Strong-field Photoelectron Holography Research Articles

Transverse asymmetry in molecular strong-field photoelectron holography induced by initial phase structure and Coulomb field

Transverse asymmetry in molecular strong-field photoelectron holography induced by initial phase structure and Coulomb field

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.

Control of Electron Wave Packets Close to the Continuum Threshold Using Near-Single-Cycle THz Waveforms.

The control of low-energy electrons by carrier-envelope-phase-stable near-single-cycle THz pulses is demonstrated. A femtosecond laser pulse is used to create a temporally localized wave packet through multiphoton absorption at a well defined phase of a synchronized THz field. By recording the photoelectron momentum distributions as a function of the time delay, we observe signatures of various regimes of dynamics, ranging from recollision-free acceleration to coherent electron-ion scattering induced by the THz field. The measurements are confirmed by three-dimensional time-dependent Schrödinger equation simulations. A classical trajectory model allows us to identify scattering phenomena analogous to strong-field photoelectron holography and high-order above-threshold ionization.

Semiclassical trajectory perspective of glory rescattering in strong-field photoelectron holography

We investigate theoretically the photoelectron momentum distribution (PMD) of the ionized atoms irradiated by a linearly polarized intense laser, focusing on the holography interference patterns in PMD that carry important information of the initial wavefunction of a tunneled electron and its experienced atomic potential in rescattering. With the help of Dyson series and semiclassical propagator, we calculate the scattering amplitudes in the cylindrical coordinate representation. In contrast to conventional recognitions that the photoelectron holography is the interference of two branches of electron trajectories, however, we find strikingly that infinite semiclassical trajectories can be deflected by the combined Coulomb potential and laser field into the same final momentum: The initial momenta are found to be distributed on a ring-shape curve in the transverse momentum plane and the initial positions of these trajectories are perpendicular to their initial momentum vectors. For the zero final transverse momentum, the above ring-source trajectories degenerate into the point-source axial caustic trajectories (or Glory trajectories) and the quantum interference of these trajectories will dramatically alter the scattering amplitudes that is termed as Glory rescattering effect. With following Berry's spirit of uniform approximation for Glory scattering in optics, we can finally derive a uniform formulation of the rescattering amplitude in the Bessel functions for the strong-field photoelectron holography (SFPH) patterns. Our results are in good agreement with solutions of the time-dependent Schr\"odinger equation and can account for recent photoelectron holography experiments. Important applications of our theory are also discussed.

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.

Theory and application of photoelectron trajectory interference holography for atomic ionization in intense laser field

The rescattering scenario that the ionized photoelectron is guided back to the vicinity of the atomic core under an oscillating laser field is the key to understanding strong field processes. Strong field photoelectron holography, which stems from the interference of direct and rescattering waves, has great potential applications in studying strong field physics and detecting ultrafast electron dynamics. The article develops the underlying quantum orbits interference picture. By including Coulomb potential, the uniform glory rescattering theory is introduced, which gives reasonably quantitative results in accord with time-dependent Schrödinger equation and experimental results. And reconstructing the ultrashort light pulses in the time domain with the Coulomb glory temporal gate is also studied. Deepening the understanding of strong field photoelectron holography will lead to further enlightening in ultrafast physics and contribute to future applications.

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.

Photoelectron holography in strong-field tunneling ionization by a spatially inhomogeneous field

Photoelectron holography in strong-field tunneling ionization is an efficient way to probe the structures and the ultrafast dynamics information of atoms and molecules. Manipulating the process of photoelectron holography is important for its application. Here, we study theoretically strong-field photoelectron holography in the spatially inhomogeneous field by solving the time-dependent Schr\"odinger equation. Our results show that the returning energy of the rescattering electron is greatly enhanced in the spatially inhomogeneous field, and the holographic interference pattern can be separated from other types of interference in the photoelectron momentum distribution. Moreover, our results show that the time window of tunneling ionization wherein the electron could be driven back to induce holography is broadened in the inhomogeneous field. These properties are beneficial for the application of photoelectron holography in probing the atomic and molecular structures and dynamics. The origin for these properties is analyzed with the classical trajectory model.

Attosecond-resolved photoelectron holography for triatomic molecule

Photoelectron holography in strong field tunneling ionization has subatomic spatial and attosecond temporal resolutions and thus it is a promising method to probe the attosecond electronic dynamics in atoms and molecules. The proof-of-concept studies have been performed in atoms and diatomic molecules. Here, we illustrate the application of the strong-field photoelectron holography in probing the attosecond electron dynamics in more complex system. As a demonstrated, by solving the time-dependent Schrödinger equation, we shown that the ultrafast charge migration in the triatomic molecule H3 could be retrieved from the holographic fringes in the photoelectron momentum distribution. Our study indicates that the concept of photoelectron holography can be extended to probe the attosecond electron dynamics in more complex molecules which is of essential significance for the newly emerging attosecond chemistry.

Subfemtosecond glory hologrammetry for vectorial optical waveform reconstruction

In this paper, we propose a new method to characterize the temporal structure of arbitrary optical laser pulses with low pulse energies. This approach is based on strong field photoelectron holography with the glory rescattering effect as the underlying mechanism in the near-forward direction. Utilizing the subfemtosecond glory rescattering process as a fast temporal gate to sample the unknown light pulse, the time-dependent vectorial electric field can be retrieved from the streaking photoelectron momentum spectra. Our method avoids the challenging task of generation or manipulation of attosecond pulses and signifies important progress in arbitrary optical waveform characterization.

Resolving strong-field tunneling ionization with a temporal double-slit interferometer

Laser-induced tunneling ionization is one of the most fundamental and ubiquitous quantum processes and it initiates various ultrafast phenomena in intense laser-atom and laser-molecule interactions. Accurately resolving tunneling ionization is essential for understanding these phenomena. Based on the advanced attosecond technologies, such as high-order harmonic spectroscopy and strong-field photoelectron holography, previous studies have resolved the temporal properties of the tunneling process for rescattering electron. Here, as a complement, we theoretically demonstrate the retrieval of the time information of the tunneling process for the direct electron with the temporal double-slit interferometer. In this scheme, a weak second harmonic parallel to the fundamental field is added. By solving the time-dependent Schr\odinger equation, the photoelectron momentum distribution (PEMD) from strong-field tunneling ionization is obtained. Varying the relative phase of the parallel two-color field, the path of the ionized electrons periodically changes, leading to a shift of the time double-slit interference fringes in PEMDs. By analyzing the response of the interference fringes to the perturbation, the time information of direct electron in strong-field tunneling ionization is reconstructed. Interestingly, our results present excellent agreement with the complex time obtained from the quantum-orbit model.

Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses.

Strong-field photoelectron holography (SFPH), originating from the interference of the direct electron and the rescattering electron in tunneling ionization, is a significant tool for probing structure and electronic dynamics in molecules. We theoretically study SFPH by counter rotating two-color circularly (CRTC) polarized laser pulses. Different from the case of the linearly polarized laser field, where the holographic structure in the photoelectron momentum distribution (PEMD) is clustered around the laser polarization direction, in the CRTC laser fields, the tunneling ionized electrons could recollide with the parent ion from different angles and thus the photoelectron hologram appears in the whole plane of laser polarization. This property enables structural information delivered by the electrons scattering the molecule from different angles to be recorded in the two-dimensional photoelectron hologram. Moreover, the electrons tunneling at different laser cycles are streaked to different angles in the two-dimensional polarization plane. This property enables us to probe the sub-cycle electronic dynamics in molecules over a long time window with the multiple-cycle CRTC laser pulses.

Strong-field photoelectron holography beyond the electric dipole approximation: A semiclassical analysis

Strong-field photoelectron holography denotes the interference of various electron paths in laser-induced ionization of atoms, leading to interference patterns in the final momentum distribution. For a quantitative description of holography beyond the electric dipole approximation and in the presence of the Coulomb potential, we develop a semiclassical model in which the initial conditions of outgoing electrons are set according to the beyond-dipole strong-field approximation for the ionization step. The phases associated with trajectories are evaluated following the prescription for semiclassical propagators. The validity of the method is confirmed by comparison to the numerical solution of the time-dependent Schr\"odinger equation in two spatial dimensions. The semiclassical model reproduces correctly the backward and forward shifts of the photoelectron momenta along the laser propagation axis that arise from beyond-dipole dynamics. The position of the central holographic interference fringe can be estimated already from a simplified Coulomb-free interference model that provides closed-form expressions for the beyond-dipole shifts. In three dimensions, Coulomb focusing causes a breakdown of the semiclassical model for final momenta with directions close to the polarization axis. We implement a beyond-dipole regularization procedure based on the concept of glory scattering, which was recently used to describe Coulomb focusing in the dipole approximation. While the position of the central maximum and higher-order fringes can already be obtained approximately by simpler semiclassical modeling, this glory model is able to predict the shape of the distribution in the close vicinity of the central maximum. The violation of the dipole approximation in holography should be observable with mid-infrared fields, for which the forward/backward shifts can be comparable with the fringe spacing.

Time-resolving tunneling ionization via strong-field photoelectron holography

Strong-field tunneling ionization is the initial step for various ultrafast dynamics in intense laser-atom and/or molecule interactions. Time-resolving tunneling ionization is of crucial importance for accurately understanding these ultrafast processes. In our previous work [Phys. Rev. Lett. 121, 253203 (2018).], we proposed an attosecond photoelectron interferometer based on strong-field photoelectron holography to resolve the tunneling ionization. Here, we show more details about how the complex ionization time of tunneling is retrieved with our scheme. We demonstrate that the Coulomb interaction, which is a tedious and complex problem in dealing with photoelectron interference in strong-field ionization, can be safely canceled in our scheme. This is further confirmed by performing our scheme for both the model atoms with short-range and Coulomb potentials. Additionally, the validity and accuracy of our scheme are confirmed by its application in different targets and different laser parameters. Our scheme provides a reliable and versatile method to resolve the time information of strong-field tunneling ionization.

Imaging charge migration in the asymmetric molecule with the holographic interference in strong-field tunneling ionization

Coherent superposition of several electronic states in molecules induces attosecond charge migration. We theoretically demonstrate a way to observe this attosecond charge migration in the asymmetric molecule HeH2+ using strong-field photoelectron holography, complementary to our previous work (He M et al 2018 Phys. Rev. Lett. 120, 133204) where the charge migration in the symmetric molecule was monitored. We disentangle the holographic interference from other types of interference in the photoelectron momentum distribution with the Fourier frequency filter method. By employing the holographic fringes originating from the ground state of HeH2+ as a reference, we develop a feasible approach to visualize the charge migration in the asymmetric molecule with attosecond temporal resolution.

Strong-field photoelectron holography of atoms by bicircular two-color laser pulses

We study photoelectron holography in strong bicircular two-color laser fields by solving the time-dependent Schr\"odinger equation (TDSE) and a semiclassical rescattering model with implementing interference effect. The holographic patterns observed in the TDSE are well recaptured by the semiclassical rescattering model. Four types of photoelectron holographic interferences between the forward scattered and nonscattered trajectories are predicted by the semiclassical rescattering model in the bicircular two-color laser field. We find that those holographic patterns are spatially separated from each other in the electron momentum distribution. We further show that the dependence of the initial transverse momentum at the tunnel exit on the ionization time for the rescattering electron is recorded by the holographic patterns.

Effects of the Coulomb potential in interference patterns of strong-field holography with photoelectrons

Using the semiclassical two-step model for strong-field ionization we investigate the interference structures emerging in strong-field photoelectron holography, taking into account the Coulomb potential of the atomic core. For every kind of the interference pattern predicted by the three-step model, we calculate the corresponding structure in the presence of the Coulomb field, showing that the Coulomb potential modifies the interference patterns significantly.

Coulomb potential effects in strong-field photoelectron holography with a midinfrared laser pulse

A profound ringlike pattern coming from the interplay between the intra- and the intercycle interference of electron trajectories can be observed in the deep tunneling ionization regime, and an appropriate experimental condition for the observation of the photoelectron holography was provided.

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.

Revealing the target structure information encoded in strong-field photoelectron hologram

By numerically solving the two-dimensional time-dependent Schrodinger equation, we investigate the strong-field photoelectron holography (SFPH) for different atomic and molecular targets. The results show that the photoelectron hologram is capable of providing structural information-the phase of scattering amplitude. In our calculations, the holographic pattern shifts with the target, indicating the phase difference between various targets. However, for the near-forward scattering, the phases of scattering amplitude for different targets are similar and thus no structural information has been retrieved in the previous works on near-forward scattering hologram. We suggest to use the backward scattering photoelectron hologram to extract this type of structural information. This paves a significant step towards time-resolved imaging of molecular structure and dynamics with the concept of SFPH.