree well with the known bond length of the CO molecule in its ground state. In addition, we discuss the influence of the back-scattering contribution that is superimposed over the analyzed forward-scattering peak in case of homo-nuclear diatomic molecules as N$_2$.

Controlling the interactions between atoms with external fields opened up new branches in physics ranging from strongly correlated atomic systems to ideal Bose and Fermi gases and Efimov physics. Such control usually prepares samples that are stationary or evolve adiabatically in time. On the other hand, in molecular physics external ultrashort laser fields are employed to create anisotropic potentials that launch ultrafast rotational wave packets and align molecules in free space. Here we combine these two regimes of ultrafast times and low energies. We apply a short laser pulse to the helium dimer, a weakly bound and highly delocalized single bound state quantum system. The laser field locally tunes the interaction between two helium atoms, imparting an angular momentum of $2\hbar$ and evoking an initially confined dissociative wave packet. We record a movie of the density and phase of this wave packet as it evolves from the inside out. At large internuclear distances, where the interaction between the two helium atoms is negligible, the wave packet is essentially free. This work paves the way for future tomography of wave packet dynamics and provides the technique for studying exotic and otherwise hardly accessible quantum systems such as halo and Efimov states., Comment: 4 figures, to be published in Nature Physics

Photoionization is one of the fundamental light-matter interaction processes in which the absorption of a photon launches the escape of an electron. The time scale of the process poses many open questions. Experiments found time delays in the attosecond ($10^{-18}$ s) domain between electron ejection from different orbitals, electronic bands, or in different directions. Here, we demonstrate that across a molecular orbital the electron is not launched at the same time. The birth time rather depends on the travel time of the photon across the molecule, which is 247 zeptoseconds ($10^{-21}$ s) for the average bond length of H$_2$. Using an electron interferometric technique, we resolve this birth time delay between electron emission from the two centers of the hydrogen molecule.

We report measurements on the H$^{+}$ + H$^{+}$ fragmentation channel following direct single-photon double ionization of neutral NH$_{3}$ at 61.5 eV, where the two photoelectrons and two protons are measured in coincidence using 3-D momentum imaging. We identify four dication electronic states that contribute to H$^{+}$ + H$^{+}$ dissociation, based on our multireference configuration-interaction calculations of the dication potential energy surfaces. The extracted branching ratios between these four dication electronic states are presented. Of the four dication electronic states, three dissociate in a concerted process, while the fourth undergoes a sequential fragmentation mechanism. We find evidence that the neutral NH fragment or intermediate NH$^+$ ion is markedly ro-vibrationally excited. We also identify differences in the relative emission angle between the two photoelectrons as a function of their energy sharing for the four different dication states, which bare some similarities to previous observations made on atomic targets., Comment: 16 pages, 13 figures, 3 tables

We present state-selective measurements on the NH$_2^{+}$ + H$^{+}$ and NH$^{+}$ + H$^{+}$ + H dissociation channels following single-photon double ionization at 61.5 eV of neutral NH$_{3}$, where the two photoelectrons and two cations are measured in coincidence using 3-D momentum imaging. Three dication electronic states are identified to contribute to the NH$_2^{+}$ + H$^{+}$ dissociation channel, where the excitation in one of the three states undergoes intersystem crossing prior to dissociation, producing a cold NH$_2^+$ fragment. In contrast, the other two states directly dissociate, producing a ro-vibrationally excited NH$_2^+$ fragment with roughly 1 eV of internal energy. The NH$^{+}$ + H$^{+}$ + H channel is fed by direct dissociation from three intermediate dication states, one of which is shared with the NH$_2^{+}$ + H$^{+}$ channel. We find evidence of autoionization contributing to each of the double ionization channels. The distributions of the relative emission angle between the two photoelectrons, as well as the relative angle between the recoil axis of the molecular breakup and the polarization vector of the ionizing field, are also presented to provide insight on both the photoionization and photodissociation mechanisms for the different dication states., Comment: 18 pages, 21 figures, 3 tables

More than 100 years after its discovery and its explanation in the energy domain, the duration of the photoelectric effect is still heavily studied. The emission time of a photoelectron can be quantified by the Wigner time delay. Experiments addressing this time delay for single-photon ionization became feasible during the last 10 years. A missing piece, which has not been studied, so far, is the Wigner time delay for strong-field ionization of molecules. Here we show experimental data on the Wigner time delay for tunnel ionization of $H_{2}$ molecules and demonstrate its dependence on the emission direction of the electron with respect to the molecular axis. We find, that the observed changes in the Wigner time delay can be quantitatively explained by elongated/shortened travel paths of the electrons that are due to spatial shifts of the electron's birth position after tunneling. This introduces an intuitive perspective towards the Wigner time delay in strong-field ionization., Comment: 17 pages, 6 figures

We show that the combination of two achiral components - atomic or molecular target plus a circularly polarized photon - can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon K-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti-)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral, if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In both scenarios, the circularly polarized photon defines a plane with a sense of rotation and an additional axis is defined by the CO molecule or one electron. This is sufficient to establish an unambiguous coordinate frame of well-defined handedness. To produce a chirally structured electron angular distribution, such a coordinate frame is necessary, but not sufficient. We show that additional electron-electron interaction or scattering processes are needed to create the chiral angular distribution.

We experimentally investigate the effects of the linear photon momentum on the momentum distributions of photoions and photoelectrons generated in one-photon ionization in an energy range of 300 eV $\leq~E_\gamma~\leq$ 40 keV. Our results show that for each ionization event the photon momentum is imparted onto the photoion, which is essentially the system's center of mass. Nevertheless, the mean value of the ion momentum distribution along the light propagation direction is backward-directed by $-3/5$ times the photon momentum. These results experimentally confirm a 90 year old prediction., Comment: 5 pages, 3 figures

Compton scattering is one of the fundamental interaction processes of light with matter. Already upon its discovery [1] it was described as a billiard-type collision of a photon kicking a quasi-free electron. With decreasing photon energy, the maximum possible momentum transfer becomes so small that the corresponding energy falls below the binding energy of the electron. Then ionization by Compton scattering becomes an intriguing quantum phenomenon. Here we report a kinematically complete experiment on Compton scattering at helium atoms below that threshold. We determine the momentum correlations of the electron, the recoiling ion, and the scattered photon in a coincidence experiment finding that electrons are not only emitted in the direction of the momentum transfer, but that there is a second peak of ejection to the backward direction. This finding links Compton scattering to processes as ionization by ultrashort optical pulses [2], electron impact ionization [3,4], ion impact ionization [5,6], and neutron scattering [7] where similar momentum patterns occur., Comment: 7 pages, 4 figures

We investigate the photoelectron angular emission distributions obtained by strong field dissociative ionization of H$_2$ using cold target recoil ion momentum spectroscopy. In case of employing laser light with an ellipticity close to 0.9 and an intensity of 1.0 $\times$ 10$^{14}$ W/cm$^2$, we find that the most probable release-time of the electron does not generally coincide with the time when the laser field maximizes. The release-time is affected by the molecular orientation. In addition, we observe that the width of the release-time distribution depends on molecular orientation. We attribute this observation to the two-center-interference.

Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. In this letter, we report on the observation of two-center interference in the molecular frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which were measured in coincidence with electrons, allowed choosing the symmetry of the continuum electronic wave function, leading to observation of both, gerade and ungerade, types of interference.

Quantum particles can penetrate potential barriers by tunneling (1). If that barrier is rotating, the tunneling process is modified (2,3). This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized laser pulses (4,5). Here we measure how the transmission probability through a rotating tunnel depends on the sign of the magnetic quantum number m of the electron and thus on the initial sense of rotation of its quantum phase. We further show that the electron keeps part of that rotary motion on its way through the tunnel by measuring m-dependent modification of the electron emission pattern. These findings are relevant for attosecond metrology as well as for interpretation of strong field electron emission from atoms and molecules (6-13) and directly demonstrates the creation of ring currents in bound states of ions with attosecond precision. In solids, this could open a way to inducing and controlling ring-current related topological phenomena (14)., Comment: 19 pages, 6 figures, Nature Physics accepted

As a fundamental property of the electron, the spin plays a decisive role in the electronic structure of matter from solids to molecules and atoms, e.g. causing magnetism. Yet, despite its importance, the spin dynamics of electrons released during the interaction of atoms with strong ultrashort laser pulses has remained unexplored. Here we report on the experimental detection of electron spin polarization by strong-field ionization of Xenon atoms and support our results by theoretical analysis. We found up to 30% spin polarization changing its sign with electron energy. This work opens the new dimension of spin to strong-field physics. It paves the way to production of subfemtosecond spin polarized electron pulses with applications ranging from probing magnetic properties of matter at ultrafast time scales to testing chiral molecular systems with subfemtosecond temporal and sub-{\AA}ngstr\"om spatial resolution., Comment: 9 pages, 3 figures

X-ray single-photon ionization and fragmentation of the chiral molecule halothane (CHBrClCF${}_{3}$) from a racemic mixture have been investigated using the COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) technique. Two important facets related to the core ionization of this species are examined: Firstly, the distinction of enantiomers (mirror isomers) and the determination of absolute configuration on a single-molecule level by four-body Coulomb explosion; secondly, the interplay of site-selective excitation and fragmentation patterns. These results are easily transferrable to other molecular species and show the wealth of features

Most large molecules are chiral in their structure: they exist as two enantiomers, which are mirror images of each other. Whereas the rovibronic sublevels of two enantiomers are almost identical, it turns out that the photoelectric effect is sensitive to the absolute configuration of the ionized enantiomer - an effect termed Photoelectron Circular Dichroism (PECD). Our comprehensive study demonstrates that the origin of PECD can be found in the molecular frame electron emission pattern connecting PECD to other fundamental photophysical effects as the circular dichroism in angular distributions (CDAD). Accordingly, orienting a chiral molecule in space enhances the PECD by a factor of about 10.

We report on electron momentum distributions from single ionization of Ar in strong orthogonally polarized two-color (OTC) laser fields measured with the COLTRIMS technique. We study the effect of Coulomb focusing whose signature is a cusp like feature in the center of the electron momentum spectrum. While the direct electrons show the expected strong dependence on the phase between the two colors, surprisingly the Coulomb focused structure is almost not influenced by the weak second harmonic streaking field. This effect is explained by the use of a CTMC simulation which describes the tunneled electron wave packet in terms of classical trajectories under the influence of the combined Coulomb- and OTC laser field. We find a subtle interplay between the initial momentum of the electron upon tunneling, the ionization phase and the action of the Coulomb field that makes the Coulomb focused part of the momentum spectrum apparently insensitive to the weaker streaking field.

Quantum theory dictates that upon weakening the two-body interaction in a three-body system, an infinite number of three-body bound states of a huge spatial extent emerge just before these three-body states become unbound. Three helium atoms have been predicted to form a molecular system that manifests this peculiarity under natural conditions without artificial tuning of the attraction between particles by an external field. Here we report experimental observation of this long predicted but experimentally elusive Efimov state of $^{4}$He$_{3}$ by means of Coulomb explosion imaging. We show spatial images of an Efimov state, confirming the predicted size and a typical structure where two atoms are close to each other while the third is far away.

The dynamics of ultra-slow electrons in the combined potential of an ionic core and a static electric field is discussed. With state-of-the-art detection it is possible to create such electrons through strong intense-field photo-absorption and to detect them via high-resolution time-of-flight spectroscopy despite their very low kinetic energy. The characteristic feature of their momentum spectrum, which emerges at the same position for different laser orientations, is derived and could be revealed experimentally with an energy resolution of the order of 1meV., Comment: 5 pages, 5 figures

We investigate electron momentum distributions from single ionization of Ar by two orthogonally polarized laser pulses of different color. The two-color scheme is used to experimentally control the interference between electron wave packets released at different times within one laser cycle. This intracycle interference pattern is typically hard to resolve in an experiment. With the two-color control scheme these features become the dominant contribution to the electron momentum distribution. Furthermore the second color can be used for streaking of the otherwise interfering wave packets establishing a which-way marker. Our investigation shows that the visibility of the interference fringes depends on the degree of the which-way information determined by the controllable phase between the two pulses., Comment: submitted to PRL

We report on the observation of discrete structures in the electron energy distribution for strong field double ionization of Argon at 394 nm. The experimental conditions were chosen in order to ensure a non-sequential ejection of both electrons with an intermediate rescattering step. We have found discrete ATI (above-threshold ionization) like peaks in the sum energy of both electrons, as predicted by all quantum mechanical calculations. More surprisingly however is the observation of two ATI combs in the energy distribution of the individual electrons., Comment: Accepted for publication in Phys. Rev. Lett

Experimental results on partial photo-ionisation cross sections of helium are analysed in the light of recent advances in the semiclassical theory of two-electron atoms. Byun et al (arXiv:physics/0701086) predict that the total photo-ionisation cross section below the double-ionisation threshold can, semiclassically, be described in terms of contributions associated with classical orbits starting and ending in the triple collision. The necessary modifications of the semiclassical theory for partial cross sections is developed here. It is argued that partial cross sections are also dominated by the triple collision dynamics. The expected semiclassical contributions can be identified in the Fourier transformation of the experimental data. This clearly demonstrates for the first time the validity of the basic assumptions made in Byun et al. Our findings explain furthermore in a natural way the self-similar structures observed in cross section signals for different channel numbers.

The availability of few-cycle optical pulses opens a window to physical phenomena occurring on the attosecond time scale. In order to take full advantage of such pulses, it is crucial to measure and stabilise their carrier-envelope (CE) phase, i.e., the phase difference between the carrier wave and the envelope function. We introduce a novel approach to determine the CE phase by down-conversion of the laser light to the terahertz (THz) frequency range via plasma generation in ambient air, an isotropic medium where optical rectification (down-conversion) in the forward direction is only possible if the inversion symmetry is broken by electrical or optical means. We show that few-cycle pulses directly produce a spatial charge asymmetry in the plasma. The asymmetry, associated with THz emission, depends on the CE phase, which allows for a determination of the phase by measurement of the amplitude and polarity of the THz pulse.