Exploring symmetries in photoelectron holography with two-color linearly polarized fields
T. Rook, C. Figueira de Morisson Faria
备注：
48 pages, 14 figures (including one in the appendix); figures have been included, there has been some restructuring and some discussions have been extended in the revised version
We investigate photoelectron holography in bichromatic linearly polarized fields of commensurate frequencies $rω$ and $sω$, with emphasis on the existing symmetries and for which values of the relative phase between the two driving waves they are kept or broken. Using group-theoretical methods, we show that, additionally to the well-known half-cycle symmetry, which is broken for $r+s$ odd, there are reflection symmetries around the field zero crossings and maxima, which may or may not be kept, depending on how both waves are dephased. The three symmetries are always present for monochromatic fields, while for bichromatic fields this is not guaranteed, even if $r+s$ is even and the half-cycle symmetry is retained. Breaking the half-cycle symmetry automatically breaks one of the other two, while, if the half-cycle symmetry is retained, the other two symmetries are either \textit{both} kept or broken. We analyze how these features affect the ionization times and saddle-point equations for different bichromatic fields. We also provide general expressions for the relative phases $ϕ$ which retain specific symmetries. As an application, we compute photoelectron momentum distributions for $ω-2ω$ fields with the Coulomb Quantum Orbit Strong-Field approximation and assess how holographic structures such as the fan, the spider and interference carpets behave, focusing on the reflection symmetries. The features encountered can be traced back to the field gradient and amplitude affecting ionization probabilities and quantum interference in different momentum regions.
We perform a detailed analysis of the different types of orbits in the Coulomb Quantum Orbit Strong-field Approximation (CQSFA), ranging from direct to those undergoing hard collisions. We show that some of them exhibit clear counterparts in the standard formulations of the strong-field approximation for direct and rescattered above-threshold ionization, and show that the standard orbit classification commonly used in Coulomb-corrected models is over-simplified. We identify several types of rescattered orbits, such as those responsible for the low-energy structures reported in the literature, …
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.
Vortex photoelectron holography in strong-field tunneling ionization
School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology（华中科技大学物理科学与技术学院与武汉光电国家研究中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Advanced Science, The University of Electro-Communications（电波大学高级科学研究所）；Hubei Fundamental Research Center for Physics（湖北物理基础研究中心）
Strong field photoelectron holography has been proposed as a means for interrogating the spatial and temporal information of electrons and ions in a dynamic system. After ionization, part of the electron wave packet may directly go to the detector (the reference wave), while another part may be driven back to the ion where it scatters off (the signal wave). The interference hologram of the two waves may be used to retrieve the target information. However, unlike conventional optical holography, the propagations of electron wave packets are affected by the Coulomb potential as well as by the la…
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 e…
We perform a systematic analysis of how ultrafast photoelectron holography is influenced by an elliptically polarized field, with emphasis on quantum interference effects. We find that the interplay of the external field and the binding potential leads to twisted holographic patterns for low ellipticities and recover well-known angular offsets for high ellipticities. Using the Coulomb quantum-orbit strong-field approximation (CQSFA), we assess how the field ellipticity affects specific holographic patterns, such as the fan and the spider. The interplay of the external field and the binding pot…
We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations present an excellent agreement with the result from time-dependent Schrödinger equation method. We show that the low-energy fan-shaped structure in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattering electron trajectories, which affects different momenta and scattering angles unequal…
Most implementations of Coulomb-distorted strong-field approaches that contain features such as tunneling and quantum interference use real trajectories in continuum propagation, while a fully consistent approach must use complex trajectories throughout. A key difficulty in the latter case are branch cuts that appear due to the specific form of the Coulomb potential. We present a method for treating branch cuts in quantum-trajectory models, which is subsequently applied to photoelectron holography. Our method is not numerically intensive, as it does not require finding the location of all bran…
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 semiclass…
We provide approximate analytic expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions (PADs). These analytic expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit stron…
A new scheme based on (i) upcoming brilliant X-ray Free Electron Laser (FEL) sources, (ii) novel energy and angular dispersive, large-area electron imagers and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium sized molecules with Ångström spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections or isomerization by a pump pulse this motion is visualized by the X-ray FEL probe pulse launching keV photoelectrons w…
Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory and experimental analysis: unit-cell averaging and time-filtering data and simulations. Together these suppress ATI rings and enable an unprecedented highly-detailed quantitative match between strong-fi…
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 …
Angular distribution of photoelectrons released by the ionization of randomly-oriented molecules with two laser fields of carrier frequencies $ω$ and $2ω$, which are linearly polarized in two mutually-orthogonal directions, is analyzed in the perturbation limit for the case of one- vs two-photon ionization process. In particular, we focus on the recently predicted [Ph.V. Demekhin {\it et al.}, Phys. Rev. Lett. \textbf{121}, 253201 (2018)] forward-backward asymmetry in the photoelectron emission, which is induced by the interference of two fields and depends on the external relative phase betwe…
We introduce a novel and concise methodology to detect the parity of atomic and molecular orbitals based on photoelectron holography, which is more general than the existing schemes. It fully accounts for the Coulomb distortions of electron trajectories, does not require sculpted fields to retrieve phase information and, in principle, is applicable to a broad range of electron momenta. By comparatively measuring the differential photoelectron spectra from strong-field ionization of N$_{2}$ molecules and their companion atoms of Ar, some photoelectron holography patterns are found to be dephase…
We consider atomic strong-field ionization in the long-pulse limit for linearly polarized infrared laser fields. We show how nondipole effects in the plane formed by the propagation and polarization directions lead to (i) a shift of the origin of the rings describing the energetically allowed final electron momenta for individual above-threshold ionization channels and (ii) a redistribution in the continuum population on each ring.
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 attose…
Ultrafast imaging of molecular chirality is a key step towards the dream of imaging and interpreting electronic dynamics in complex and biologically relevant molecules. Here, we propose a new ultrafast chiral phenomenon exploiting recent advances in electron optics allowing access to the orbital angular momentum of free electrons. We show that strong-field ionization of a chiral target with a few-cycle linearly polarized 800 nm laser pulse yields photoelectron vortices, whose chirality reveals that of the target, and we discuss the mechanism underlying this phenomenon. Our work opens new persp…
Photoelectron angular distributions (PADs) of oriented polar molecules in response to different polarized lasers are systematically investigated. It is found that the PADs of polar CO molecules show three distinct styles excited by linearly, elliptically and circularly polarized lasers respectively. In the case of elliptical polarization, a deep suppression is observed along the major axis and the distribution concentrates approximately along the minor axis. Additionally, it is also found that the concentrated distributions rotate clockwise as the ellipticity increases. Our investigation prese…
We theoretically study multiphoton ionization of the Ca atom irradiated by the second (photon energy 3.1 eV) and third (photon energy 4.65 eV) harmonics of Ti:sapphire laser pulses (photon energy 1.55 eV). Because of the dense energy level structure the second and third harmonics of a Ti:sapphire laser are nearly single-photon resonant with the ${4s4p}$ $^1P^o$ and ${4s5p}$ $^1P^o$ states, respectively. Although two-photon ionization takes place through the near-resonant intermediate states with the same symmetry in both cases, it turns out that there are significant differences between them. …
We theoretically study multiphoton ionization through the triplet states of Mg by linearly polarized (LP) and circularly polarized (CP) fs laser pulses. After the construction of the atomic basis using the frozen-core Hartree-Fock potential (FCHFP) as well as the model potential (MP) approaches for both singlet and triplet series which show rather good agreements with the existing data in terms of state energies and dipole matrix elements, we solve time-dependent Schrödinger equations with $3s3p$ $^{3}P_{1}$ as an initial state, and calculate the total ionization yield and photoelectron energy…
Calculating strong-field, momentum-resolved photoelectron spectra (PES) from numerical solutions of the time-dependent Schrödinger equation (TDSE) is a very demanding task due to the large spatial excursions and drifts of electrons in intense laser fields. The time-dependent surface flux (t-SURFF) method for the calculation of PES [L. Tao, A. Scrinzi, New Journal of Physics 14, 013021 (2012)] allows to keep the numerical grid much smaller than the space over which the wavefunction would be spread at the end of the laser pulse. We present an implementation of the t-SURFF method in the well esta…
We review the semiclassical two-step model for strong-field ionization. The semiclassical two-step model describes quantum interference and accounts for the ionic potential beyond the semiclassical perturbation theory. We discuss formulation and implementation of this model, its further developments, as well as some of the applications. The reviewed applications of the model include strong-field holography with photoelectrons, multielectron polarization effects in ionization by an intense laser pulse, and strong-field ionization of the hydrogen molecule.
We investigate the influence of relativistic nondipole effects on the photoelectron spectra of argon, particularly in the low kinetic energy region (0 eV - 5 eV). In our experiment, we use intense linearly polarised 800 nm laser pulse to ionise Ar from a jet and we record photoelectron energy and momentum distributions using a reaction microscope (REMI). Our measurements show that nondipole effect can cause an energy-dependent asymmetry along the laser propagation direction in the photoelectron energy and momentum spectra. Model simulation based on time-dependent Dirac equation (TDDE) can repr…
The phenomenon of spatial (polar) asymmetry of produced photoelectron emission due to strong-field multiphoton process of above-threshold ionization (ATI) in atoms irradiated by a linearly polarized two-color (bichromatic) laser field consisting of coherent superposition of two commensurate harmonics (of frequencies and is considered and studied theoretically. The problem is addressed within the conventional strong-field approximation (SFA) in standard velocity gauge (VG) formulation under condition of arbitrary value of the so-called Keldysh parameter $γ$ , including both the multiphoton (for…
High-resolution photoelectron momentum distributions of Xe atoms ionized by 800-nm linearly polarized laser fields have been traced at intensities from 1.1*1013 to 3.5*1013W/cm2 using velocity-map imaging techniques. At certain laser intensities, the momentum spectrum exhibits a distinct double-ring structure for low-order above-threshold ionization, which appears to be absent at lower or higher laser intensities. By investigating the intensity-resolved photoelectron energy spectrum, we find that this double-ring structure originates from resonant multiphoton ionization involving multiple Rydb…
The role of the Coulomb potential of the atomic core for creation of caustics in the photoelectron momentum distribution for tunneling ionization in a linearly polarized strong laser field, usually termed as Coulomb focusing, is investigated within classical theory beyond the dipole approximation. Coulomb focusing is addressed by analytical calculation of Coulomb momentum transfer to the tunneled electron due to rescatterings, while applying perturbation theory and classifying the recollisions either as fast or as slow. The accuracy of the obtained analytical formulas for the Coulomb momentum …
We study the ionization dynamics of oriented HeH$^+$ in strong linearly-polarized laser fields by numerically solving the time-dependent Schrödinger equation. The calculated photoelectron momentum distributions for parallel orientation show a striking asymmetric structure. With a developed model pertinent to polar molecules, we trace the electron motion in real time. We show that this asymmetric structure arises from the interplay of the Coulomb effect and the permanent dipole in strong laser fields. This structure can be used to probe the degree of orientation which is important in ultrafast …
Ionization of atoms by linearly polarized strong laser fields produces cylindrically symmetric 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 jumps occurring when trajectories pass through focal points. Such phase jumps are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Most importantly, because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a…
In strong-field ionization interferences between electron trajectories create a variety of interference structures in the final momentum distributions. Among them, the interferences between electron pathways that are driven directly to the detector and the ones that rescatter significantly with the parent ion lead to holography-type interference patterns that received great attention in recent years. In this work, we study the influence of the magnetic field component onto the holographic interference pattern, an effect beyond the electric dipole approximation, in experiment and theory. The ex…
We study the ionization of atomic hydrogen in the direction of polarization due to a linearly polarized XUV pulse in the presence a strong field IR. We describe the photoelectron spectra as an interference problem in the time domain. Electron trajectories steming from different optical laser cycles give rise to intercycle interference energy peaks known as sidebands. These sidebands are modulated by a grosser structure coming from the intracycle interference of the two electron trajectories born during the same optical cycle. We make use of a simple semiclassical model which offers the possibi…
A theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an IR laser is presented. Well-established theories are usually used to describe the problem of laser assisted photoelectron effect. However, the well-known soft-photon approximation firstly posed by Maquet et al in Journal of Modern Optics 54, 1847 (2007) and Kazansky's theory in Phys. Rev. A 82, 033420 (2010) completely fails to predict the electron emission prependicularly to the polarization direction. Making use of a simple semiclassical model, we study the angle-resolved energy distribution of p…
We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the two-dimensional photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. Specifically, for the hydrogen molecule the electron energy spectrum falls off slower with increasing energy, and th…
In the semiclassical picture of photoionization process in intense laser fields, the ionization rate solely depends on the amplitude of the electric field and the final photoelectron momentum corresponds to the instant of ionization of the photoelectron, however, this picture has never been checked rigorously. Recently an attosecond angular streaking technique based on this semiclassical perspective has been widely applied to temporal measurement of the atomic and molecular dynamics in intense laser fields. We use a Wigner-distribution-like function to calculate the time-emission angle distrib…
We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single attosecond pulse (in both the streaking and sideband regimes) and ii) an attosecond pulse train. The process takes place assisted by a linearly polarized infrared (IR) laser field. In all these cases the energy and angle-resolved photoelectron spectrum (PES) is determined by a leading contribution, related to the intracycle factor [Gramajo et al., J. Phys. B 51, 055603 (2018)], complemented by other ones, d…
We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in Helium prepared in an excited $p$ state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using ab initio B-spline Algebraic Diagrammatic Construction (ADC), and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the Strong-Field Approximation and the Coulomb-Quantum Orbit Strong-Field Approximation (CQSFA), we find that these specific physical mechanisms leave signifi…
We consider the ionization of neon induced by a femtosecond laser pulse composed of overlapping, linearly polarized bichromatic extreme ultraviolet and infrared fields. In particular, we study the effects of the infrared light on a two-pathway ionization scheme for which Ne 2s22p53s1P is used as intermediate state. Using time-dependent calculations, supported by a theoretical approach based on the strong-field approximation, we analyze the ionization probability and the photoelectron angular distributions associated with the different sidebands of the ionization spectrum. Complex oscillations …
We describe an ab initio and non-perturbative $R$-matrix with time-dependence theory for ultrafast atomic processes in light fields of arbitrary polarization. The theory is applicable to complex, multielectron atoms and atomic ions subject to ultrashort (particularly few-femtosecond and attosecond) laser pulses with any given ellipticity, and generalizes previous time-dependent $R$-matrix techniques restricted to linearly polarized fields. We discuss both the fundamental equations, required to propagate the multielectron wavefunction in time, as well as the computational developments necessary…
