Two-Color Strong-Field Photoelectron Spectroscopy and the Phase of the Phase

Towards simultaneous imaging of ultrafast nuclear and electronic dynamics in small molecules

When a chemical bond is broken, the molecular structure undergoes a transformation. An ideal experiment should probe the change in the electronic and nuclear structure simultaneously. Here, we present a method for the simultaneous time-resolved imaging of nuclear and electron dynamics by combining Coulomb explosion imaging with strong-field photoelectron momentum imaging. We study the dissociative photoionization of H2 and N2O using time-resolved photoion-photoelectron coincidence spectroscopy. The measured delay-dependent kinetic energy release clearly reveals the ultrafast nuclear dynamics. The transient changes in the electronic structure of the dissociating [Formula: see text] molecular ion are studied by solving the three-dimensional Schrödinger equation in the fixed-nuclei approximation. A detailed comparison of the numerical results to those from a simple imaging model is conducted. The numerical results reflect the evolution in the electron density in the molecular ion as its bond is first stretched and then breaks apart. While these details remain unresolved in the H2 experiment, we demonstrate the sensitivity of the photoelectron signal to the site of electron localization following bond cleavage for the case of N2O. Our work shows opportunities and challenges on the track towards capturing simple gas-phase chemical dynamics in complete molecular movies.

Observation of Attosecond Time Delays in Above-Threshold Ionization

Attosecond-scale temporal characterization of photoionization is essential in understanding how light and matter interact on the most fundamental level. However, characterizing the temporal property of strong-field above-threshold ionization has remained unreached. Here, we propose a novel photoelectron interferometric method to disentangle the contribution of Coulomb effect from an attoclock, allowing us to clock energy-resolved time delays of strong-field above-threshold ionization. We disentangle two types of Coulomb effects for the attoclock, i.e., one arising from the Coulomb disturbance of a single electron trajectory and the second effect arising from the photoelectron phase space distortion due to the Coulomb field. We find that the second Coulomb effect manifests itself as an energy-resolved attosecond time delay in the electron emission, which is relevant to the effect of nonadiabatic initial longitudinal momentum at the tunnel exit. Our study further indicates a sensitivity of the time delay to the temporal profile of the released electron wave packet within one half laser cycle. The temporal width of the released electron wave packet is found to increase with energy, which contradicts the common assumption in the adiabatic picture.

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.

Tracing attosecond electron emission from a nanometric metal tip

Solids exposed to intense electric fields release electrons through tunnelling. This fundamental quantum process lies at the heart of various applications, ranging from high brightness electron sources in d.c. operation1,2 to petahertz vacuum electronics in laser-driven operation3-8. In the latter process, the electron wavepacket undergoes semiclassical dynamics9,10 in the strong oscillating laser field, similar to strong-field and attosecond physics in the gas phase11,12. There, the subcycle electron dynamics has been determined with a stunning precision of tens of attoseconds13-15, but at solids the quantum dynamics including the emission time window has so far not been measured. Here we show that two-colour modulation spectroscopy of backscattering electrons16 uncovers the suboptical-cycle strong-field emission dynamics from nanostructures, with attosecond precision. In our experiment, photoelectron spectra of electrons emitted from a sharp metallic tip are measured as function of the relative phase between the two colours. Projecting the solution of the time-dependent Schrödinger equation onto classical trajectories relates phase-dependent signatures in the spectra to the emission dynamics and yields an emission duration of 710 ± 30 attoseconds by matching the quantum model to the experiment. Our results open the door to the quantitative timing and precise active control of strong-field photoemission from solid state and other systems and have direct ramifications for diverse fields such as ultrafast electron sources17, quantum degeneracy studies and sub-Poissonian electron beams18-21, nanoplasmonics22 and petahertz electronics23.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400 nm laser pulse, the ionization probability is reduced if another relatively weak 800 nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800 nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Full experimental determination of tunneling time with attosecond-scale streaking method

Tunneling is one of the most fundamental and ubiquitous processes in the quantum world. The question of how long a particle takes to tunnel through a potential barrier has sparked a long-standing debate since the early days of quantum mechanics. Here, we propose and demonstrate a novel scheme to accurately determine the tunneling time of an electron. In this scheme, a weak laser field is used to streak the tunneling current produced by a strong elliptically polarized laser field in an attoclock configuration, allowing us to retrieve the tunneling ionization time relative to the field maximum with a precision of a few attoseconds. This overcomes the difficulties in previous attoclock measurements wherein the Coulomb effect on the photoelectron momentum distribution has to be removed with theoretical models and it requires accurate information of the driving laser fields. We demonstrate that the tunneling time of an electron from an atom is close to zero within our experimental accuracy. Our study represents a straightforward approach toward attosecond time-resolved imaging of electron motion in atoms and molecules.

Phase-of-the-Phase Electron Momentum Spectroscopy on Single Metal Atoms in Helium Nanodroplets

Magnesium atoms fully embedded in helium nanodroplets are exposed to two-color laser pulses, which trigger multiphoton above-threshold ionization (ATI). This allows exemplary study of the contribution of a dense, neutral, and finite medium on single electron propagation. The angular-resolved photoelectron spectra show striking differences with respect to results obtained on free atoms. Scattering of the individual Mg photoelectrons, when traversing the neutral helium environment, causes the angular distribution to become almost isotropic. Furthermore, the appearance of higher-energy electrons is observed, indicating the impact of the droplet on the concerted emission process. Phase-of-the-phase spectroscopy, however, reveals a marked loss in the 2ω-ω phase dependence of the electron signal. Taking into account sideband formation on a quantitative level, a Monte Carlo simulation which includes laser-assisted electron scattering can reproduce the experimental spectra and give insights into the strong-field-induced electron emission from disordered systems.

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.

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.

Cresting the Coulomb Barrier of Polyanionic Metal Clusters

Combining photoelectron spectroscopy with tunable laser pulse excitation allows us to characterize the Coulomb barrier potential of multiply negatively charged silver clusters. The spectra of mass- and charge-selected polyanionic systems, with z=2-5 excess electrons, show a characteristic dependence on the excitation energy, which emphasizes the role of electron tunneling through the barrier. By evaluating experimental data from an 800-atom system, the electron yield is parametrized with respect to tunneling near the photoemission threshold. This analysis results in the first experimentally based potential energy functions of polyanionic metal clusters.

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.

Universal High-Energy Photoelectron Emission from Nanoclusters Beyond the Atomic Limit

Rescattering by electrons on classical trajectories is central to understand photoelectron and high-harmonic emission from isolated atoms or molecules in intense laser pulses. By controlling the cluster size and the quiver amplitude of electrons, we demonstrate how rescattering influences the energy distribution of photoelectrons emitted from noble gas nanoclusters. Our experiments reveal a universal dependence of photoelectron energy distributions on the cluster size when scaled by the field driven electron excursion, establishing a unified rescattering picture for extended systems with the known atomic dynamics as the limit of zero extension. The result is supported by molecular dynamics calculations and rationalized with a one-dimensional classical model.

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.

Attosecond-Scale Streaking Methods for Strong-Field Ionization by Tailored Fields

Streaking with a weak probe field is applied to ionization in a two-dimensional strong field tailored to mimic linear polarization, but without disturbance by recollision or intracycle interference. This facilitates the observation of electron-momentum-resolved times of ionization with few-attosecond precision, as demonstrated by simulations for a model helium atom. Aligning the probe field along the ionizing field provides meaningful ionization times in agreement with the attoclock concept that ionization at maximum field corresponds to the peak of the momentum distribution, which is shifted due to the Coulomb force on the outgoing electron. In contrast, this attoclock shift is invisible in orthogonal streaking. Even without a probe field, streaking happens naturally along the laser propagation direction due to the laser magnetic field. As with an orthogonal probe field, the attoclock shift is not accessible by the magnetic-field scheme. For a polar molecule, the attoclock shift depends on orientation, but this does not imply an orientation dependence in ionization time.

Attosecond Time Delay of Retrapped Resonant Ionization

A recent ultrafast pump-probe technique has allowed measurement of time delays during photoemission in a variety of systems ranging from atoms and molecules to solids with unprecedented temporal resolution. However, identifying the underlying physics is still a challenge especially in complicated multichannel above-threshold ionization (ATI) experiments. Here we demonstrate that the time delays of different ionization pathways in ATI can be clearly resolved and extracted with a semiclassical statistical method. The remarkable phase shift of near threshold photoelectrons can be attributed to a temporary retrapping of a photoelectron by the atomic potential in a quasibound state after emerging in the continuum state. This continuum-bound-continuum scattering manifests as a new resonant effect in strong-field photoemission. Our results unify the seemingly opposing quantum Eisenbud-Wigner-Smith time delay and classical Coulomb-induced time delay by highlighting the same physical picture, which holds promise for an intuitive interpretation of time-resolved fundamental electronic processes in strong-field experiments and epistemological reexamination of the quantum-classical correspondence.

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.

Attosecond time-resolved photoelectron holography

Ultrafast strong-field physics provides insight into quantum phenomena that evolve on an attosecond time scale, the most fundamental of which is quantum tunneling. The tunneling process initiates a range of strong field phenomena such as high harmonic generation (HHG), laser-induced electron diffraction, double ionization and photoelectron holography—all evolving during a fraction of the optical cycle. Here we apply attosecond photoelectron holography as a method to resolve the temporal properties of the tunneling process. Adding a weak second harmonic (SH) field to a strong fundamental laser field enables us to reconstruct the ionization times of photoelectrons that play a role in the formation of a photoelectron hologram with attosecond precision. We decouple the contributions of the two arms of the hologram and resolve the subtle differences in their ionization times, separated by only a few tens of attoseconds.

Field induced tunneling is one of the fundamental processes of light-matter interaction. Here the authors reconstruct the  temporal properties of tunneling using two-color electron holography with attosecond time resolution using argon atoms.

Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths

A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

Self-probing spectroscopy of XUV photo-ionization dynamics in atoms subjected to a strong-field environment

Single-photon ionization is one of the most fundamental light matter interactions in nature, serving as a universal probe of the quantum state of matter. By probing the emitted electron, one can decode the full dynamics of the interaction. When photo-ionization is evolving in the presence of a strong laser field, the fundamental properties of the mechanism can be signicantly altered. Here we demonstrate how the liberated electron can perform a self-probing measurement of such interaction with attosecond precision. Extreme ultraviolet attosecond pulses initiate an electron wavepacket by photo-ionization, a strong infrared field controls its motion, and finally electron-ion collision maps it into re-emission of attosecond radiation bursts. Our measurements resolve the internal clock provided by the self-probing mechanism, obtaining a direct insight into the build-up of photo-ionization in the presence of the strong laser field.

Enhancement of the second plateau in solid high-order harmonic spectra by the two-color fields

We theoretically investigate high-order harmonic generation (HHG) from solids in two-color fields. It is found that under the premise of maintaining the same amplitude, the intensity of the second plateau can be enhanced by two to three orders in a proper two-color field compared with the result in the monochromatic field with the same frequency as the driving pulse of the two-color field. This can be attributed to the fact that most excited electrons can be driven to the top of the first conduction band due to the larger vector potential of the two-color fields, which leads to the higher electron population of upper conduction bands. Moreover, we also find that isolated attosecond pulses can be generated from solids by choosing a proper two-color field that allows the electrons to reach the top of the first conduction band only once. This work provides a promising method for extending the range of solid HHG spectra in experiments.

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.