Probing Molecular Dynamics by Laser-Induced Backscattering Holography

Strong-field photoelectron holography in the subcycle limit

Strong-field photoelectron holography is promising for the study of electron dynamics and structure in atoms and molecules, with superior spatiotemporal resolution compared to conventional electron and X-ray diffractometry. However, the application of strong-field photoelectron holography has been hindered by inter-cycle interference from multicycle fields. Here, we address this challenge by employing a near-single-cycle field to suppress the inter-cycle interference. We observed and separated two distinct holographic patterns for the first time. Our measurements allow us not only to identify the Gouy phase effect on electron wavepackets and holographic patterns but also to correctly extract the internuclear separation of the target molecule from the holographic pattern. Our work leads to a leap jump from theory to application in the field of strong-field photoelectron holography-based ultrafast imaging of molecular structures.

Spatiotemporal imaging and shaping of electron wave functions using novel attoclock interferometry

Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Characterizing and shaping the electron wave function on its natural timescale is of paramount importance for understanding and controlling ultrafast electron dynamics in atoms, molecules and condensed matter. Here we propose a novel attoclock interferometry to shape and image the electron wave function in atomic photoionization. Using a combination of a strong circularly polarized second harmonic and a weak linearly polarized fundamental field, we spatiotemporally modulate the atomic potential barrier and shape the electron wave functions, which are mapped into a temporal interferometry. By analyzing the two-color phase-resolved and angle-resolved photoelectron interference, we are able to reconstruct the spatiotemporal evolution of the shaping on the amplitude and phase of electron wave function in momentum space within the optical cycle, from which we identify the quantum nature of strong-field ionization and reveal the effect of the spatiotemporal properties of atomic potential on the departing electron. This study provides a new approach for spatiotemporal shaping and imaging of electron wave function in intense light-matter interactions and holds great potential for resolving ultrafast electronic dynamics in molecules, solids, and liquids.

Identifying the complexity of the holographic structures in strong field ionization

We present numerical investigations of the strong-field attosecond photoelectron holography by analyzing the holographic interference structures in the two-dimensional photoelectron momentum distribution (PMD) in hydrogen atom target induced by a strong infrared laser pulse. The PMDs are calculated by solving the full-dimensional time-dependent Schrödinger equation. The effect of the number of optical cycles on the PMD is considered and analyzed. We show how the complex interference patterns are formed from a single-cycle pulse to multi-cycle pulses. Furthermore, snapshots of the PMD during the time evolution are presented for a single-cycle pulse in order to track the formation of the so-called fish-bone like holographic structure. The spider- and fan-like holographic structures are also identified and investigated. We found that the fan-like structure could only be identified clearly for pulses with three or more optical cycles and its symmetry depends closely on the number of optical cycles. In addition, we found that the intensity and wavelength of the laser pulse affect the density of interference fringes in the holographic patterns. We show that the longer the wavelength, the more the holographic structures are confined to the polarization axis.

Photoelectron interference of He atoms in the attosecond ionization gating

We theoretically investigate the photoelectron momentum distribution of He atoms by numerically solving the time-dependent Schro¨dinger equation (TDSE) in few-cycle ionization gating, which is synthesized by two linearly polarized laser pulses. When applying the TDSE, we can clearly see the spider-like structures in the photoelectron momentum spectra. We also find that the spider-like structures can be isolated by changing the relative phase. The directionality of the spider-like structure is changed from right-side to left-side and the ring-like interference structure gradually appears in the photoelectron momentum spectra when increasing the relative phase. The interference patterns observed in TDSE are recaptured well by the quantum-trajectory Monte Carlo (QTMC) model. We separate the ionization time window of the tunneling electron by analyzing the ionization rate. With the help of QTMC simulation, we illustrate the change of the interference structure and its directionality in the photoelectron momentum spectra. By changing the relative phase, the forward-backward asymmetry of the momentum distribution of the emitted electrons can also be controlled. Moreover, we find that the relative contribution of the nonrescattering and the rescattering trajectories can be controlled. These properties are beneficial for the application of photoelecron holography in probing atomic and molecular structures and dynamics.

Picometer-Resolved Photoemission Position within the Molecule by Strong-Field Photoelectron Holography

Laser-induced tunneling ionization is one of the fundamental light-matter interaction processes. An accurate description of the tunnel-ionized electron wave packet is central to understanding and controlling subsequent electron dynamics. Because of the anisotropic molecular structure, tunneling ionization of molecules involves considerable challenges in accurately describing the tunneling electron wave packet. Up to now, some basic properties of the tunneling electron from molecules still remain unexplored. Here, we demonstrate that the tunneling electron from a molecule is not always emitted from the geometric center of the molecule along the tunnel direction. Rather, the photoemission position depends on the molecular orientation. Using a photoelectron holographic technique, we determine the photoemission position for a nitrogen molecule relative to the molecular geometric center to be 95±21  pm when the molecular axis is oriented along the tunnel direction. Our Letter poses, and answers experimentally, a fundamental question as to where the molecular photoionization actually begins, which has significant implications for time-resolved probing of valence electron dynamics in molecules.

Tracking the Ionization Site in Neutral Molecules

When a diatomic molecule is exposed to intense light, the valence electron may tunnel from a higher potential (corresponding to an upfield atom) due to the suppressed internuclear barrier. This process is known as ionization enhancement and is a key mechanism in strong field ionization of molecules. Alternatively, the bound electron wave function can evolve adiabatically in the laser field, resulting in ionization from the downfield atom. Here, we introduce a method to quantify the relative contribution of these two processes. Applying this method to experimentally measured electron momenta distributions following strong field ionization of N_{2} with infrared laser light, we find approximately a 2∶1 ratio of electrons ionized from a downfield atom, relative to upfield. This suggests that the bound state wave function largely adapts adiabatically to the changing laser field, although the nonadiabatic process of ionization enhancement still contributes even in neutral molecules. Our method can be applied to any diatomic neutral molecule to better understand the evolution of the initially bound electron wave packet and hence the nature of the molecular ionization process.

Analyzing the electron trajectories in strong-field tunneling ionization with the phase-of-the-phase spectroscopy

By numerically solving the time-dependent Schrödinger equation, we theoretically study strong-field tunneling ionization of Ar atom in the parallel two-color field which consists of a strong fundamental pulse and a much weaker second harmonic component. Based on the quantum orbits concept, we analyzed the photoelectron momentum distributions with the phase-of-the-phase spectroscopy, and the relative contributions of the two parts of the photoelectrons produced during the rising and falling edges of the adjacent quarters of the laser cycle are identified successfully. Our results show that the relative contributions of these two parts depend on both of the transverse and longitude momenta. By comparing the results from model atoms with Coulomb potential and short-range potential, the role of the long-range Coulomb interaction on the relative contributions of these two parts of electrons is revealed. Additionally, we show that the effects of Coulomb interaction on ionization time are vital for identifying their relative contributions.

High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau

Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

Gouy's Phase Anomaly in Electron Waves Produced by Strong-Field Ionization

Ionization of atoms by strong laser fields produces photoelectron momentum distributions that exhibit modulations due to the interference of outgoing electron trajectories. For a faithful modeling, it is essential to include previously overlooked phase shifts occurring when trajectories pass through focal points. Such phase shifts are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a focal point as it crosses the symmetry axis in momentum space. In addition, there exist observable Maslov phases already in two dimensions. Clustering algorithms enable us to implement a semiclassical model with the correct preexponential factor that affects both the weight and the phase of each trajectory. We also derive a simple rule to relate two-dimensional and three-dimensional models for linear polarization. It explains the shifted interference fringes and weaker high-energy yield in three dimensions. The results are in excellent agreement with solutions of the time-dependent Schrödinger equation.

Experimental Separation of Subcycle Ionization Bursts in Strong-Field Double Ionization of H_{2}

We report on the unambiguous observation of the subcycle ionization bursts in sequential strong-field double ionization of H_{2} and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase, in combination with multiparticle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state-specific Coulomb distortions on emitted electrons in polyatomic molecules.

It is all about phases: ultrafast holographic photoelectron imaging

Photoelectron holography constitutes a powerful tool for the ultrafast imaging of matter, as it combines high electron currents with subfemtosecond resolution, and gives information about transition amplitudes and phase shifts. Similarly to light holography, it uses the phase difference between the probe and the reference waves associated with qualitatively different ionization events for the reconstruction of the target and for ascertaining any changes that may occur. These are major advantages over other attosecond imaging techniques, which require elaborate interferometric schemes in order to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.

Subfemtosecond Tracing of Molecular Dynamics during Strong-Field Interaction

We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750 nm, 4.5 fs laser pulses were focused to an intensity of 9×10^{14}  W/cm^{2} onto H_{2}. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the 1sσ_{g} state of H_{2}^{+} during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

Determination of the Ionization Time Using Attosecond Photoelectron Interferometry

Laser-induced electron tunneling ionization from atoms and molecules plays as the trigger for a broad class of interesting strong-field phenomena in attosecond community. Understanding the time of electron tunneling ionization is vital to achieving the ultimate accuracy in attosecond metrology. We propose a novel attosecond photoelectron interferometer, which is based on the interference of the direct and near-forward rescattering electron wave packets, to determine the time information characterizing the tunneling process. Adding a weak perturbation in orthogonal to the strong fundamental field, the phases of the direct and the near-forward rescattering electron wave packets are modified, leading to the shift of the interferogram in the photoelectron momentum distributions. By analyzing the response of the interferogram to the perturbation, the real part of the ionization time, which denotes the instant when the electron exits the potential barrier, and the associated rescattering time are precisely retrieved. Moreover, the imaginary part of the ionization time, which has been interpreted as a quantity related to electron motion under the potential barrier, is also unambiguously determined.

Quantum Interference of Glory Rescattering in Strong-Field Atomic Ionization

During the ionization of atoms irradiated by linearly polarized intense laser fields, we find for the first time that the transverse momentum distribution of photoelectrons can be well fitted by a squared zeroth-order Bessel function because of the quantum interference effect of glory rescattering. The characteristic of the Bessel function is determined by the common angular momentum of a number of semiclassical paths termed as glory trajectories, which are launched with different nonzero initial transverse momenta distributed on a specific circle in the momentum plane and finally deflected to the same asymptotic momentum, which is along the polarization direction, through post-tunneling rescattering. Glory rescattering theory based on the semiclassical path-integral formalism is developed to address this effect quantitatively. Our theory can resolve the long-standing discrepancies between existing theories and experiments on the fringe location, predict the sudden transition of the fringe structure in holographic patterns, and shed light on the quantum interference aspects of low-energy structures in strong-field atomic ionization.

Dynamic interference as signature of atomic stabilization

We study the ionization of atoms by very intense linearly polarized pulse with moderately high frequency by numerically solving the time-dependent Schrödinger equation (TDSE). In this regime, the photon energy exceeds the ionization potential allowing for one-photon ionization which is, however, strongly influenced by strong nonlinear photon-atom interactions. We find that the onset of atomic stabilization can be monitored by the appearance of a dynamic interference pattern in the photoelectron spectrum.

Accurate measurement of laser intensity using photoelectron interference in strong-field tunneling ionization

Accurate determination of laser intensity is of fundamental importance to study various phenomena in intense laser-atom/molecule interactions. We theoretically demonstrate a scheme to measure laser intensity by examining the holographic structure originating from the interference between the direct and near-forward rescattering electrons in strong-field tunneling ionization. By adding a weak second-harmonic field with polarization orthogonal to the strong fundamental driving field, the interference pattern oscillates with the changing relative phases of the two-color fields. Interestingly, the amplitude of this oscillation in the photoelectron momentum spectrum depends on the parallel momentum. With the quantum-orbit analysis, we show that the amplitude of the oscillation minimizes when the time difference between the recollision and ionization of near-forward rescattering electron is half cycle of the fundamental driving field. This enables us to measure accurately the laser intensity by seeking the minimum of the oscillation amplitude. Moreover, we show that this minimum can be determined without scanning the relative phases, instead, by just monitoring the interference patterns for two relative phases. This facilitates the application of our scheme in experiment.

Photoelectron holography and forward scattering in atomic ionization by elliptically polarized laser pulses

We report on the scaling of the photoelectron holography with the laser ellipticity in strong-field atomic ionization. We find that the spacing of the holographic fringe gradually decreases with increasing of the ellipticity. In terms of the strong-field approximation, the scaling of the fringe spacing with the laser ellipticity is explained by the effect of the initial transverse momenta at the tunnel exit. With increasing of the laser ellipticity, a ridge structure arising from forward scattering electrons is observed in the low-energy region of the electron momentum distribution. An analytic formula is obtained that demarcates the phase diagram for the observation of the holographic pattern and ridge structure in elliptically polarized laser fields.

Direct Visualization of Valence Electron Motion Using Strong-Field Photoelectron Holography

Watching the valence electron move in molecules on its intrinsic timescale has been one of the central goals of attosecond science and it requires measurements with subatomic spatial and attosecond temporal resolutions. The time-resolved photoelectron holography in strong-field tunneling ionization holds the promise to access this realm. However, it remains to be a challenging task hitherto. Here we reveal how the information of valence electron motion is encoded in the hologram of the photoelectron momentum distribution (PEMD) and develop a novel approach of retrieval. As a demonstration, applying it to the PEMDs obtained by solving the time-dependent Schrödinger equation for the prototypical molecule H_{2}^{+}, the attosecond charge migration is directly visualized with picometer spatial and attosecond temporal resolutions. Our method represents a general approach for monitoring attosecond charge migration in more complex polyatomic and biological molecules, which is one of the central tasks in the newly emerging attosecond chemistry.

Disentangling Intracycle Interferences in Photoelectron Momentum Distributions Using Orthogonal Two-Color Laser Fields

We use orthogonally polarized two-color (OTC) laser pulses to separate quantum paths in the multiphoton ionization of Ar atoms. Our OTC pulses consist of 400 and 800 nm light at a relative intensity ratio of 10∶1. We find a hitherto unobserved interference in the photoelectron momentum distribution, which exhibits a strong dependence on the relative phase of the OTC pulse. Analysis of model calculations reveals that the interference is caused by quantum pathways from nonadjacent quarter cycles.

Revealing the Sub-Barrier Phase using a Spatiotemporal Interferometer with Orthogonal Two-Color Laser Fields of Comparable Intensity

We measure photoelectron momentum distributions of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. The synthesized laser field is used to manipulate the oscillating tunneling barrier and the subsequent motion of electrons onto two spatial dimensions. The subcycle structures associated with the temporal double-slit interference are spatially separated and enhanced. We use such a spatiotemporal interferometer to reveal sub-barrier phase of strong-field tunneling ionization. This study shows that the tunneling process transfers the initial phase onto momentum distribution. Our work has the implication that the sub-barrier phase plays an indispensable role in photoelectron interference processes.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Capturing ultrafast molecular dynamics is difficult as the process involves coupled and very fast motions of electrons and nuclei. Here the authors study non-adiabatic dynamics in the NO molecule using strong-field photoelectron holography to shed light on the valence-shell electron dynamics.

Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

Identifying backward-rescattering photoelectron hologram with orthogonal two-color laser fields

Backscattering photoelectron hologram (BPH) originating from direct and backward-rescattering electrons encodes important structural information and ultrafast dynamics of the underlying processes. However, the BPH is usually overshadowed by other interference structures in the photoelectrons momentum spectra, preventing a direct extraction of information using BPH. Here we theoretically demonstrate disentanglement of the BPH from other types of interference with the orthogonal two-color field, where a weak orthogonal component is used to streak the BPH. By carefully adjusting the relative phase of the two-color field, the BPH is effectively separated from other interferences in the photoelectron momentum spectra and thus the BPH is unambiguously identified. This takes a significant step to time-resolved imaging of the attosecond dynamics with strong-field photoelectron holography.