Photoelectron angular distributions following the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening effects of the inactive electrons can significantly affect the photoelectron distributions and can also lead to a strong elliptical dichroism. Numerical results are resented for the case of two-photon K-shell ionization of neutral Ne, Ge, Xe, and U atoms.
Chiral molecules ionized by circularly polarized fields produce a photoelectron current orthogonal to the polarization plane. This current has opposite directions for opposite enantiomers and provides an extremely sensitive probe of molecular handedness. Recently, such photoelectron currents have been measured in the strong-field ionization regime, where they may serve as an ultrafast probe of molecular chirality. Here we provide a mechanism for the emergence of such strong-field photoelectron currents in terms of two propensity rules that link the properties of the initial electronic chiral s…
Multiphoton ionization of sodium by laser pulses of 800 nm wavelength and 57 fs duration is studied in the range of laser peak intensities belonging to over-the-barrier ionization regime. Photoelectron momentum distributions (PMD) and the energy spectra are determined numerically by solving the time dependent Schrödinger equation. The calculated spectra agree well with the spectra obtained experimentally by Hart et al. [Phys. Rev. A 93, 063426 (2016)]. The contributions of photoelectrons with different values of the orbital quantum number in the PMD are determined by expanding the photoelectro…
Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level reso…
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
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.
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 report fully differential photoelectron spectra from an {\it ab-inito} coupled channels treatment of CO$_2$. Photoionization by laser pulses centered at 400 nm and 800 nm wavelength are considered, with arbitrary molecular alignment and polarization (linear and elliptic). Calculations reveal significant excited state channel contributions that are, at certain molecular orientations, an order of magnitude larger than the ground state channel in the rescattering plateau. Partial wash out of the multiphoton structure in the ATI spectra and of the nodal features in angle resolved spectra is obs…
We consider the process of atomic ionization driven by a laser pulse with varying ellipticity. We study distribution of the momenta of the photoelectrons, ionized by a strong laser field, emitted in the direction perpendicular to the polarization plane (transverse distribution). We show, that with changing laser pulse ellipticity, the transverse distribution evolves from the singular cusp-like distribution for the close to linear polarization to the smooth gaussian-like structure for the close to circular polarization. In the latter case, when the ellipticity parameter $ε\to 1$ the strong-fiel…
We show that zero ejection energy of the photoelectrons is classically impossible for hydrogen-like ions, even when field ionization occurs adiabatically. To prove this we transform the basic equations to those describing two 2D anharmonic oscillators. The same method yields an alternative way to derive the anomalous critical field of hydrogen-like ions. The analytical results are confirmed and illustrated by numerical simulations. PACS Number: 32.80.Rm
We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in one-photon Rabi-flopping regime. The time-dependent Schrödinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground $2s$ state and the excit…
We analyze the photoelectron angular distribution in two-pathway interference between non\-resonant one-photon and resonant two-photon ionization of neon. We consider a bichromatic femtosecond XUV pulse whose fundamental frequency is tuned near the $2p^5 3s$ atomic states of neon. The time-dependent Schrödinger equation is solved and the results are employed to compute the angular distribution and the associated anisotropy parameters at the main photoelectron line. We also employ a time-dependent perturbative approach, which allows obtaining information on the process for a large range of puls…
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）
Recently, in a strong Coulomb field regime of tunneling ionization an unexpected large enhancement of photoelectron spectra due to the Coulomb field of the atomic core has been identified by numerical solution of time-dependent Schrödinger equation [Phys. Rev. Lett. \textbf{117}, 243003 (2016)] in the upper energy range of the tunnel-ionized direct electrons. We investigate the origin of the enhancement employing a classical theory with Monte Carlo simulations of trajectories, and a quantum theory of Coulomb-corrected strong field approximation based on the generalized eikonal approximation fo…
We theoretically study the photoelectron angular distributions (PADs) from two-color two-photon near-threshold ionization of hydrogen and noble gas (He, Ne, and Ar) atoms by a combined action of femtosecond extreme ultraviolet (EUV) and near-infrared (IR) laser pulses. Using the second-order time-dependent perturbation theory, we clarify how the two-photon ionization process depends on EUV-IR pulse delay and how it is connected to the interplay between resonant and nonresonant ionization paths. Furthermore, by solving the time-dependent Schrödinger equation, we calculate the anisotropy paramet…
We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneli…
Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. In this letter, we report on the observation of two-center interference in the molecular frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which were measured in coincidence with e…
Photoelectron ionization spectra of a system interacting with a neighbor two-level atom are investigated using the Laplace-transform method. These spectra are typically composed of several peaks. Photoelectron ionization spectra conditioned by the measurement on the two-level atom show oscillations at the Rabi frequency. The presence of spectral zeros occurring periodically with the Rabi period is predicted. This phenomenon is analyzed in detail.
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…
The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules the photoelectron energy does not depend on the electron's emission direction but theoretical studies have questioned this since 1990. Here we provide experimental evidence, that the energies of photoelectrons emitt…
We show that the combination of two achiral components - atomic or molecular target plus a circularly polarized photon - can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon K-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti-)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral, if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In b…
Phase-shift differences and amplitude ratios of the outgoing $s$ and $d$ continuum wave packets generated by two-photon ionization of helium atoms are determined from the photoelectron angular distributions obtained using velocity map imaging. Helium atoms are ionized with ultrashort extreme-ultraviolet free-electron laser pulses with a photon energy of 20.3, 21.3, 23.0, and 24.3 eV, produced by the SPring-8 Compact SASE Source test accelerator. The measured values of the phase-shift differences are distinct from scattering phase-shift differences when the photon energy is tuned to an excited …
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…
We analyzed the two-dimensional (2D) electron momentum distributions of high-energy photoelectrons of atoms in an intense laser field using the second-order strong field approximation (SFA2). The SFA2 accounts for the rescattering of the returning electron with the target ion to first order and its validity is established by comparing with results obtained by solving the time-dependent Schrödinger equation (TDSE) for short pulses. By analyzing the SFA2 theory, we confirmed that the yield along the back rescattered ridge (BRR) in the 2D momentum spectra can be interpreted as due to the elastic …
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…
A new pathway of strong laser field induced ionization of an atom is identified which is based on recollisions under the tunneling barrier. With an amended strong field approximation, the interference of the direct and the under-the-barrier recolliding quantum orbits are shown to induce a measurable shift of the peak of the photoelectron momentum distribution. The scaling of the momentum shift is derived relating the momentum shift to the tunneling delay time according to the Wigner concept. This allows to extend the Wigner concept for the quasistatic tunneling time delay into the nonadiabatic…
We theoretically investigate the effects of laser polarization on photoelectron angular distribution through laser-induced continuum structure. We focus on a polarization geometry where the probe and dressing lasers are both linearly polarized, and change the relative polarization angle between them. We find that the total ionization yield and the branching ratio into different ionization channels change as a function of the relative polarization angle, and accordingly the photoelectron angular distribution is altered. We present specific results for the $4p_{1/2}$-$6p_{1/2}$ and $4p_{3/2}$-$6…
We analyze atomic photoelectron momentum distributions induced by bichromatic and monochromatic laser fields within the strong field approximation (SFA), separable Coulomb-Volkov approximation (SCVA), and ab initio treatment. We focus on the high frequency regime -- the smallest frequency used is larger than the ionization potential of the atom. We observe a remarkable agreement between the ab initio and velocity gauge SFA results while the velocity gauge SCVA fails to agree. Reasons of such a failure are discussed.
We use a quantum trajectory-based semi-classical method to account for Coulomb interaction between the photoelectron and the parent ion in the classically forbidden, sub-barrier region during strong-field tunneling ionization processes. We show that---besides the well-known modification of the tunneling ionization probability---there is also an influence on the interference pattern in the photoelectron spectra. In the long-wavelength limit, the shift of the intra-cycle interference fringes caused by sub-barrier Coulomb effects in the laser polarization direction can be derived analytically. We…
In this paper, a quasistatic model is extended to describe the double ionization of Helium in intense linearly polarized field, yielding achieve an insight to the two-electron correlation effect in the ionization dynamics. Our numerical calculations reproduce the excessive double ionization and the photoelectron spectra observed experimentally both quantitatively and qualitatively. Moreover, it is shown that the classical collisional trajectories are the main source of the double ionization in the knee regime and responsible for the unusual angular distribution of the photoelectrons.
Relativistic tunnel ionization of atoms by intense, elliptically polarized light is considered. The relativistic version of the Landau-Dykhne formula is employed. The general analytical expression is obtained for the relativistic photoelectron spectra. The most probable angle of electron emission, the angular distribution near this angle, the position of the maximum and the width of the energy spectrum are calculated. In the weak field limit we obtain the familiar non-relativistic results. For the case of circular polarization our analytical results are in agreement with recent derivations of …
We consider an analytic approach to the elucidation of the role played by Coulomb interaction in the formation of the spectrum and angular distributions of the electrons produced by above threshold ionization of the atoms. Our approach is based on allowance for the multiple scattering of a photoelectron by the Coulomb potential of the residual ion, with pickup of a field photon in each scattering act. The amplitude of a process with direct ionization of the atom and subsequent scattering of the photoelectron in the continuum by the Coulomb potential of the residual ion are found.
Coherent control of interfering one- and two-photon processes has for decades been the subject of research to achieve the redirection of photocurrent. The present study develops two-pathway coherent control of ground state helium atom above-threshold photoionization for energies up to the $N=2$ threshold, based on a multichannel quantum defect and R-matrix calculation. Three parameters are controlled in our treatment: the optical interference phase $ΔΦ$, the reduced electric field strength $χ=\mathcal{E}_ω^2/{\mathcal{E}_{2ω}}$, and the final state energy $ε$. A small energy change near a reso…
Above-threshold ionization (ATI) results from strong field laser-matter interaction and it is one of the fundamental processes that may be used to extract electron structural and dynamical information about the atomic or molecular target. Moreover, it can also be used to characterize the laser field itself. Here, we develop an analytical description of ATI, which extends the theoretical Strong Field Approximation (SFA), for both the direct and re-scattering transition amplitudes in atoms. From a non-local, but separable potential, the bound-free dipole and the re-scattering transition matrix e…
Time-resolving the birth of photoelectrons in strong-filed ionization with an isolated attosecond pulse
School of Physical Sciences, Great Bay University（大湾大学物理科学学院）；School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology（华中科技大学物理学院与武汉光电国家研究中心）；Research Center for Advanced Optics and Photoelectronics, Department of Physics, College of Science, Shantou University（汕头大学理学院物理系先进光学与光电子学研究中心）
Ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong-field quantum electrodynamics. Our main focus is on the formation of ionization supercontinua. More specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. These supercontinua extend over hundreds of driving photon energies, thus corresponding to high-order nonlinear processes. The corresponding polar-angle distributions show asymmetries which are at…
Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical…
Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We …
High-order above-threshold ionization (HATI) spectrum in IR+XUV two-color laser fields has been investigated. We found that the quantum features corresponding to the absorption of the XUV photon is well illustrated by a peculiar dip structure in the second plateau of the HATI spectrum. By the channel analysis, we show that the angular distribution of the spectrum is attributed to the coherent summation over contributions of different channels, and the dip structure in the spectrum is directly related to the absorption of one XUV photon of the ionized electron during the laser-assisted collisio…
During multi-photon ionization of an atom it is well understood how the involved photons transfer their energy to the ion and the photoelectron. However, the transfer of the photon linear momentum is still not fully understood. Here, we present a time-resolved measurement of linear momentum transfer along the laser pulse propagation direction. Beyond the limit of the electric dipole approximation we observe a time-dependent momentum transfer. We can show that the time-averaged photon radiation pressure picture is not generally applicable and the linear momentum transfer to the photoelectron de…
Nonlinear relativistic ionization phenomena induced by a strong linearly polarized laser field are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. This action has been used to calculate semiclassical transition rates. Simple analytical expressions for the ionization rate, the photoelectron emission velocity and for the drift momentum distribution of the photoelectron have been found. The analytical formulas apply to nonrelativistic bound systems as well as to initial states with an energ…
We measure the photoelectron energy spectra from strong-field ionization of Kr in a two-color laser pulse consisting of a strong 400-nm field and a weak 800-nm field. The intensities of the main above-threshold ionization (ATI) and sideband peaks in the photoelectron energy spectra oscillate roughly oppositely with respect to the relative phase between the two-color components. We study the photoelectron interferometry in strong-field ATI regime from the view of interference of different electron trajectories in order to extend RABBITT type analysis to the strong-field regime. Based on the str…
Photoelectron ionization spectra of an autoionization system with one discrete level interacting with a neighbor two-level atom are discussed. The formula for long-time ionization spectra is derived. According to this formula, the spectra can be composed of up to eight peaks. Moreover, the Fano-like zeros for weak optical pumping have been identified in these spectra. The conditional ionization spectra depending on the state of the neighbor atom exhibit oscillations at the Rabi frequency. Dynamical spectral zeros occurring once per the Rabi period have been revealed in these spectra.
Multiphoton ionization of sodium by femtosecond laser pulses of 800 nm wavelength in the range of laser peak intensities entering over-the-barrier ionization domain is studied. Photoelectron momentum distributions and the energy spectra are determined numerically by solving the time dependent Schroedinger equation for three values of the laser intensity from this domain. The calculated spectra agree well with the spectra obtained experimentally by Hart et al (Phys. Rev. A 2016 93 063426). A partial wave analysis of the spectral peaks related to Freeman resonances has shown that each peak is a …
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…
We investigate the carrier-envelope phase and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above-threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750\,nm is varied in a range between $0.7 \times 10^{14}$ and $\unit[5.5 \times 10^{14}]{W/cm^2}$. Our measurements reveal a prominent maximum in the carrier-envelope phase-dependent asymmetry at photoelectron energies of 2\,$U_\mathrm{P}$ ($U_\mathrm{P}$ being the ponderomotive potential), that is persistent over the entire intensity ra…
Using a semiclassical model which incorporates tunneling and Coulomb field effects, the origin of the unexpected low-energy structure (LES) in above-threshold ionization spectrum observed in recent experiments [C. I. Blaga et al., Nature Phys. {\bf 5}, 335 (2009) and W. Quanet al., Phys. Rev. Lett. {\bf 103}, 093001 (2009)] is identified. We show that the LES arises due to an interplay between multiple forward scattering of an ionized electron and the electron momentum disturbance by the Coulomb field immediately after the ionization. The multiple forward scattering is mainly responsible for t…
We report measurements on the H$^{+}$ + H$^{+}$ fragmentation channel following direct single-photon double ionization of neutral NH$_{3}$ at 61.5 eV, where the two photoelectrons and two protons are measured in coincidence using 3-D momentum imaging. We identify four dication electronic states that contribute to H$^{+}$ + H$^{+}$ dissociation, based on our multireference configuration-interaction calculations of the dication potential energy surfaces. The extracted branching ratios between these four dication electronic states are presented. Of the four dication electronic states, three disso…
Photoelectron circular dichroism (PECD) is a fascinating phenomenon both from a fundamental science aspect but also due to its emerging role as a highly sensitive analytic tool for chiral recognition in the gas phase. PECD has been studied with single-photon as well as multi-photon ionization. The latter has been investigated in the short pulse limit with femtosecond laser pulses, where ionization can be thought of as an instantaneous process. In this contribution, we demonstrate that multiphoton PECD still can be observed when using an ultra-violet nanosecond pulse to ionize chiral showcase f…
The combination of photoelectron spectroscopy and ultrafast light sources is on track to set new standards for detailed interrogation of dynamics and reactivity of molecules. A crucial prerequisite for further progress is the ability to not only detect the electron kinetic energy, as done in traditional photoelectron spectroscopy, but also the photoelectron angular distributions (PADs) in the molecular frame. Here carbonylsulfide (OCS) and benzonitrile molecules, fixed in space by combined laser and electrostatic fields, are ionized with intense, circularly polarized, 30 femtosecond laser puls…
