Photoelectron Momentum Research Articles

Complete 3D photoelectron momentum vector reconstruction from time-position charged particle imaging

Abstract Many charged particle imaging techniques exist which directly measure, at a detector, the transverse position (x, y) and time-of-flight (t) of individual events in order to obtain a full set of 3D coordinates. Where curved velocity-mapping electric field lines are implemented, as in the case of 3D Velocity Map Imaging (3D VMI) and certain COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) instruments, the general transformation of (x, y, t)-data into initial 3D recoil momentum vectors (px , py , pz ) is challenging and has not yet been fully addressed. Here we present a detailed and general method for this transformation, illustrated using our 3D VMI spectrometer and the well-known narrow-band photoionization of nitric oxide, for which we demonstrate quantitative agreement with reported values. We additionally show how to measure and correct (i) small errors in the laser polarization axis alignment at the interaction region of a 3D charged particle imaging spectrometer, and (ii) the spatial variation of gain on a microchannel plate (MCP) detector. Improvements to and characterization of our 3D VMI spectrometer yield an electron time-of-flight resolution of 72 ps across the full 40 mm MCP, in combination with pixel-level spatial resolution.

Symmetries in three-dimensional photoelectron momentum spectroscopy as precursory methods for dichroic and enantiosensitive measurements

Symmetries in three-dimensional photoelectron momentum spectroscopy as precursory methods for dichroic and enantiosensitive measurements

Numerical investigation on circular interference photoelectron momentum distributions induced by spatiotemporal optical vortex pulse

Using the strong field approximation theory, we conducted a detailed numerical investigation on the photoelectron momentum distributions (PMDs) arising from the ionization of hydrogen atoms by a circularly polarized spatiotemporal optical vortex (STOV) pulse. STOV pulses have a unique spatial structure and peculiar phase properties. Our simulations reveal that PMDs exhibit a complex interference structure characterized by circular momentum bands intertwined with intricate interference fringes. A thorough examination of the multi-photon process provides a comprehensive explanation for the circular momentum band formation. We develop an expression to elucidate their center momentum positions within the PMDs. Furthermore, we perform a detailed analysis of the fine interference fringes, attributing their origin to the singular phase of the STOV pulse. Despite their distinct manifestations, we infer that the circular momentum bands and fine interference fringes stem from the simultaneous dependence upon the space and time variables of the STOV phase.

Transformation by Rabi oscillation of the photoelectron momentum distribution produced by oppositely circularly polarized laser pulses

Transformation by Rabi oscillation of the photoelectron momentum distribution produced by oppositely circularly polarized laser pulses

Sub-attosecond time delays of photoemission from asymmetric cores of molecules

We theoretically study the extreme ultraviolet (XUV) photoemission of the asymmetric molecular ion HeH2+ beyond the dipole approximation. Based on the double-slit interference of the photoelectron emitted from two atomic cores, we propose a scheme to obtain the XUV photoemission time delays originated from different physical mechanisms. In our study, two types of sub-attosecond photoemission time delays are identified and extracted from the observable photoelectron momentum distributions. One is the so-called birth time delay, originated from the travel time of the photon across the molecule, and the other is the escaping time delay of the photoelectron from two different cores. The present study shows the observable evidence demonstrating that in single-photon ionization, it takes more time for the photoelectron escaping from the helium nucleus than that from the proton. Published by the American Physical Society 2024

Orientation-dependent production of normal Archimedean and dynamical spirals for revealing orbital symmetries in diatomic multi-orbital molecules

The discovery and measurements of symmetric normal Archimedean spirals from atomic ionization by a pair of time-delayed broadband oppositely circularly polarized pulses revealed their potential of discerning orbital symmetry in atoms. Transferring this tool to molecules substantially increases experimental and theoretical challenges. Here, we show how Einstein’s photoelectric effect bypasses the congestion of electronic intermediate states and can access the orbital symmetry in heteronuclear, multi-orbital aligned molecules. Thanks to the broad bandwidth, multi-orbital ionization leads to multiplexed molecular-frame photoelectron momentum distributions, hiding thus any molecular orbital information. Only when molecular orientation is used to manipulate the ionization channels that one can identify a robust doorway into the molecular quantum world in which the asymmetry inherent to the highest-occupied molecular orbital can be unambiguously revealed by the asymmetric molecular spirals from single-color pulses. Our results demonstrate the potential of polarization-tailored attopulse sequences for the retrieval of spectroscopic details on molecular orbital symmetries.

Photoelectron momentum distribution in structured strong fields

Abstract In this study, a reaction microscope is used to explore the behavior of electrons in shaped beams under strong field conditions. Photoelectron momentum spectra indicate that the inclusion of orbital angular momentum (OAM) of light does not significantly impact the available electron angular momentum states. However, the distinctive donut shape of the beam plays a crucial role in determining the observed Photoelectron Angular Distributions (PADs). TDSE simulations, incorporating focal volume averaging indicates that the geometric properties of the focal region of the OAM and the Gaussian beams affect the photoelectron spectra differently. By averaging the spectra across different intensity regions, we have provided a qualitative explanation for the variations in photoelectron spectra resulting from the shapes of the individual beams. This result shows that the transfer of OAM in ultrashort light pulses cannot be detected in gas ensembles due to the ionization being overwhelmed by atoms in the most intense region with minimal spatial phase variation within the laser field. We demonstrate that the differences in the momentum spectra arising from shaped beams can be qualitatively explained using models that incorporate the spatial averaging of the beam, rather than focusing on the OAM content.

Energy- and angle-resolved coherent control on photoelectron dynamics by a directionality orthogonal double-slit interferometry.

We propose a directionality orthogonal double-slit interferometry to control photoelectron dynamics in energy- and angle-resolved fashion. The two orthogonal components of polarization-skewed (PS) laser pulse, in which the total polarization vector rotates as time evolves, can be regarded as the double-slit in the time domain. Our results demonstrate that the peak splitting and shift in photoelectron momentum distributions can be controlled by the relative optical phase between two components of the PS pulse. Based on the analysis from time-dependent perturbation theory, the behaviors of photoelectrons in angle-integrated energy spectra between 1s and 2p initial states can be attributed to the significant discrepancy of an interference pattern, which is reflected in energy- and angle-dependent phase difference of transition amplitudes from two orthogonal components of PS pulse. In addition, the influences of time delay and intensity ratio between two subpulses on this coherent control are also discussed. Our work provides a feasible protocol for controlling photoelectron dynamics in energy and angular resolutions and enriches the potential applications of the double-slit interference in the time domain.

Momentum distributions of symmetric (H2+) and asymmetric (HeH2+) molecular ions in a circularly polarized laser field under different ionization mechanisms

Abstract By numerically solving the two-dimensional (2D) time-dependent Schrödinger equation (TDSE), we present photoelectron momentum distributions (PMDs) and photoelectron angular distributions (PADs) of symmetric ( H 2 + ) and asymmetric (HeH2+) molecular ions in circularly polarized (CP) laser pulses. By adjusting the laser wavelength, two circumstances of resonance excitation and direct ionization were considered. The ionization mechanism of the resonance excitation was mainly investigated. The results show that the PMDs of H 2 + and HeH2+ in the y-direction gradually increase with increasing intensity, and the number of PMDs lobes is in good agreement with the results predicted by the ultrafast ionization model. In the resonance excitation scenario, the PMDs of H 2 + are dominated by two-photon ionization, whereas the PMDs of HeH2+ are dominated by three-photon ionization. Furthermore, the PMDs of HeH2+ are stronger in the resonance excitation scenario than those of H 2 + , which can be explained by the time-dependent population of electrons. In addition, the molecular structure is clearly imprinted onto the PMDs.

Coulomb focusing in attosecond angular streaking

Angular streaking technique employs a close-to-circularly polarized laser pulse to build a mapping between the instant of maximum ionization and the most probable emission angle in the photoelectron momentum distribution, thereby enabling the probe of laser-induced electron dynamics in atoms and molecules with attosecond temporal resolution. Here, through the jointed experimental observations and improved Coulomb-corrected strong-field approximation statistical simulations, we identify that electrons emitted at different initial ionization times converge to the most probable emission angle due to the previously-unexpected Coulomb focusing triggered by the nonadiabatic laser-induced electron tunneling. We reveal that the Coulomb focusing induces the observed nonintuitive energy-dependent trend in the angular streaking measurements on the nonadiabatic tunneling, and that tunneling dynamics under the classically forbidden barrier can leave fingerprints on the resulting signals. Our findings have significant implications for the decoding of the intricate tunneling dynamics with attosecond angular streaking.

XUV-beamline for photoelectron imaging spectroscopy with shaped pulses.

We introduce an extreme ultraviolet (XUV)-beamline designed for the time-resolved investigation and coherent control of attosecond (as) electron dynamics in atoms and molecules by polarization-shaped as-laser pulses. Shaped as-pulses are generated through high-harmonic generation (HHG) of tailored white-light supercontinua (WLS) in noble gases. The interaction of shaped as-pulses with the sample is studied using velocity map imaging (VMI) techniques to achieve the differential detection of photoelectron wave packets. The instrument consists of the WLS-beamline, which includes a hollow-core fiber compressor and a home-built 4f polarization pulse shaper, and the high-vacuum XUV-beamline, which combines an HHG-stage and a versatile multi-experiment vacuum chamber equipped with a home-built VMI spectrometer. The VMI spectrometer allows the detection of photoelectron wave packets from both the multiphoton ionization (MPI) of atomic or molecular samples by the tailored WLS-pulses and the single-photon ionization (SPI) by the shaped XUV-pulses. To characterize the VMI spectrometer, we studied the MPI of xenon atoms by linearly polarized WLS pulses. To validate the interplay of these components, we conducted experiments on the SPI of xenon atoms with linearly polarized XUV-pulses. Our results include the reconstruction of the 3D photoelectron momentum distribution (PMD) and initial findings on the coherent control of the PMD by tuning the spectrum of the XUV-pulses with the spectral phase of the WLS. Our results demonstrate the performance of the entire instrument for HHG-based photoelectron imaging spectroscopy with prototypical shaped pulses. Perspectively, we will employ polarization-tailored WLS-pulses to generate polarization-shaped as-pulses.

Photoelectron momentum distributions of triatomic CO2 molecules by circularly polarized attosecond pulses

Abstract Molecular-frame photoelectron momentum distributions (MF-PMDs) have been studied for imaging molecular structures. We investigate the MF-PMDs of CO2 molecules exposed to circularly polarized (CP) attosecond laser pulses by solving the time-dependent Schrödinger equations based on the single-active-electron approximation frames. Results show that high-frequency photons lead to photoelectron diffraction patterns, indicating molecular orbitals, these diffraction patterns can be illustrated by the ultrafast photoionization models. However, for the driving pulses with 30 nm, a deviation between MF-PMDs and theoretically predicted results of the ultrafast photoionization models is produced because the Coulomb effect strongly influences the molecular photoionization. Meanwhile, the MF-PMDs rotates in the same direction as the helicity of driving laser pulses. Our results also demonstrate that the MF-PMDs in a CP laser pulse are the superposition of those in the parallel and perpendicular linearly polarized cases. The simulations efficiently visualize molecular orbital geometries and structures by ultrafast photoelectron imaging. Furthermore, we determine the contribution of HOMO and HOMO-1 orbitals to ionization by varying the relative phase and the ratio of these two orbitals.

Anisotropic effects in the nondipole relativistic photoionization of hydrogen

In the nonrelativistic and dipole regime of multiphoton ionization, spherical symmetry in all but the polarization direction of the laser pulse ensures that directional dependency in the photoelectron spectra is limited to the laser polarization direction, with the final distribution exhibiting no asymmetry along the propagation direction of the laser. When relativistic effects and spatial dependency in the external potential are accounted for however, the addition of time dilation and radiation pressure both impose anisotropic effects. Previously we have found that nondipole effects induce a redshift in the photoelectron energy distribution, while conversely relativistic effects induce a blueshift, with the net effect of an apparent near-cancellation of the two. In this work we study these effects further. By examining photoelectron momentum distributions acquired from simulations with the time-dependent Dirac equation we propose explanatory models for both phenomena and present a simplified model of the shifts as a function of the angle relative to the propagation direction of the laser pulse. It is found that both nondipole and relativistic effects must be accounted for on an equal footing in order to correctly describe the photoelectron momentum distribution in the high-intensity regime.

Modulation of H atom photoelectron momentum distribution by chirped laser pulses of different wavelengths

The wavelength dependence of the holographic interference structure in the photoelectron momentum distribution (PMD) of hydrogen atoms under a few-cycle chirped laser field is investigated using a two-dimensional (2D) semiclassical two-step (SCTS) model. Under the constraint of a fixed chirp parameter, we observe an amplification in the impact of the chirp parameter on the laser field waveform as the wavelength increases. This enhancement facilitates effective modulation of the ionization time window. As the wavelength reaches a certain threshold, the double-slit interference pattern undergoes an observable expansion towards the left. Furthermore, based on the variations in X-axis momentum (Px) concerning ionization time at different wavelengths and the corresponding distribution of classical electron trajectories at those wavelengths, we present a more comprehensive explanation for the expansion of interference patterns. This expansion can be attributed to changes in wavelength, which result in modifications to the laser field’s waveform, consequently leading to a significant acceleration of ionized electrons when exposed to chirped laser pulses. It is worth noting that by tuning the negative chirp parameter, the leftward expansion of the double-slit interference pattern can also be achieved, particularly when shorter wavelengths of chirped laser pulses are employed.

Influence of catastrophes and hidden dynamical symmetries on ultrafast backscattered photoelectrons

We discuss the effect of using potentials with a Coulomb tail and different degrees of softening in photoelectron momentum distributions (PMDs) using the recently implemented hybrid forward-boundary CQSFA (H-CQSFA). We show that introducing a softening in the Coulomb interaction influences the ridges observed in the PMDs associated with backscattered electron trajectories. In the limit of a hard-core Coulomb interaction, the rescattering ridges close along the polarization axis, while for a soft-core potential, they are interrupted at ridge-specific angles. We analyze the momentum mapping of the different orbits leading to the ridges. For the hard-core potential, there exist two types of saddle-point solutions that coalesce at the ridge. By increasing the softening, we show that two additional solutions emerge as the result of breaking a hidden dynamical symmetry associated exclusively with the Coulomb potential. Further signatures of this symmetry breaking are encountered in subsets of momentum-space trajectories. Finally, we use scattering theory to show how the softening affects the maximal scattering angle and provide estimates that agree with our observations from the CQSFA. This implies that, in the presence of residual binding potentials in the electron's continuum propagation, the distinction between purely kinematic and dynamic caustics becomes blurred. Published by the American Physical Society 2024

Asymmetric electrostatic dodecapole: compact bandpass filter with low aberrations for momentum microscopy.

Imaging energy filters in photoelectron microscopes and momentum microscopes use spherical fields with deflection angles of 90°, 180° and even 2 × 180°. These instruments are optimized for high energy resolution, and exhibit image aberrations when operated in high transmission mode at medium energy resolution. Here, a new approach is presented for bandpass-filtered imaging in real or reciprocal space using an electrostatic dodecapole with an asymmetric electrode array. In addition to energy-dispersive beam deflection, this multipole allows aberration correction up to the third order. Here, its use is described as a bandpass prefilter in a time-of-flight momentum microscope at the hard X-ray beamline P22 of PETRA III. The entire instrument is housed in a straight vacuum tube because the deflection angle is only 4° and the beam displacement in the filter is only ∼8 mm. The multipole is framed by transfer lenses in the entrance and exit branches. Two sets of 16 different-sized entrance and exit apertures on piezomotor-driven mounts allow selection of the desired bandpass. For pass energies between 100 and 1400 eV and slit widths between 0.5 and 4 mm, the transmitted kinetic energy intervals are between 10 eV and a few hundred electronvolts (full width at half-maximum). The filter eliminates all higher or lower energy signals outside the selected bandpass, significantly improving the signal-to-background ratio in the time-of-flight analyzer.

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

Development of dual-beamline photoelectron momentum microscopy for valence orbital analysis.

The soft X-ray photoelectron momentum microscopy (PMM) experimental station at the UVSOR Synchrotron Facility has been recently upgraded by additionally guiding vacuum ultraviolet (VUV) light in a normal-incidence configuration. PMM offers a very powerful tool for comprehensive electronic structure analyses in real and momentum spaces. In this work, a VUV beam with variable polarization in the normal-incidence geometry was obtained at the same sample position as the soft X-ray beam from BL6U by branching the VUV beamline BL7U. The valence electronic structure of the Au(111) surface was measured using horizontal and vertical linearly polarized (s-polarized) light excitations from BL7U in addition to horizontal linearly polarized (p-polarized) light excitations from BL6U. Such highly symmetric photoemission geometry with normal incidence offers direct access to atomic orbital information via photon polarization-dependent transition-matrix-element analysis.

Photoemission Orbital Tomography Using a Robust Sparse PhaseLift.

Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) is a powerful technique that visualizes the shape of the molecular orbitals (MOs) of molecular films. For further utilization of POT, a simple and low-cost method of POT is highly required. Here, we propose a new POT method based on the PhaseLift algorithm (PhaseLift POT). This method utilizes a lifting procedure to convert the PMM, which is a second-order polynomial of MO coefficients, into a first-order polynomial of the lifted MO coefficients and further relaxes the equality constraint for a given PMM. We also established a method to improve the accuracy of phase retrieval from the noisy PMM data by using sparsity for MO coefficients (sparse PhaseLift POT). These methods make it possible to reconstruct the three-dimensional MOs, including phases of the wave function, directly from a single experimental PMM. This method can also precisely determine the adsorption-induced molecular deformations with an accuracy of 0.05 [Å]. Furthermore, the robust sparse PhaseLift POT is robust against unavoidable noise in the experimental PMMs due to the relaxation of the matching condition for a given PMM. Therefore, this will be an innovative tool for POT, especially for analyzing the dynamics of the molecules during the chemical reaction and excitation processes.

Impact of the continuum Coulomb interaction in quantum-orbit-based treatments of high-order above-threshold ionization

We perform a systematic comparison between photoelectron momentum distributions computed with the rescattered quantum-orbit strong-field approximation (RQSFA) and the Coulomb quantum-orbit strong-field approximation (CQSFA). We exclude direct, hybrid, and multiply scattered CQSFA trajectories and focus on the contributions of trajectories that undergo a single act of rescattering. For this orbit subset, one may establish a one-to-one correspondence between the RQSFA and CQSFA contributions for backscattered and forward-scattered trajectory pairs. We assess the influence of the Coulomb potential on the ionization and rescattering times of specific trajectory pairs, kinematic constraints determined by rescattering, and quantum interference between specific pairs of trajectories. We analyze how the Coulomb potential alters their ionization and return times, and their interference in photoelectron momentum distributions. We show that Coulomb effects are not significant for high or medium photoelectron energies and shorter orbits, while for lower momentum ranges or longer electron excursion times in the continuum, the residual Coulomb potential is more important. We also assess the agreement of both theories for different field parameters and show that it improves with the increase of the wavelength. Published by the American Physical Society 2024