Large-angle electron diffraction structure in laser-induced rescattering from rare gases

Extraction of Molecular-Frame Electron-Ion Differential Scattering Cross Sections Based on Elliptical Laser-Induced Electron Diffraction

We extracted the molecular-frame elastic differential cross sections (MFDCSs) for electrons scattering from N_{2}^{+} based on elliptical laser-induced electron diffraction (ELIED), wherein the structural evolution is initialized by the same tunneling ionization and probed by incident angle-resolved laser-induced electron diffraction imaging. To establish ELIED, an intuitive interpretation of the ellipticity-dependent rescattering electron momentum distributions was first provided by analyzing the transverse momentum distribution. It was shown that the incident angle of the laser-induced returning electrons could be tuned within 20° by varying the ellipticity and handedness of the driving laser pulses. Accordingly, the incident angle-resolved DCSs of returning electrons for spherically symmetric targets (Xe^{+} and Ar^{+}) were successfully extracted as a proof-of-principle for ELIED. The MFDCSs for N_{2}^{+} were experimentally obtained at incident angles of 4° and 7°, which were well reproduced by the simulations. The ELIED approach is the only successful method so far for obtaining incident angle-resolved ionic MFDCS, which provides a new sensitive observable for the transient structure retrieval of N_{2}^{+}. Our results suggest that the ELIED has the potential to extract the structural tomographic information of polyatomic molecules with femtosecond and subangstrom spatiotemporal resolutions that can enable the visualization of the nuclear motions in complex chemical reactions as well as chiral recognition.

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

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

Magnetic-Field Effect in High-Order Above-Threshold Ionization

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Imaging of electron transition and bond breaking in the photodissociation of H2+ via ultrafast X-ray photoelectron diffraction

We theoretically investigate the photodissociation dynamics of H2+ using the methodology of ultrafast X-ray photoelectron diffraction (UXPD). We use a femtosecond infrared pulse to prompt a coherent excitation from the molecular vibrational state (v = 9) of the electronic ground state (1sσ_g) and then adopt another time-delayed attosecond X-ray pulse to probe the dynamical properties. We have calculated photoionization momentum distributions by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). We unambiguously identify the phenomena associated with the g - u symmetry breakdown in the time-resolved photoelectron diffraction spectra. Using the two-center interference model, we can determine the variation in nuclear spacing with high accuracy. In addition, we use a strong field approximation (SFA) model to interpret the UXPD profile, and the SFA simulations can reproduce the TDSE results in a quantitative way.

Diffractive Imaging of C_{60} Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100 fs (1  fs=10^{-15}  s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6  μm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

Laser-Induced Inelastic Diffraction from Strong-Field Double Ionization

In this Letter, we propose a novel laser-induced inelastic diffraction (LIID) scheme based on the intense-field-driven atomic nonsequential double ionization (NSDI) process and demonstrate that, with this LIID approach, the doubly differential cross sections (DDCSs) of the target ions, e.g., Ar^{+} and Xe^{+}, can be accurately extracted from the two-dimensional photoelectron momentum distributions in the NSDI process of the corresponding atoms. The extracted DDCSs exhibit a strong dependence on both the target and the laser intensity, in good agreement with calculated DDCSs from the scattering of free electrons. The LIID scheme may be extended to molecular systems and provides a promising approach for imaging of the gas-phase molecular dynamics induced by a strong laser field with unprecedented spatial and temporal resolution.

Disentangling Intracycle Interferences in Photoelectron Momentum Distributions Using Orthogonal Two-Color Laser Fields

We use orthogonally polarized two-color (OTC) laser pulses to separate quantum paths in the multiphoton ionization of Ar atoms. Our OTC pulses consist of 400 and 800 nm light at a relative intensity ratio of 10∶1. We find a hitherto unobserved interference in the photoelectron momentum distribution, which exhibits a strong dependence on the relative phase of the OTC pulse. Analysis of model calculations reveals that the interference is caused by quantum pathways from nonadjacent quarter cycles.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Capturing ultrafast molecular dynamics is difficult as the process involves coupled and very fast motions of electrons and nuclei. Here the authors study non-adiabatic dynamics in the NO molecule using strong-field photoelectron holography to shed light on the valence-shell electron dynamics.

Extracting conformational structure information of benzene molecules via laser-induced electron diffraction

We have measured the angular distributions of high energy photoelectrons of benzene molecules generated by intense infrared femtosecond laser pulses. These electrons arise from the elastic collisions between the benzene ions with the previously tunnel-ionized electrons that have been driven back by the laser field. Theory shows that laser-free elastic differential cross sections (DCSs) can be extracted from these photoelectrons, and the DCS can be used to retrieve the bond lengths of gas-phase molecules similar to the conventional electron diffraction method. From our experimental results, we have obtained the C-C and C-H bond lengths of benzene with a spatial resolution of about 10 pm. Our results demonstrate that laser induced electron diffraction (LIED) experiments can be carried out with the present-day ultrafast intense lasers already. Looking ahead, with aligned or oriented molecules, more complete spatial information of the molecule can be obtained from LIED, and applying LIED to probe photo-excited molecules, a "molecular movie" of the dynamic system may be created with sub-Ångström spatial and few-ten femtosecond temporal resolutions.

Near-Forward Rescattering Photoelectron Holography in Strong-Field Ionization: Extraction of the Phase of the Scattering Amplitude

We revisit the concept of near-forward rescattering strong-field photoelectron holography introduced by Y. Huismans et al. [Science 331, 61 (2011)]. The recently developed adiabatic theory is used to show how the phase of the scattering amplitude for near-forward rescattering of an ionized electron by the parent ion is encoded in and can be read out from the corresponding interference pattern in photoelectron momentum distributions (PEMDs) produced in the ionization of atoms and molecules by intense laser pulses. A procedure to extract the phase is proposed. Its application to PEMDs obtained by solving the time-dependent Schrödinger equation for a model atom yields results in good agreement with scattering calculations. This establishes a novel general approach to extracting structural information from strong-field observables capable of providing time-resolved imaging of ultrafast processes.

Imaging an aligned polyatomic molecule with laser-induced electron diffraction

Laser-induced electron diffraction is an evolving tabletop method that aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-Ångström spatial and femtosecond temporal resolutions. Here we demonstrate the retrieval of multiple bond lengths from a polyatomic molecule by simultaneously measuring the C–C and C–H bond lengths in aligned acetylene. Our approach takes the method beyond the hitherto achieved imaging of simple diatomic molecules and is based on the combination of a 160 kHz mid-infrared few-cycle laser source with full three-dimensional electron–ion coincidence detection. Our technique provides an accessible and robust route towards imaging ultrafast processes in complex gas-phase molecules with atto- to femto-second temporal resolution.

Laser-induced electron diffraction can provide structural information on gas-phase molecules with high spatial and temporal resolution. Going beyond previous diatomic cases, Pullen et al. apply this approach to acetylene and show that it can be used to measure bond lengths for polyatomic molecules.

Observation of laser-induced electronic structure in oriented polyatomic molecules

All attosecond time-resolved measurements have so far relied on the use of intense near-infrared laser pulses. In particular, attosecond streaking, laser-induced electron diffraction and high-harmonic generation all make use of non-perturbative light-matter interactions. Remarkably, the effect of the strong laser field on the studied sample has often been neglected in previous studies. Here we use high-harmonic spectroscopy to measure laser-induced modifications of the electronic structure of molecules. We study high-harmonic spectra of spatially oriented CH3F and CH3Br as generic examples of polar polyatomic molecules. We accurately measure intensity ratios of even and odd-harmonic orders, and of the emission from aligned and unaligned molecules. We show that these robust observables reveal a substantial modification of the molecular electronic structure by the external laser field. Our insights offer new challenges and opportunities for a range of emerging strong-field attosecond spectroscopies.

Laser-induced electron diffraction for probing rare gas atoms

Recently, using midinfrared laser-induced electron diffraction (LIED), snapshots of a vibrating diatomic molecule on a femtosecond time scale have been captured [C.I. Blaga et al., Nature (London) 483, 194 (2012)]. In this Letter, a comprehensive treatment for the atomic LIED response is reported, a critical step in generalizing this imaging method. Electron-ion differential cross sections (DCSs) of rare gas atoms are extracted from measured angular-resolved, high-energy electron momentum distributions generated by intense midinfrared lasers. Following strong-field ionization, the high-energy electrons result from elastic rescattering of a field-driven wave packet with the parent ion. For recollision energies ≥100 eV, the measured DCSs are indistinguishable for the neutral atoms and ions, illustrating the close collision nature of this interaction. The extracted DCSs are found to be independent of laser parameters, in agreement with theory. This study establishes the key ingredients for applying LIED to femtosecond molecular imaging.

Validity of factorization of the high-energy photoelectron yield in above-threshold ionization of an atom by a short laser pulse

An analytic description for the yield, P(p), of high-energy electrons ionized from an atom by a short (few-cycle) laser pulse is obtained quantum mechanically. Factorization of P(p) in terms of an electron wave packet and the cross section for elastic electron scattering (EES) is shown to occur only for an ultrashort pulse, while in general P(p) involves interference of EES amplitudes with laser-field-dependent momenta. The analytic predictions agree well with accurate numerical results.

Strong field electron emission from fixed in space H(2)(+) ions

We have studied electron emission from the H(2)(+) ion by a circularly polarized laser pulse (800 nm, 6×10(14)  W/cm(2)). The electron momentum distribution in the body fixed frame of the molecule is experimentally obtained by a coincident detection of electrons and protons. The data are compared to a solution of the time-dependent Schrödinger equation in two dimensions. We find radial and angular distributions which are at odds with the quasistatic enhanced ionization model. The unexpected momentum distribution is traced back to a complex laser-driven electron dynamics inside the molecule influencing the instant of ionization and the initial momentum of the electron.

Extracting electron-ion differential scattering cross sections for partially aligned molecules by laser-induced rescattering photoelectron spectroscopy

We extract large-angle elastic differential cross sections (DCSs) for electrons scattering from partially aligned O2+ and CO2+ molecules using rescattering photoelectrons generated by infrared laser pulses. The extracted DCSs are in good agreement with those calculated theoretically, demonstrating that accurate DCSs for electron-ion scattering can be extracted from the laser-induced rescattering spectra, thus paving the way for dynamic imaging of chemical reactions by rescattering photoelectron spectroscopy.

Structure effects in angle-resolved high-order above-threshold ionization of molecules

We present energy-resolved angular distributions of photoelectrons generated in above-threshold ionization (ATI) of nonaligned diatomic molecules N2 and O2 in high-intensity short laser pulses, with emphasis on the most energetic part of the spectra. The angular distribution for photoelectrons with energy of 10U(p) (U(p): ponderomotive energy), i.e., the plateau cutoff in ATI spectra, is found to be broader in O2 than in N2. Resorting to the analyses from both an S-matrix theory and an intuitive semiclassical model, we attribute the observation to the effect of the ground state molecular orbital structure on high-energy electron emission in strong-field molecular ionization.

Electron rescattering in above-threshold photodetachment of negative ions

We present experimental and theoretical results on photodetachment of Br(-) and F(-) in a strong infrared laser field. The observed photoelectron spectra of Br(-) exhibit a high-energy plateau along the laser polarization direction, which is identified as being due to the rescattering effect. The shape and the extension of the plateau is found to be influenced by the depletion of negative ions during the interaction with the laser pulse. Our findings represent the first observation of electron rescattering in above-threshold photodetachment of an atomic system with a short-range potential.

Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms

When an electron from a diatomic molecule undergoes tunneling-rescattering ionization, a novel form of destructive interference can be realized that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for O_{2} but not for N_{2}. This effect is different from the suppression of ionization that is well known to occur for O_{2}.

Attosecond quantum stroboscope

Electron disco: A "quantum stroboscope" for capturing the electron motion on a subfemtosecond timescale for a particular class of problems is highlighted. The picture shows a diffraction pattern caused by wave packets obtained by synchronizing attosecond UV pulses to a near-IR field and ionizing rare-gas atoms.

Observation of electronic structure minima in high-harmonic generation

We report detailed measurements of the high-harmonic spectra generated from argon atoms. The spectra exhibit a deep minimum that is shown to be independent of the laser intensity, and is thus a clear measure of the electronic structure of the atom. We show that exact field-free continuum wave functions reproduce the minimum, but plane wave and Coulomb wave functions do not. This remarkable observation suggests that electronic structure can be accurately determined in high-harmonic experiments despite the presence of the strong laser field. Our results clarify the relation between high-harmonic generation and photoelectron spectroscopy. The use of exact continuum functions also resolves the ambiguity associated with the choice of the dispersion relation.

Accurate retrieval of target structures and laser parameters of few-cycle pulses from photoelectron momentum spectra

We illustrate a new method of analyzing three-dimensional momentum images of high-energy photoelectrons generated by intense phase-stabilized few-cycle laser pulses. Using photoelectron momentum spectra that were obtained by velocity-map imaging of above-threshold ionization of xenon and argon targets, we show that the absolute carrier-envelope phase, the laser peak intensity, and pulse duration can be accurately determined simultaneously (with an error of a few percent). We also show that the target structure, in the form of electron-target ion elastic differential cross sections, can be retrieved over a range of energies. The latter offers the promise of using laser-generated electron spectra for probing dynamic changes in molecular targets with subfemtosecond resolution.