Electron vortices in photoionization by circularly polarized attosecond pulses

High-order above-threshold ionisation of diatomic molecules by few-cycle bicircular and orthogonally polarised two-colour pulses

Improved molecular strong-field approximation theory is used to calculate the ionisation probability for the high-order above-threshold ionisation process induced by a few-cycle pulse with two carrier frequencies and one envelope. The asymmetry in the photoelectron momentum distribution is due to the ultrashort nature of the driving pulse and due to the relative orientation of the molecule with respect to the laser field. We introduce the generalised asymmetry parameter, which can be used to quantitatively measure the asymmetry between the photoelectron spectra along arbitrarily many selected directions. We investigate the difference between the asymmetry parameters calculated for atomic and molecular targets and show that the contributions to the asymmetry strongly depend on the type of the employed driving pulse. For the driving pulse with components that are linearly polarised with mutually orthogonal polarisations, we find that the main source of the asymmetry, especially in the high-energy part of the spectrum, is the ultrashort nature of the pulse. The relative orientation of the molecule with respect to the laser pulse only affects the low- and medium-energy parts of the spectrum. On the other hand, for the driving pulse with circularly polarised counterrotating components, the asymmetry introduced by molecular orientation is more pronounced. We also analyse the influence of the characteristics of molecular orbitals on the asymmetries using the examples of N2 and O2 molecules.

Separation of photoionization and measurement-induced delays

Photoionization of matter is one of the fastest electronic processes in nature. Experimental measurements of photoionization dynamics have become possible through attosecond metrology. However, all experiments reported to date contain a so-far unavoidable measurement-induced contribution, known as continuum-continuum (CC) or Coulomb-laser-coupling delay. In traditional attosecond metrology, this contribution is nonadditive for most systems and nontrivial to calculate. Here, we introduce the concept of mirror symmetry-broken attosecond interferometry, which enables the direct and separate measurement of both the native one-photon ionization delays and the CC delays. Our technique solves the longstanding challenge of experimentally isolating these two contributions. This advance opens the door to the next generation of accurate measurements and precision tests that will set standards for benchmarking the accuracy of electronic structure and electron-dynamics methods.

Tunable Tesla-Scale Magnetic Attosecond Pulses through Ring-Current Gating

Coherent control over electron dynamics in atoms and molecules using high-intensity circularly polarized laser pulses gives rise to current loops, resulting in the emission of magnetic fields. We propose, and demonstrate with ab initio calculations, "current-gating" schemes to generate direct or alternating-current magnetic pulses in the infrared spectral region, with highly tunable waveform and frequency, and showing femtosecond-to-attosecond pulse duration. In optimal conditions, the magnetic pulse can be highly isolated from the driving laser and exhibits a high flux density (∼1 T at a few hundred nanometers from the source, with a pulse duration of 787 attoseconds) for application in forefront experiments of ultrafast spectroscopy. Our work paves the way toward the generation of attosecond magnetic fields to probe ultrafast magnetization, chiral responses, and spin dynamics.

Femtosecond Polarization Shaping of Free-Electron Laser Pulses

We demonstrate the generation of extreme-ultraviolet (XUV) free-electron laser (FEL) pulses with time-dependent polarization. To achieve polarization modulation on a femtosecond timescale, we combine two mutually delayed counterrotating circularly polarized subpulses from two cross-polarized undulators. The polarization profile of the pulses is probed by angle-resolved photoemission and above-threshold ionization of helium; the results agree with solutions of the time-dependent Schrödinger equation. The stability limit of the scheme is mainly set by electron-beam energy fluctuations, however, at a level that will not compromise experiments in the XUV. Our results demonstrate the potential to improve the resolution and element selectivity of methods based on polarization shaping and may lead to the development of new coherent control schemes for probing and manipulating core electrons in matter.

Carrier-envelope-phase and helicity control of electron vortices and spirals in photodetachment

Formation of electron vortices and spirals in photodetachment from the H^- anion driven by isolated ultrashort laser pulses of circular polarization or by pairs of such pulses (of either co-rotating or counter-rotating polarizations) are analyzed under the scope of the strong-field approximation. It is demonstrated that the carrier-envelope phase (CEP) and helicity of each individual pulse can be used to actively manipulate and control the vortical and spiral patterns in the probability amplitude of photodetachment. Specifically, we show that the vortical patterns can be rotated in momentum space by the CEP of the driving pulse (or, of two identical pulses); thus, offering a tool of pulse characterization. For co-rotating pulses of arbitrary CEPs, a novel type of structured vortices is discovered. Also, we demonstrate that the momentum spirals are formed when photodetachment is driven by two pulses of time-reversal symmetry, which is accompanied by absolute disappearance of vortical structures. Hence, we attribute the spiral formation to annihilation of vortices with antivortices, which are generated by time-reversed pulses comprising the train. Finally, the CEP and helicity control of spiral structures is demonstrated, leading to their rotation in momentum space.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

Controlling the atomic-orbital-resolved photoionization for neon atoms by counter-rotating circularly polarized attosecond pulses

We theoretically investigate the atomic-orbital-resolved vortex-shaped photoelectron momentum distributions (PMDs) and ionization probabilities by solving the two-dimensional time-dependent Schrödinger equation (2D-TDSE) of neon in a pair of delayed counter-rotating circularly polarized attosecond pulses. We found that the number of spiral arms in vortex patterns is twice the number of absorbed photons when the initial state is the ψ_m=±1 state, which satisfy a change from c_2n+2 to c_2n (n is the number of absorbed photons) rotational symmetry of the vortices if the 2p state is replaced by 2p₊ or 2p_- states. For two- and three-photon ionization, the magnetic quantum number dependence of ionization probabilities is quite weak. Interestingly, single-photon ionization is preferred when the electron and laser field corotate and ionization probabilities of 2p_- is much larger than that of 2p₊ if the proper time delay and wavelength are used. The relative ratio of ionization probabilities between 2p_- and 2p₊ is insensitive to laser peak intensity, which can be controlled by changing the wavelength, time delay, relative phase and amplitude ratio of two attosecond pulses.

Signature of Molecular Orbital Symmetry in High-Order Harmonic Generation by Bichromatic Circularly Polarized Laser Pulses

Molecular orbital symmetry is shown to be an important factor in determining orders and helicities (polarizations) of high-order harmonic generation (HHG) by intense femtosecond counter-rotating bichromatic circularly polarized laser pulses. Numerical solutions of time-dependent Schrödinger equations (TDSE) for the one-electron molecular ions H₂⁺ and H₃²⁺ for different initial electronic states show that harmonic orders and helicities are dependent on orbital symmetries and of the net incident pulse electric field. The numerical results and properties of the harmonics are described by dynamical symmetry theory and time profile analysis of the high-order harmonics, thus confirming that orbital and laser pulse symmetry dependence are generic in HHG of molecules.

Conservation laws for electron vortices in strong-field ionisation

ABSTRACT

We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation.

Multi-photon above threshold ionization of multi-electron atoms and molecules using the R-matrix approach

We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to calculate the infinite-range free-free dipole integrals analytically in the outer region, beyond the range of the initial bound wave function. This approach is valid for an arbitrary order, that is, any number of photons absorbed both in the bound and the continuum part of the spectrum (below- and above-threshold ionization). We calculate generalized multi-photon cross sections and angular distributions of different systems (H, He, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}_{{2}}$$\end{document}H2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_{{2}}$$\end{document}CO2) and validate our approach by comparison with data from the literature.

Manipulating twisted electrons in strong-field ionization

We investigate the discrete orbital angular momentum (OAM) of photoelectrons freed in strong-field ionization. We use these 'twisted' electrons to provide an alternative interpretation on existing experimental work of vortex interferences caused by strong field ionization mediated by two counter-rotating circularly polarized pulses separated by a delay. Using the strong field approximation, we derive an interference condition for the vortices. In computations for a neon target we find very good agreement of the vortex condition with photoelectron momentum distributions computed with the strong field approximation, as well as with the time-dependent methods Qprop and R-Matrix. For each of these approaches we examine the OAM of the photoelectrons, finding a small number of vortex states localized in separate energy regions. We demonstrate that the vortices arise from the interference of pairs of twisted electron states. The OAM of each twisted electron state can be directly related to the number of arms of the spiral in that region. We gain further understanding by recreating the vortices with pairs of twisted electrons and use this to determine a semiclassical relation for the OAM. A discussion is included on measuring the OAM in strong field ionization directly or by employing specific laser pulse schemes as well as utilizing the OAM in time-resolved imaging of photo-induced dynamics.

Investigation of electron vortices in time-delayed circularly polarized laser pulses with a semiclassical perspective

We theoretically investigate strong-filed electron vortices in time-delayed circularly polarized laser pulses by a generalized quantum-trajectory Monte Carlo (GQTMC) model. Vortex interference patterns in photoelectron momentum distributions (PMDs) with various laser parameters can be well reproduced by the semiclassical simulation. The phase difference responsible for the interference structures is analytically identified through trajectory-based analysis and simple-man theory, which reveal the underlying mechanism of electron vortex phenomena for both co-rotating and counter-rotating component. This semiclassical analysis can also demonstrate the influences of laser intensity and wavelength on the number of arms of vortices. Furthermore, we show the influence of the Coulomb effect on the PMDs. Finally, the controlling of the ionization time intervals in the tens to hundreds of attosecond magnitude is qualitatively discussed.

Proposal for detecting ring current via electron vortices

In an intense circularly polarized laser field, the excitation of the atoms shows a strong dependence on the orbital helicity. The resonant excitation starting from the ground state with $ m = - 1 $m=-1 occurs much more easily in the left-handed circularly polarized (LCP with $ m = + 1 $m=+1) pulse than in the right-handed circularly polarized (RCP with $ m = - 1 $m=-1) pulse. In this Letter, we numerically demonstrate that the orbital-helicity-dependent two-photon-resonant excitation leads to the photoelectron vortex pattern in the polarization plane being sensitive to the sequence of the two counter-rotating circularly polarized pulses in xenon, which enables the detection of the ring currents associated with different quantum states. These results also provide an effective way for controlling the rotational symmetry of the electron vortex.

Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.

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.

Odd electron wave packets from cycloidal ultrashort laser fields

Polarization-tailored bichromatic femtosecond laser fields with cycloidal polarization profiles have emerged as a powerful tool for coherent control of quantum processes. We present an optical scheme to create and manipulate three-dimensional free electron wave packets with arbitrary rotational symmetry by combining advanced supercontinuum pulse shaping with high resolution photoelectron tomography. Here we use carrier-envelope phase-stable polarization-tailored bichromatic (3ω:4ω) counter- and corotating femtosecond laser pulses to generate 7-fold rotational symmetric and asymmetric photoelectron momentum distributions by multiphoton ionization of sodium atoms. To elucidate the physical mechanisms, we investigate the interplay between the symmetry properties of the driving field and the resulting electron wave packets by varying the optical field parameters. Our results show that the symmetry properties of electron wave packets are not fully determined by the field symmetry, but completely described by multipath quantum interference of states with different angular momenta.

Laser fields can be tuned to probe electronic motion in atoms and molecules. Here the authors ionize Na atoms using bichromatic pulses to generate electron wave packets of crescent-shaped and 7-fold rotational symmetry which do not follow the field symmetry but are determined by multiphoton interference.

Proposal for Measuring Electron Displacement Induced by a Short Laser Pulse

In laser-matter interaction, most previous studies have focused on the change of the electron momentum induced by the external fields. Here, we theoretically investigate the electron displacement induced by an ultrashort pulse, whose precise waveform is hard to determine experimentally. We propose and numerically demonstrate a scheme to accurately measure the electron displacement using a ruler formed by the interfering spirals in the photoelectron momentum distribution generated by two oppositely circularly polarized pulses. The scheme is robust against the focusing volume effects and the jitter of the carrier envelope phase of the two circular pulses. The ability to measure the electron displacement by an arbitrary pulse may pave the way to quantitative control of the charge migration in matter on the scale of Ångström.

Attosecond Control of Restoration of Electronic Structure Symmetry

Laser pulses can break the electronic structure symmetry of atoms and molecules by preparing a superposition of states with different irreducible representations. Here, we discover the reverse process, symmetry restoration, by means of two circularly polarized laser pulses. The laser pulse for symmetry restoration is designed as a copy of the pulse for symmetry breaking. Symmetry restoration is achieved if the time delay is chosen such that the superposed states have the same phases at the temporal center. This condition must be satisfied with a precision of a few attoseconds. Numerical simulations are presented for the C_{6}H_{6} molecule and ^{87}Rb atom. The experimental feasibility of symmetry restoration is demonstrated by means of high-contrast time-dependent Ramsey interferometry of the ^{87}Rb atom.

Quantum simulation of ultrafast dynamics using trapped ultracold atoms

Ultrafast electronic dynamics are typically studied using pulsed lasers. Here we demonstrate a complementary experimental approach: quantum simulation of ultrafast dynamics using trapped ultracold atoms. Counter-intuitively, this technique emulates some of the fastest processes in atomic physics with some of the slowest, leading to a temporal magnification factor of up to 12 orders of magnitude. In these experiments, time-varying forces on neutral atoms in the ground state of a tunable optical trap emulate the electric fields of a pulsed laser acting on bound charged particles. We demonstrate the correspondence with ultrafast science by a sequence of experiments: nonlinear spectroscopy of a many-body bound state, control of the excitation spectrum by potential shaping, observation of sub-cycle unbinding dynamics during strong few-cycle pulses, and direct measurement of carrier-envelope phase dependence of the response to an ultrafast-equivalent pulse. These results establish cold-atom quantum simulation as a complementary tool for studying ultrafast dynamics.

Helicity asymmetry in strong-field ionization of atoms by a bicircular laser field

Ionization of atoms by an intense bicircular laser field is considered, which consists of two coplanar corotating or counterrotating circularly polarized field components with frequencies that are integer multiples of a fundamental frequency. Emphasis is on the effect of a reversal of the helicities of the two field components on the photoelectron spectra. The velocity maps of the liberated electrons are calculated using the direct strong-field approximation (SFA) and its improved version (ISFA), which takes into account rescattering off the parent ion. Under the SFA all symmetries of the driving field are preserved in the velocity map while the ISFA violates certain reflection symmetries. This allows one to assess the significance of rescattering in actual data obtained from an experiment or a numerical simulation.

Dynamic Stark induced vortex momentum of hydrogen in circular fields

In this paper, we report our numerical simulation on the symmetry distortion and mechanism of the vortex-shaped momentum distribution of hydrogen atom by taking into account of the dynamic Stark effect. By deploying the strong field approximation (SFA) theory, we performed extensive simulation on the momentum pattern of hydrogen ionized by two time-delayed oppositely circularly polarized attosecond pulses. We deciphered that this distortion is originated from the temporal characteristics of the dynamic Stark phase which is nonlinear in time.

Electron Vortices in Femtosecond Multiphoton Ionization

Multiphoton ionization of potassium atoms with a sequence of two counter-rotating circularly polarized femtosecond laser pulses produces vortex-shaped photoelectron momentum distributions in the polarization plane describing Archimedean spirals. The pulse sequences are produced by polarization shaping and the three-dimensional photoelectron distributions are tomographically reconstructed from velocity map imaging measurements. We show that perturbative ionization leads to electron vortices with c_{6} rotational symmetry. A change from c_{6} to c_{4} rotational symmetry of the vortices is demonstrated for nonperturbative interaction.

Attospiral generation upon interaction of circularly polarized intense laser pulses with conelike targets

The generation of high-intensity attopulses has been investigated in cylindrical geometry by using a three-dimensional particle-in-cell plasma simulation code. Due to the rotation-symmetric target, a circularly polarized laser pulse is considered, propagating on the axis of a hollow conelike target. The large incidence angle and constant ponderomotive pressure lead to nanobunching of relativistic electrons responsible for the laser-driven synchrotron emission. A numerical method is developed to find the source and direction of the coherent radiation that ensures the existence of attopulses. The intensity modulation in the harmonic spectrum is well described by the model of coherent synchrotron emission extended to the regime of higher order γ spikes. The spatial distribution of the higher harmonics resembles a spiral shape which gets focused into a small volume behind the target.