Attosecond photoionization delays in the vicinity of molecular Feshbach resonances.

Temporal delays extracted from photoionization phases are currently determined with attosecond resolution by using interferometric methods. Such methods require special care when photoionization occurs near Feshbach resonances due to the interference between direct ionization and autoionization. Although theory can accurately handle these interferences in atoms, in molecules, it has to face an additional, so far insurmountable problem: Autoionization is slow, and nuclei move substantially while it happens, i.e., electronic and nuclear motions are coupled. Here, we present a theoretical framework to account for this effect and apply it to evaluate time-resolved and vibrationally resolved photoelectron spectra and photoionization phases of N2 irradiated by a combination of an extreme ultraviolet (XUV) attosecond pulse train and an infrared pulse. We show that Feshbach resonances lead to unusual non-Franck-Condon vibrational progressions and to ionization phases that strongly vary with photoelectron energy irrespective of the vibrational state of the remaining molecular cation.

Attosecond Intramolecular Scattering and Vibronic Delays.

We study the temporal and vibrational signature of the universal nuclear recoil associated with the electron emission and intramolecular scattering that accompanies the photoelectric effect. We illustrate these phenomena in the photoionization of the CO molecule from the C-1s orbital using an analytical model that reproduces the entangled character of the nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Photoionization by a broadband x-ray pulse results in a coherent vibrational ionic state delayed compared to the classical sudden-photoemission limit.

Molecular-Frame Photoelectron Angular Distributions of CO in the Vicinity of Feshbach Resonances: An XCHEM Approach.

The advent of ultrashort XUV pulses is pushing for the development of accurate theoretical calculations to describe ionization of molecules in regions where electron correlation plays a significant role. Here, we present an extension of the XCHEM methodology to evaluate laboratory- and molecular-frame photoelectron angular distributions in the region where Feshbach resonances are expected to appear. The performance of the method is demonstrated in the CO molecule, for which information on Feshbach resonances is very scarce. We show that photoelectron angular distributions are dramatically affected by the presence of resonances, to the point that they can completely reverse the preferred electron emission direction observed in direct nonresonant photoionization. This is the consequence of significant changes in the electronic structure of the molecule when resonances decay, an effect that is mostly driven by electron correlation in the ionization continuum. The present methodology can thus be helpful for the interpretation of angularly resolved photoionization time delays in this and more complex molecules.

Disentangling Spectral Phases of Interfering Autoionizing States from Attosecond Interferometric Measurements.

We have determined spectral phases of Ne autoionizing states from extreme ultraviolet and midinfrared attosecond interferometric measurements and ab initio full-electron time-dependent theoretical calculations in an energy interval where several of these states are coherently populated. The retrieved phases exhibit a complex behavior as a function of photon energy, which is the consequence of the interference between paths involving various resonances. In spite of this complexity, we show that phases for individual resonances can still be obtained from experiment by using an extension of the Fano model of atomic resonances. As simultaneous excitation of several resonances is a common scenario in many-electron systems, the present work paves the way to reconstruct electron wave packets coherently generated by attosecond pulses in systems larger than helium.

Anisotropic photoemission time delays close to a Fano resonance.

Electron correlation and multielectron effects are fundamental interactions that govern many physical and chemical processes in atomic, molecular and solid state systems. The process of autoionization, induced by resonant excitation of electrons into discrete states present in the spectral continuum of atomic and molecular targets, is mediated by electron correlation. Here we investigate the attosecond photoemission dynamics in argon in the 20-40 eV spectral range, in the vicinity of the 3s-1np autoionizing resonances. We present measurements of the differential photoionization cross section and extract energy and angle-dependent atomic time delays with an attosecond interferometric method. With the support of a theoretical model, we are able to attribute a large part of the measured time delay anisotropy to the presence of autoionizing resonances, which not only distort the phase of the emitted photoelectron wave packet but also introduce an angular dependence.

Electron Correlation in the Ionization Continuum of Molecules: Photoionization of N2 in the Vicinity of the Hopfield Series of Autoionizing States.

Direct measurement of autoionization lifetimes by using time-resolved experimental techniques is a promising approach when energy-resolved spectroscopic methods do not work. Attosecond time-resolved experiments have recently provided the first quantitative determination of autoionization lifetimes of the lowest members of the well-known Hopfield series of resonances in N2. In this work, we have used the recently developed XCHEM approach to study photoionization of the N2 molecule in the vicinity of these resonances. The XCHEM approach allows us to describe electron correlation in the molecular electronic continuum at a level similar to that provided by multireference configuration interaction methods in bound state calculations, a necessary condition to accurately describe autoionization, shakeup, and interchannel couplings occurring in this range of photon energies. Our results show that electron correlation leading to interchannel mixing is the main factor that determines the magnitude and shape of the N2 photoionization cross sections, as well as the lifetimes of the Hopfield resonances. At variance with recent speculations, nonadiabatic effects do not seem to play a significant role. These conclusions are supported by the very good agreement between the calculated cross sections and those determined in synchrotron radiation and attosecond experiments.

Hybrid-Basis Close-Coupling Interface to Quantum Chemistry Packages for the Treatment of Ionization Problems.

The theoretical description of observables in attosecond pump-probe experiments requires a good representation of the system's ionization continuum. For polyelectronic molecules, however, this is still a challenge, due to the complicated short-range structure of correlated electronic wave functions. Whereas quantum chemistry packages (QCP) implementing sophisticated methods to compute bound electronic molecular states are well-established, comparable tools for the continuum are not widely available yet. To tackle this problem, we have developed a new approach that, by means of a hybrid Gaussian-B-spline basis, interfaces existing QCPs with close-coupling scattering methods. To illustrate the viability of this approach, we report results for the multichannel ionization of the helium atom and of the hydrogen molecule that are in excellent agreement with existing accurate benchmarks. These findings, together with the versatility of QCPs to describe a broad range of chemical systems, indicate that this is a valid approach to study the ionization of polyelectronic systems in which correlation and exchange symmetry play a major role.

Reconstruction and control of a time-dependent two-electron wave packet.

The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes including chemical reactions, and hence there is much interest in developing a detailed understanding of such electron dynamics in the quantum regime. However, there is no exact solution for the quantum three-body problem, and as a result even the minimal system of two active electrons and a nucleus is analytically intractable. This makes experimental measurements of the dynamics of two bound and correlated electrons, as found in the helium atom, an attractive prospect. However, although the motion of single active electrons and holes has been observed with attosecond time resolution, comparable experiments on two-electron motion have so far remained out of reach. Here we show that a correlated two-electron wave packet can be reconstructed from a 1.2-femtosecond quantum beat among low-lying doubly excited states in helium. The beat appears in attosecond transient-absorption spectra measured with unprecedentedly high spectral resolution and in the presence of an intensity-tunable visible laser field. We tune the coupling between the two low-lying quantum states by adjusting the visible laser intensity, and use the Fano resonance as a phase-sensitive quantum interferometer to achieve coherent control of the two correlated electrons. Given the excellent agreement with large-scale quantum-mechanical calculations for the helium atom, we anticipate that multidimensional spectroscopy experiments of the type we report here will provide benchmark data for testing fundamental few-body quantum dynamics theory in more complex systems. They might also provide a route to the site-specific measurement and control of metastable electronic transition states that are at the heart of fundamental chemical reactions.

Modulation of attosecond beating in resonant two-photon ionization.

We present a theoretical study of the photoelectron attosecond beating due to interference of two-photon transitions in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, both the phase shift and frequency of the sideband beating significantly vary with photon energy. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a nonholographic interferometric means to reconstruct coherent metastable wave packets. We characterize these phenomena by means of a general analytical model that accounts for the effect of both intermediate and final resonances on two-photon processes. The model predictions are in excellent agreement with those of accurate ab initio calculations for the helium atom in the region of the N=2 doubly excited states.

Ionization branching ratio control with a resonance attosecond clock.

We investigate the possibility to monitor the dynamics of autoionizing states in real-time and control the yields of different ionization channels in helium by simulating extreme ultraviolet (XUV) pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates a coherent superposition of doubly excited states which is found to decay by ejecting electrons in bursts. Prominent interference fringes in the photoelectron angular distribution of the 2s and 2p ionization channels are observed, along with significant out-of-phase quantum beats in the yields of the corresponding parent ions.

Two-particle coulomb Green function method with projected potential: application to He double photoionization.

A new method to compute fully differential double photoionization cross sections of atoms has been devised and fully developed for two-electron systems. The method exploits the Green function for two noninteracting electrons in the field of a nuclear charge to infer the effects of the residual potential projected on a set of L(2)-basis functions. Test calculations on helium at 100 eV excess energy indicate that, as long as the relevant part of the interaction potential is accounted for, the fully differential cross sections calculated in acceleration and velocity gauges converge in absolute value and reproduce measured angular distributions with a tunable accuracy. Generalization of the method to treat double photoionization of many-electron atoms is sketched.