Attosecond spectroscopy of size-resolved water clusters.

Electron dynamics in water are of fundamental importance for a broad range of phenomena1-3, but their real-time study faces numerous conceptual and methodological challenges4-6. Here we introduce attosecond size-resolved cluster spectroscopy and build up a molecular-level understanding of the attosecond electron dynamics in water. We measure the effect that the addition of single water molecules has on the photoionization time delays7-9 of water clusters. We find a continuous increase of the delay for clusters containing up to four to five molecules and little change towards larger clusters. We show that these delays are proportional to the spatial extension of the created electron hole, which first increases with cluster size and then partially localizes through the onset of structural disorder that is characteristic of large clusters and bulk liquid water. These results indicate a previously unknown sensitivity of photoionization delays to electron-hole delocalization and indicate a direct link between electronic structure and attosecond photoionization dynamics. Our results offer new perspectives for studying electron-hole delocalization and its attosecond dynamics.

Wave-Packet Surface Propagation for Light-Induced Molecular Dynamics.

Recent advances in laser technology have enabled tremendous progress in light-induced molecular reactions, at the heart of which the breaking and formation of chemical bonds are located. Such progress has been greatly facilitated by the development of an accurate quantum-mechanical simulation method, which, however, does not necessarily accompany clear dynamical scenarios and is rather computationally heavy. Here, we develop a wave-packet surface propagation (WASP) approach to describe the molecular bond-breaking dynamics from a hybrid quantum-classical perspective. Via the introduction of quantum elements including state transitions and phase accumulations to the Newtonian propagation of the nuclear wave packet, the WASP approach naturally comes with intuitive physical scenarios and accuracies. It is carefully benchmarked with the H_{2}^{+} molecule and is shown to be capable of precisely reproducing experimental observations. The WASP method is promising for the intuitive visualization of light-induced molecular dynamics and is straightforward extensible towards complex molecules.

Probing and Steering Attosecond Electron Motion Using Tailored Ultrafast Laser Fields.

An ultrafast intense laser field is one of the most important tools to observe and manipulate electronic and nuclear dynamics with subcycle precision in highly nonlinear light-matter interactions, which provides access to attosecond chemistry and physics. In this review, we briefly summarize the protocol of attosecond chronoscopy and its application in probing the attosecond photoemission dynamics from atoms and molecules. We also review the control schemes of attosecond electron motion in atoms and molecules as well as molecular bond formation and cleavage with the assistance of tailored femtosecond laser fields.

Identifying photoelectron releasing order in strong-field dissociative ionization of H2.

Driven by intense laser fields, the outgoing photoelectrons in molecules possess a quiver motion, resulting in the rise of the effective ionization potential. The coupling of the field-dressed ionization potential with abundant molecular dynamics complicates the laser-molecule interactions. Here, we demonstrate an approach to resolve photoelectron releasing order in the dissociative and non-dissociative channels of multiphoton ionization driven by an orthogonally polarized two-color femtosecond laser pulse. The photoelectron kinetic energy releases and the regular nodes in the photoelectron angular distributions due to the participation of different continuum partial waves allow us to deduce the field-dressed ionization potential of various channels. It returns the ponderomotive energy experienced by the outgoing electron and reveals the corresponding photoionization instants within the laser pulse. Our results provide a route to explore the complex strong-field ionization dynamics of molecules using two-dimensional photoelectron momentum spectroscopy.

Enhancing Strong-Field Dissociation of H_{2}

We investigate the above-threshold multiphoton ionization of H_{2} embedded in superfluid He nanodroplets driven by ultraviolet femtosecond laser pulses. We find that the surrounding He atoms enhance the dissociation of in-droplet H_{2}^{+} from lower vibrational states as compared to that of isolated gas-phase molecules. As a result, the discrete peaks in the photoelectron energy spectrum correlated with the HHe^{+} from the dissociative in-droplet molecule shift to higher energies. Based on the electron-nuclear correlation, the photoelectrons with higher energies are correlated to the nuclei of the low-vibrationally excited molecular ion as the nuclei share less photon energy. Our time-dependent nuclear wave packet quantum simulation using a simplified He-H_{2}^{+} system confirms the joint contribution of the driving laser field and the neighboring He atoms to the dissociation dynamics of the solute molecular ion. The results strengthen our understanding of the role of the environment on light-induced ultrafast dynamics of molecules.

Resolving Quantum Interference Black Box through Attosecond Photoionization Spectroscopy.

Multiphoton light-matter interactions invoke a so-called "black box" in which the experimental observations contain the quantum interference between multiple pathways. Here, we employ polarization-controlled attosecond photoelectron metrology with a partial wave manipulator to deduce the pathway interference within this quantum 'black box" for the two-photon ionization of neon atoms. The angle-dependent and attosecond time-resolved photoelectron spectra are measured across a broad energy range. Two-photon phase shifts for each partial wave are reconstructed through the comprehensive analysis of these photoelectron spectra. We resolve the quantum interference between the degenerate p→d→p and p→s→p two-photon ionization pathways, in agreement with our theoretical simulations. Our approach thus provides an attosecond time-resolved microscope to look inside the "black box" of pathway interference in ultrafast dynamics of atoms, molecules, and condensed matter.

Two-Center Interference in the Photoionization Delays of Kr_{2}.

We present the experimental observation of two-center interference in the ionization time delays of Kr_{2}. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schrödinger equation of a 1D double-well potential, as well as coupled-channel multiconfigurational quantum-scattering calculations of Kr_{2}. This work opens the door to the study of a broad class of quantum-interference effects in photoionization delays and demonstrates the potential of attosecond coincidence spectroscopy for studying weakly bound systems.

Probing Resonant Photoionization Time Delay by Self-Referenced Molecular Attoclock.

Attosecond time-resolved electron tunneling dynamics have been investigated by using attosecond angular streaking spectroscopy, where a clock reference to the laser field vector is required in atomic strong-field ionization and the situation becomes complicated in molecules. Here we reveal a resonant ionization process via a transient state by developing an electron-tunneling-site-resolved molecular attoclock in Ar-Kr^{+}. Two distinct deflection angles are observed in the photoelectron angular distribution in the molecular frame, corresponding to the direct and resonant ionization pathways. We find the electron is temporally trapped in the Coulomb potential wells of the Ar-Kr^{+} before finally releasing into the continuum when the electron tunnels through the internal barrier. By utilizing the direct tunneling ionization as a self-referenced arm of the attoclock, the time delay of the electron trapped in the resonant state is revealed to be 3.50±0.04 fs. Our results give an impetus to exploring the ultrafast electron dynamics in complex systems and also endow a semiclassical presentation of the electron trapping dynamics in a quantum resonant state.

Femtosecond Rotational Dynamics of D_{2} Molecules in Superfluid Helium Nanodroplets.

Rotational dynamics of D_{2} molecules inside helium nanodroplets is induced by a moderately intense femtosecond pump pulse and measured as a function of time by recording the yield of HeD^{+} ions, created through strong-field dissociative ionization with a delayed femtosecond probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant B_{He} of the in-droplet D_{2} molecule, determined by Fourier analysis, is the same as B_{gas} for an isolated D_{2} molecule. Our observations show that the D_{2} molecules inside helium nanodroplets essentially rotate as free D_{2} molecules.

Attosecond Photoionization Dynamics: from Molecules over Clusters to the Liquid Phase.

Photoionization is a process taking place on attosecond time scales. How its properties evolve from isolated particles to the condensed phase is an open question of both fundamental and practical relevance. Here, we review recent work that has advanced the study of photoionization dynamics from atoms to molecules, clusters and the liquid phase. The first measurements of molecular photoionization delays have revealed the attosecond dynamics of electron emission from a molecular shape resonance and their sensitivity to the molecular potential. Using electron-ion coincidence spectroscopy these measurements have been extended from isolated molecules to clusters. A continuous increase of the delays with the water-cluster size has been observed up to a size of 4-5 molecules, followed by a saturation towards larger clusters. Comparison with calculations has revealed a correlation of the time delay with the spatial extension of the created electron hole. Using cylindrical liquid-microjet techniques, these measurements have also been extended to liquid water, revealing a delay relative to isolated water molecules that was very similar to the largest water clusters studied. Detailed modeling based on Monte-Carlo simulations confirmed that these delays are dominated by the contributions of the first two solvation shells, which agrees with the results of the cluster measurements. These combined results open the perspective of experimentally characterizing the delocalization of electronic wave functions in complex systems and studying their evolution on attosecond time scales.

Clocking Dissociative Above-Threshold Double Ionization of H_{2} in a Multicycle Laser Pulse.

The dissociative above-threshold double ionization (ATDI) of H_{2} in strong laser fields involves the sequential releasing of two electrons at specific instants with the stretching of the molecular bond. By mapping the releasing instants of two electrons to their emission directions in a multicycle polarization-skewed femtosecond laser pulse, we experimentally clock the dissociative ATDI of H_{2} via distinct photon-number-resolved pathways, which are distinguished in the kinetic energy release spectrum of two protons measured in coincidence. The timings of the experimentally resolved dissociative ATDI pathways are in good accordance with the classical predictions. Our results verify the multiphoton scenario of the dissociative ATDI of H_{2} in both time and energy fashion, strengthening the understanding of the strong-field phenomenon and providing a robust tool with a subcycle time resolution to clock abundant ultrafast dynamics of molecules.

High-order above-threshold dissociation of molecules.

Electrons bound to atoms or molecules can simultaneously absorb multiple photons via the above-threshold ionization featured with discrete peaks in the photoelectron spectrum on account of the quantized nature of the light energy. Analogously, the above-threshold dissociation of molecules has been proposed to address the multiple-photon energy deposition in the nuclei of molecules. In this case, nuclear energy spectra consisting of photon-energy spaced peaks exceeding the binding energy of the molecular bond are predicted. Although the observation of such phenomena is difficult, this scenario is nevertheless logical and is based on the fundamental laws. Here, we report conclusive experimental observation of high-order above-threshold dissociation of H2 in strong laser fields where the tunneling-ionized electron transfers the absorbed multiphoton energy, which is above the ionization threshold to the nuclei via the field-driven inelastic rescattering. Our results provide an unambiguous evidence that the electron and nuclei of a molecule as a whole absorb multiple photons, and thus above-threshold ionization and above-threshold dissociation must appear simultaneously, which is the cornerstone of the nowadays strong-field molecular physics.

Timing Dissociative Ionization of H_{2} Using a Polarization-Skewed Femtosecond Laser Pulse.

We experimentally observe the bond stretching time of one-photon and net-two-photon dissociation pathways of singly ionized H_{2} molecules driven by a polarization-skewed femtosecond laser pulse. By measuring the angular distributions of the ejected photoelectron and nuclear fragments in coincidence, the cycle-changing polarization of the laser field enables us to clock the photon-ionization starting time and photon-dissociation stopping time, analogous to a stopwatch. After the single ionization of H_{2}, our results show that the produced H_{2}^{+} takes almost the same time in the one-photon and net-two-photon dissociation pathways to stretch to the internuclear distance of the one-photon coupled dipole-transition between the ground and excited electronic states. The spatiotemporal mapping character of the polarization-skewed laser field provides us a straightforward route to clock the ultrafast dynamics of molecules with sub-optical-cycle time resolution.

Orientation-dependent strong-field dissociative single ionization of CO.

The dissociative ionization of CO in orthogonally polarized femtosecond laser pulses are studied in a pump-probe scheme. The ionization of CO by the pump pulse and the dissociation of the created CO+ by the probe pulse can be fully disentangled by identifying the photoelectron momentum distributions. Different from the dissociative ionization by a single pulse in which the CO molecule mostly breaks along the field polarization, in this pump-probe strategy, the CO+ ion created from ionization by the pump pulse is favored to dissociate when it orients orthogonal to the polarization direction of the probe pulse. It is attributed to the laser-coupling of various electronic states of the molecular ion in the dissociation process, supported by the numerical simulation of a modeled time-dependent Schrödinger equation.

Rotated echoes of molecular alignment: fractional, high order and imaginary.

We report experimental observations of rotated echoes of alignment induced by a pair of time-delayed and polarization-skewed femtosecond laser pulses interacting with an ensemble of molecular rotors. Rotated fractional echoes, rotated high order echoes and rotated imaginary echoes are directly visualized by using the technique of coincident Coulomb explosion imaging. We show that the echo phenomenon not only exhibits temporal recurrences but also spatial rotations determined by the polarization of the time-delayed second pulse. The dynamics of echo formation is well described by the laser-induced filamentation in rotational phase space. The quantum-mechanical simulation shows good agreements with the experimental results.

Energy-Resolved Ultrashort Delays of Photoelectron Emission Clocked by Orthogonal Two-Color Laser Fields.

A phase-controlled orthogonal two-color (OTC) femtosecond laser pulse is employed to probe the time delay of photoelectron emission in the strong-field ionization of atoms. The OTC field spatiotemporally steers the emission dynamics of the photoelectrons and meanwhile allows us to unambiguously distinguish the main and sideband peaks of the above-threshold ionization spectrum. The relative phase shift between the main and sideband peaks, retrieved from the phase-of-phase of the photoelectron spectrum as a function of the laser phase, gradually decreases with increasing electron energy, and becomes zero for the fast electron which is mainly produced by the rescattering process. Furthermore, a Freeman resonance delay of 140±40 attoseconds between photoelectrons emitted via the 4f and 5p Rydberg states of argon is observed.

Visualizing and Steering Dissociative Frustrated Double Ionization of Hydrogen Molecules.

We experimentally visualize the dissociative frustrated double ionization of hydrogen molecules by using few-cycle laser pulses in a pump-probe scheme, in which process the tunneling ionized electron is recaptured by one of the outgoing nuclei of the breaking molecule. Three internuclear distances are recognized to enhance the dissociative frustrated double ionization of molecules at different instants after the first ionization step. The recapture of the electron can be further steered to one of the outgoing nuclei as desired by using phase-controlled two-color laser pulses. Both the experimental measurements and numerical simulations suggest that the Rydberg atom is favored to emit to the direction of the maximum of the asymmetric optical field. Our results on the one hand intuitively visualize the dissociative frustrated double ionization of molecules, and on the other hand open the possibility to selectively excite the heavy fragment ejected from a molecule.

Comparison Study of Strong-Field Ionization of Molecules and Atoms by Bicircular Two-Color Femtosecond Laser Pulses.

We experimentally investigate the single and double ionization of N_{2} and O_{2} molecules in bicircular two-color femtosecond laser pulses, and compare with their companion atoms of Ar and Xe with comparable ionization thresholds. Electron recollision assisted enhanced ionization is observed in N_{2} and Ar by controlling the helicity and field ratio between the two colors, whereas the enhanced ionization via the recollision is almost absent in O_{2} and Xe. Our S-matrix simulations clearly reveal the crucial role of the detailed electronic structures of N_{2} and O_{2} on the two-dimensional recollision of the electrons driven by the bicircular two-color laser fields. As compared to Ar, the resonant multiphoton excitation dominates the double ionization of Xe.

Photon Energy Deposition in Strong-Field Single Ionization of Multielectron Molecules.

Molecules exposed to strong laser fields may coherently absorb multiple photons and deposit the energy into electrons and nuclei, triggering the succeeding dynamics as the primary stage of the light-molecule interaction. We experimentally explore the electron-nuclear sharing of the absorbed photon energy in above-threshold multiphoton single ionization of multielectron molecules. Using CO as a prototype, vibrational and orbital resolved electron-nuclear sharing of the photon energy is observed. Different from the simplest one- or two-electron systems, the participation of the multiple orbitals and the coupling of various electronic states in the strong-field ionization and dissociation processes alter the photon energy deposition dynamics of the multielectron molecule. The population of numerous vibrational states of the molecular cation as the energy reservoir in the ionization process plays an important role in photon energy sharing between the emitted electron and the nuclear fragments.

Channel-resolved above-threshold double ionization of acetylene.

We experimentally investigate the channel-resolved above-threshold double ionization (ATDI) of acetylene in the multiphoton regime using an ultraviolet femtosecond laser pulse centered at 395 nm by measuring all the ejected electrons and ions in coincidence. As compared to the sequential process, diagonal lines in the electron-electron joint energy spectrum are observed for the nonsequential ATDI owing to the correlative sharing of the absorbed multiphoton energies. We demonstrate that the distinct channel-resolved sequential and nonsequential ATDI spectra can clearly reveal the photon-induced acetylene-vinylidene isomerization via proton migration on the cation or dication states.