Three-dimensional momentum imaging of electron wave packet interference in few-cycle laser pulses

Identifying photoelectron releasing order in strong-field dissociative ionization of H2

Driven by intense laser fields, the outgoing photoelectrons in molecules possess a quiver motion, resulting in the rise of the effective ionization potential. The coupling of the field-dressed ionization potential with abundant molecular dynamics complicates the laser-molecule interactions. Here, we demonstrate an approach to resolve photoelectron releasing order in the dissociative and non-dissociative channels of multiphoton ionization driven by an orthogonally polarized two-color femtosecond laser pulse. The photoelectron kinetic energy releases and the regular nodes in the photoelectron angular distributions due to the participation of different continuum partial waves allow us to deduce the field-dressed ionization potential of various channels. It returns the ponderomotive energy experienced by the outgoing electron and reveals the corresponding photoionization instants within the laser pulse. Our results provide a route to explore the complex strong-field ionization dynamics of molecules using two-dimensional photoelectron momentum spectroscopy.

Photoelectron interference of He atoms in the attosecond ionization gating

We theoretically investigate the photoelectron momentum distribution of He atoms by numerically solving the time-dependent Schro¨dinger equation (TDSE) in few-cycle ionization gating, which is synthesized by two linearly polarized laser pulses. When applying the TDSE, we can clearly see the spider-like structures in the photoelectron momentum spectra. We also find that the spider-like structures can be isolated by changing the relative phase. The directionality of the spider-like structure is changed from right-side to left-side and the ring-like interference structure gradually appears in the photoelectron momentum spectra when increasing the relative phase. The interference patterns observed in TDSE are recaptured well by the quantum-trajectory Monte Carlo (QTMC) model. We separate the ionization time window of the tunneling electron by analyzing the ionization rate. With the help of QTMC simulation, we illustrate the change of the interference structure and its directionality in the photoelectron momentum spectra. By changing the relative phase, the forward-backward asymmetry of the momentum distribution of the emitted electrons can also be controlled. Moreover, we find that the relative contribution of the nonrescattering and the rescattering trajectories can be controlled. These properties are beneficial for the application of photoelecron holography in probing atomic and molecular structures and dynamics.

Gouy's Phase Anomaly in Electron Waves Produced by Strong-Field Ionization

Ionization of atoms by strong laser fields produces 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 shifts occurring when trajectories pass through focal points. Such phase shifts are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a focal point as it crosses the symmetry axis in momentum space. In addition, there exist observable Maslov phases already in two dimensions. Clustering algorithms enable us to implement a semiclassical model with the correct preexponential factor that affects both the weight and the phase of each trajectory. We also derive a simple rule to relate two-dimensional and three-dimensional models for linear polarization. It explains the shifted interference fringes and weaker high-energy yield in three dimensions. The results are in excellent agreement with solutions of the time-dependent Schrödinger equation.

It is all about phases: ultrafast holographic photoelectron imaging

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 to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.

Ultrafast Field-Emission Electron Sources Based on Nanomaterials

The search for electron sources with simultaneous optimal spatial and temporal resolution has become an area of intense activity for a wide variety of applications in the emerging fields of lightwave electronics and attosecond science. Most recently, increasing efforts are focused on the investigation of ultrafast field-emission phenomena of nanomaterials, which not only are fascinating from a fundamental scientific point of view, but also are of interest for a range of potential applications. Here, the current state-of-the-art in ultrafast field-emission, particularly sub-optical-cycle field emission, based on various nanostructures (e.g., metallic nanotips, carbon nanotubes) is reviewed. A number of promising nanomaterials and possible future research directions are also established.

Photoelectron momentum distributions of F- ions by a few-cycle laser pulse

The two-dimensional photoelectron momentum distributions (PMD) of F^- ions induced by a linearly polarized few-cycle laser pulse are analyzed with the saddle-point (SP) method. The validity of the SP method is confirmed by comparing the PMD with those obtained from direct numerical integration of the transition probability amplitude in the context of strong-field approximation (SFA). We analyze the intra- and inter-cycle interference patterns in the two-dimensional PMD and show that the two-dimensional PMD can be effectively monitored by changing the carrier-envelope phase of few-cycle laser pulse. In addition, by separately calculating the two-dimensional PMD formed in the different detachment steps, we find that the rich oscillatory patterns in the two-dimensional PMD can be mainly attributed to the interference effects of electronic wave packets in the classical propagation step after the ionization, and part of intra-cycle interference fringes' shape is affected by the sub-barrier phase.

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.

Energy-Resolved Ultrashort Delays of Photoelectron Emission Clocked by Orthogonal Two-Color Laser Fields

A phase-controlled orthogonal two-color (OTC) femtosecond laser pulse is employed to probe the time delay of photoelectron emission in the strong-field ionization of atoms. The OTC field spatiotemporally steers the emission dynamics of the photoelectrons and meanwhile allows us to unambiguously distinguish the main and sideband peaks of the above-threshold ionization spectrum. The relative phase shift between the main and sideband peaks, retrieved from the phase-of-phase of the photoelectron spectrum as a function of the laser phase, gradually decreases with increasing electron energy, and becomes zero for the fast electron which is mainly produced by the rescattering process. Furthermore, a Freeman resonance delay of 140±40 attoseconds between photoelectrons emitted via the 4f and 5p Rydberg states of argon is observed.

Efficient time-sampling method in Coulomb-corrected strong-field approximation

One of the main goals of strong-field physics is to understand the complex structures formed in the momentum plane of the photoelectron. For this purpose, different semiclassical methods have been developed to seek an intuitive picture of the underlying mechanism. The most popular ones are the quantum trajectory Monte Carlo (QTMC) method and the Coulomb-corrected strong-field approximation (CCSFA), both of which take the classical action into consideration and can describe the interference effect. The CCSFA is more widely applicable in a large range of laser parameters due to its nonadiabatic nature in treating the initial tunneling dynamics. However, the CCSFA is much more time consuming than the QTMC method because of the numerical solution to the saddle-point equations. In the present work, we present a time-sampling method to overcome this disadvantage. Our method is as efficient as the fast QTMC method and as accurate as the original treatment in CCSFA. The performance of our method is verified by comparing the results of these methods with that of the exact solution to the time-dependent Schrödinger equation.

Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

Probing Molecular Dynamics by Laser-Induced Backscattering Holography

We use differential holography to overcome the forward scattering problem in strong-field photoelectron holography. Our differential holograms of H_{2} and D_{2} molecules exhibit a fishbonelike structure, which arises from the backscattered part of the recolliding photoelectron wave packet. We demonstrate that the backscattering hologram can resolve the different nuclear dynamics between H_{2} and D_{2} with subangstrom spatial and subcycle temporal resolution. In addition, we show that attosecond electron dynamics can be resolved. These results open a new avenue for ultrafast studies of molecular dynamics in small molecules.

Two-dimensional attosecond electron wave-packet interferometry

We propose a two-dimensional interferometry based on the electron wave-packet interference by using a cycle-shaped orthogonally polarized two-color laser field. With such a method, the subcycle and intercycle interferences can be disentangled into different directions in the measured photoelectron momentum spectra. The Coulomb influence can be minimized and the overlapping of interference fringes with the complicated low-energy structures can be avoided as well. The contributions of the excitation effect and the long-range Coulomb potential can be traced in the Fourier domain of the photoelectron distribution. Because of these advantages, precise information on valence electron dynamics of atoms or molecules with attosecond temporal resolution and additional spatial information with angstrom resolution can be obtained with the two-dimensional electron wave-packet interferometry.

Revealing backward rescattering photoelectron interference of molecules in strong infrared laser fields

Photoelectrons ionized from atoms and molecules in a strong laser field are either emitted directly or rescattered by the nucleus, both of which can serve as efficiently useful tools for molecular orbital imaging. We measure the photoelectron angular distributions of molecules (N2, O2 and CO2) ionized by infrared laser pulses (1320 nm, 0.2 ~ 1 × 10(14) W/cm(2)) from multiphoton to tunneling regime and observe an enhancement of interference stripes in the tunneling regime. Using a semiclassical rescattering model with implementing the interference effect, we show that the enhancement arises from the sub-laser-cycle holographic interference of the contributions of the back-rescattering and the non-rescattering electron trajectory. It is shown that the low-energy backscattering photoelectron interference patterns have encoded the structural information of the molecular initial orbitals and attosecond time-resolved dynamics of photoelectron, opening new paths in high-resolution imaging of sub-Ångström and sub-femtosecond structural dynamics in molecules.

Molecular photoelectron holography by an attosecond XUV pulse in a strong infrared laser field

We have investigated the photoelectron spectra from ionization of diatomic molecules by an attosecond XUV pulse in a strong infrared laser field by quantum calculations. A clear holographic interference structure is observed in the two-dimensional photoelectron momentum spectrum. Moreover, this holographic structure depends sensitively on the electron orbitals and internuclear distance of diatomic molecules. Based on the orbital dependence of the holographic structure, one can identify the symmetries and electron density distributions of molecular orbitals. This indicates that the photoelectron holography by an attosecond XUV pulse in a strong infrared field can be used as an efficient tool for molecular imaging.

Photoionization of clusters in intense few-cycle near infrared femtosecond pulses

In this article we present a perspective on the current state of the art in the photoionization of atomic clusters in few-cycle near-infrared laser pulses.

Broadband evolution of phononic-crystal-waveguide eigenstates in real- and k-spaces

Control of sound in phononic band-gap structures promises novel control and guiding mechanisms. Designs in photonic systems were quickly matched in phononics, and rows of defects in phononic crystals were shown to guide sound waves effectively. The vast majority of work in such phononic guiding has been in the frequency domain, because of the importance of the phononic dispersion relation in governing acoustic confinement in waveguides. However, frequency-domain studies miss vital information concerning the phase of the acoustic field and eigenstate coupling. Using a wide range of wavevectors k, we implement an ultrafast technique to probe the wave field evolution in straight and L-shaped phononic crystal surface-phonon waveguides in real- and k-space in two spatial dimensions, thus revealing the eigenstate-energy redistribution processes and the coupling between different frequency-degenerate eigenstates. Such use of k-t space is a first in acoustics, and should have other interesting applications such as acoustic-metamaterial characterization.

Pump-probe scheme to study the autoionization decay of optically-forbidden H2 doubly excited states

A pump-probe scheme is proposed to investigate the autoionization dynamics of the optically forbidden Q(1)(1)Σ(g)(+) doubly excited states of the H(2) molecule. The scheme consists of a pump that contains an attosecond pulse train (APT) and an infrared (IR) pulse, which is phase-locked with the APT, and an IR probe identical to the former IR pulse. The dynamical information is obtained by analyzing the electron kinetic energy spectra (EKE) and proton kinetic energy spectra (PKE) as a function of the time delay between the pump and the probe. The essential requirement for an efficient population of the Q(1)(1)Σ(g)(+) states is that they are resonantly coupled to both the dipole-allowed Q(1)(1)Σ(u)(+) doubly excited states and the ground state of H(2) by the combined effect of the APT + IR fields.

Interference carpets in above-threshold ionization: from the Coulomb-free to the Coulomb-dominated regime

The velocity map recorded in above-threshold ionization of xenon at 800 nm exhibits a distinct carpetlike pattern of maxima and minima for emission in the direction approximately perpendicular to the laser polarization. The pattern is well reproduced by a numerical solution of the time-dependent Schrödinger equation. In terms of the simple-man model and the strong-field approximation, it is explained by the constructive and destructive interference of the contribution of the long and the short orbit. Strictly perpendicular emission is caused by ionization at the two peaks of the laser field per cycle, which results in a 2ħω separation of the above-threshold ionization rings.

Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields

We experimentally and theoretically demonstrate a self-referenced wave-function retrieval of a valence-electron wave packet during its creation by strong-field ionization with a sculpted laser field. Key is the control over interferences arising at different time scales. Our work shows that the measurement of subcycle electron wave-packet interference patterns can serve as a tool to retrieve the structure and dynamics of the valence-electron cloud in atoms on a sub-10-as time scale.

Strong-field above-threshold photoemission from sharp metal tips

We present energy-resolved measurements of electron emission from sharp metal tips driven with low energy pulses from a few-cycle laser oscillator. We observe above-threshold photoemission with a photon order of up to 9. At a laser intensity of ∼ 2 × 10(11)  W/cm2 the suppression of the lowest order peak occurs, indicating the onset of strong-field effects. We also observe peak shifting linearly with intensity, with a slope of around -1.0 eV/(10(12)  W/cm2). We attribute the magnitude of the laser field effects to field enhancement taking place at the tip's surface.

Low-energy structures in strong field ionization revealed by quantum orbits

Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the time-dependent Schrödinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise successful work horse of strong field laser physics: the "strong field approximation" (SFA). In the semiclassical limit, the SFA possesses an appealing interpretation in terms of interfering quantum trajectories. It is shown that a conceptually simple extension towards the inclusion of Coulomb effects yields very good agreement with exact TDSE results. Moreover, the Coulomb quantum orbits allow for a physically intuitive interpretation and detailed analysis of all low-energy features in the semiclassical regime, in particular, the recently discovered "low-energy structure" [C. I. Blaga, Nature Phys. 5, 335 (2009) and W. Quan, Phys. Rev. Lett. 103, 093001 (2009).

Creating and manipulating vortices in atomic wave functions with short electric field pulses

We demonstrate the creation of vortices in the electronic probability density of an atom subject to short electric field pulses, how these vortices evolve and can be manipulated by varying the applied pulses, and that they persist to macroscopic distances in the spectrum of ejected electrons. This opens the possibility to use practical femtosecond or shorter laser pulses to create and manipulate these vortex quasiparticles at the atomic scale and observe them in the laboratory. Within a hydrodynamic interpretation we also show, since the Schrödinger equation is a particular instance of the Navier-Stokes equations, that for compressible fluids vortices can appear spontaneously and with a certain time delay, which is not expected to occur from the conventional point of view, illustrating applicability of the present study to vortex formation more broadly.

Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses

Fully differential data for H2 dissociation in ultrashort (6 fs, 760 nm), linearly polarized, intense (0.44 PW/cm{2}) laser pulses with a stabilized carrier-envelope phase (CEP) were recorded with a reaction microscope. Depending on the CEP, the molecular orientation, and the kinetic energy release (KER), we find asymmetric proton emission at low KERs (0-3 eV), basically predicted by Roudnev and Esry, and much stronger than reported by Kling et al. Wave packet propagation calculations reproduce the salient features and discard, together with the observed KER-independent electron asymmetry, the first ionization step to be the reason for the asymmetric proton emission.