Understanding electron-electron correlations in matter ranging from atoms to solids represents a grand challenge for both experiment and theory. These correlations occur on attosecond timescales and have only recently become experimentally accessible. In the case of highly excited systems, the task of understanding and probing correlated interactions is even greater. In this work, we combine state-of-the-art light sources and advanced detection techniques with ab initio calculations to unravel the role of electron-electron correlation in D2 photoionization by mapping the dissociation of a highly excited D2+ molecule. Correlations between the two electrons dictate the pathways along which the molecule dissociates and lead to a superposition of excited ionic states. Using 3D Coulomb explosion imaging and electron-ion coincidence techniques, we assess the relative contribution of competing parent ion states to the dissociation process for different orientations of the molecule with respect to the laser polarization, which is consistent with a shake-up ionization process. As a step toward observing coherent superposition experimentally, we map the relevant nuclear potentials using Coulomb explosion imaging and show theoretically that such an experiment could confirm this coherence via two-path interference.

D$_2$ molecules, excited by linearly cross-polarized femtosecond extreme ultraviolet (XUV) and near-infrared (NIR) light pulses, reveal highly structured D$^+$ ion fragment momenta and angular distributions that originate from two different 4-step dissociative ionization pathways after four photon absorption (1 XUV + 3 NIR). We show that, even for very low dissociation kinetic energy release $\le$~240~meV, specific electronic excitation pathways can be identified and isolated in the final ion momentum distributions. With the aid of {\it ab initio} electronic structure and time-dependent Schr\"odinger equation calculations, angular momentum, energy, and parity conservation are used to identify the excited neutral molecular states and molecular orientations relative to the polarization vectors in these different photoexcitation and dissociation sequences of the neutral D$_2$ molecule and its D$_2^+$ cation. In one sequential photodissociation pathway, molecules aligned along either of the two light polarization vectors are excluded, while another pathway selects molecules aligned parallel to the light propagation direction. The evolution of the nuclear wave packet on the intermediate \Bstate electronic state of the neutral D$_2$ molecule is also probed in real time.

The role of the nuclear degrees of freedom in nonlinear two-photon single ionization of H_{2} molecules interacting with short and intense vacuum ultraviolet pulses is investigated, both experimentally and theoretically, by selecting single resonant vibronic intermediate neutral states. This high selectivity relies on the narrow bandwidth and tunability of the pulses generated at the FERMI free-electron laser. A sustained enhancement of dissociative ionization, which even exceeds nondissociative ionization, is observed and controlled as one selects progressively higher vibronic states. With the help of ab initio calculations for increasing pulse durations, the photoelectron and ion energy spectra obtained with velocity map imaging allow us to identify new photoionization pathways. With pulses of the order of 100 fs, the experiment probes a timescale that lies between that of ultrafast dynamical processes and that of steady state excitations.

The original version of this Article contained an error in the fifth sentence of the first paragraph of the 'Application on H₂' section of the Results, which incorrectly read 'The role of electron correlation is quite apparent in this presentation: Fig. 1a is empty for the uncorrelated Hartree-Fock wave function, since projection of the latter wave function onto the 2pσ_u orbital is exactly zero, while this is not the case for the fully correlated wave function (Fig. 1d); also, Fig. 1b, c for the uncorrelated description are identical, while Fig. 1e, f for the correlated case are significantly different.' The correct version replaces 'Fig. 1e, f' with 'Fig. 2e and f'.

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H₂ two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.