Sub-cycle Electron Dynamics Research Articles

Tracing attosecond electron emission from a nanometric metal tip.

Solids exposed to intense electric fields release electrons through tunnelling. This fundamental quantum process lies at the heart of various applications, ranging from high brightness electron sources in d.c. operation1,2 to petahertz vacuum electronics in laser-driven operation3-8. In the latter process, the electron wavepacket undergoes semiclassical dynamics9,10 in the strong oscillating laser field, similar to strong-field and attosecond physics in the gas phase11,12. There, the subcycle electron dynamics has been determined with a stunning precision of tens of attoseconds13-15, but at solids the quantum dynamics including the emission time window has so far not been measured. Here we show that two-colour modulation spectroscopy of backscattering electrons16 uncovers the suboptical-cycle strong-field emission dynamics from nanostructures, with attosecond precision. In our experiment, photoelectron spectra of electrons emitted from a sharp metallic tip are measured as function of the relative phase between the two colours. Projecting the solution of the time-dependent Schrödinger equation onto classical trajectories relates phase-dependent signatures in the spectra to the emission dynamics and yields an emission duration of 710 ± 30 attoseconds by matching the quantum model to the experiment. Our results open the door to the quantitative timing and precise active control of strong-field photoemission from solid state and other systems and have direct ramifications for diverse fields such as ultrafast electron sources17, quantum degeneracy studies and sub-Poissonian electron beams18-21, nanoplasmonics22 and petahertz electronics23.

Nonadiabatic effect on temporal double-slit interference structures in an orthogonal two-color laser field

We theoretically investigate the temporal double-slit interference (DSI) structures in photoelectron momentum distribution driven by an orthogonally polarized two-color (OTC) laser field and focus on the nonadiabatic effect on the subcycle electron dynamics. Distinct discrepancies in the interference structures simulated with a time-dependent Schr\"odinger equation (TDSE) and an adiabatic semiclassical Monte Carlo approach are observed. By adopting the initial conditions derived from the nonadiabatic tunneling picture into the Monte Carlo algorithm, the improved nonadiabatic model well reproduces the TDSE result. Further analysis shows that the improvement is mainly attributed to the nonzero electron initial longitudinal velocity from the nonadiabatic tunneling and moreover, its influence on the subsequent electron dynamics is revealed. Our work demonstrates the sensitivity of the temporal DSI structures in an OTC field to the exit momentum, providing a way for comprehension of the nonadiabatic tunneling electron dynamics.

Characterizing subcycle electron dynamics of polar molecules by asymmetry in photoelectron momentum distributions

Strong-field ionization of polar molecules contains rich dynamical processes such as tunneling, excitation, and Stark shift. These processes occur on a sub-cycle time scale and are difficult to distinguish in ultrafast measurements. Here, with a developed strong-field model considering effects of both Coulomb and permanent dipole, we show that photoelectron momentum distributions (PMDs) in orthogonal two-color laser fields can be utilized to resolve these processes with attosecond-scale resolution. A feature quantity related to the asymmetry in PMDs is obtained, with which the complex electron dynamics of polar molecules in each half laser cycle is characterized and the subtle time difference when electrons escaping from different sides of the polar molecule is identified.

Principal frequency of an ultrashort laser pulse

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain.

Extracting sub-cycle electronic and nuclear dynamics from high harmonic spectra

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of tau _0 = 4 pm 1 fs, in good agreement with the tau _0 = 3.5 fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

Strong-field control and attosecond probing of multielectron dynamics

The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.

Observation of attosecond electron dynamics in the photoelectron momentum distribution of atoms using few-cycle laser pulses

The method of time-resolved measurement with ultrashort laser pulses is vital to the development of attosecond science. Pump-probe measurements using a train of attosecond pulses in combination with a near-infrared (NIR) multicycle driving laser have been successful in capturing the intercycle electron dynamics which repeats every optical cycle and leads to above-threshold ionization (ATI) spectra in the frequency domain. In this work, we study the effect of a carrier-envelope phase (CEP) in a few-cycle ($l6$ fs) NIR laser pulse on the photoelectron momentum distribution (PMD) of a hydrogen atom and show that interference patterns in a PMD change dramatically with CEPs in the few-cycle regime. When the few-cycle driving laser pulse has a sine shape, the double-slit interference with characteristic modulation of ATI peaks dominates the PMD. On the other hand, when the driving pulse has a cosine shape, the holographical interference featured by a spider-like pattern is isolated. Our results suggest that the CEP-stable few-cycle laser pulses can be used to identify different types of intracycle interference structures in a PMD which reveal the underlying subcycle electron dynamics on an attosecond timescale.

Sub-cycle temporal evolution of light-induced electron dynamics in hexagonal 2D materials

Two-dimensional materials with hexagonal symmetry such as graphene and transition metal dichalcogenides are unique materials to study light-field-controlled electron dynamics inside of a solid. Around the K-point, the dispersion relation represents an ideal system to study intricately coupled intraband motion and interband (Landau-Zener) transitions driven by the optical field of phase-controlled few-cycle laser pulses. Based on the coupled nature of the intraband and interband processes, we have recently observed in graphene repeated coherent Landau-Zener transitions between valence and conduction band separated by around half an optical period of ∼1.3 fs (Higuchi et al Nature 550, 224 (2017)). Due to the low temporal symmetry of the applied laser pulse, a residual current density and a net electron polarization are formed. Here we show extended numerical data on the temporal evolution of the conduction band population of 2D materials with hexagonal symmetry during the light–matter interaction, yielding deep insights to attosecond-fast electron dynamics. In addition, we show that a residual ballistic current density is formed, which strongly increases when a band gap is introduced. Both, the sub-cycle electron dynamics and the resulting residual current are relevant for the fundamental understanding and future applications of strongly driven electrons in two-dimensional materials, including graphene or transition metal dichalcogenide monolayers.

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.

Velocity map imaging of scattering dynamics in orthogonal two-color fields

In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states.

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

High-energy mid-infrared sub-cycle pulse synthesis from a parametric amplifier

High-energy phase-stable sub-cycle mid-infrared pulses can provide unique opportunities to explore phase-sensitive strong-field light–matter interactions in atoms, molecules and solids. At the mid-infrared wavelength, the Keldysh parameter could be much smaller than unity even at relatively modest laser intensities, enabling the study of the strong-field sub-cycle electron dynamics in solids without damage. Here we report a high-energy sub-cycle pulse synthesiser based on a mid-infrared optical parametric amplifier and its application to high-harmonic generation in solids. The signal and idler combined spectrum spans from 2.5 to 9.0 µm. We coherently synthesise the passively carrier-envelope phase-stable signal and idler pulses to generate 33 μJ, 0.88-cycle, multi-gigawatt pulses centred at ~4.2 μm, which is further energy scalable. The mid-infrared sub-cycle pulse is used for driving high-harmonic generation in thin silicon samples, producing harmonics up to ~19th order with a continuous spectral coverage due to the isolated emission by the sub-cycle driver.

Strong-field photoemission in nanotip near-fields: from quiver to sub-cycle electron dynamics

Metallic nanotips exhibit large electric field enhancements over an extremely broad bandwidth spanning from the optical domain down to static fields. They therefore constitute ideal model systems for the investigation of the inherent frequency scalings of highly nonlinear and strong-field phenomena. Here, we present a comprehensive study of strong-field photoemission from individual metallic nanotips. Combining high local fields and variable-wavelength mid-infrared pulses, we investigate electron dynamics governed by the nanoscale confinement of the optical near-field. In particular, we characterize a transition to sub-cycle, field-driven electron acceleration. The experimental findings are corroborated by semiclassical calculations within a two-step model.

Half-cycle cutoff in near-threshold harmonic generation

A half-cycle cutoff is identified in the harmonic generation spectra near the ionization potential for short driving laser pulses. Unlike the half-cycle cutoff in the high-energy region, the newly found low-energy cutoff is strongly affected by the ionic potential and multiple return trajectories. We show their contribution clearly in the observable harmonic spectrum based on the reference of this cutoff structure. Our results are calculated from a numerical solution to the 3D time-dependent Schrödinger equation and a classical trajectory Monte Carlo method. By comparing the results from both methods, we analyze the time-dependent sub-cycle electron dynamics and provide a transparent explanation to this half-cycle cutoff. We further investigate the low-energy harmonic yield as a function of CEP for different pulse durations. The modulation depth of this yield drops rapidly when the pulse duration is increased, which can explain the CEP-dependence recently observed in the experiment.

Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities.

We theoretically investigate the nonadiabatic subcycle electron dynamics in orthogonally polarized two-color laser fields with comparable intensities. The photoelectron dynamics is simulated by exact solution to the 3D time-dependent Schrödinger equation, and also by two other semiclassical methods, i.e., the quantum trajectory MonteCarlo simulation and the Coulomb-corrected strong field approximation. Through these methods, we identify the underlying mechanisms of the subcycle electron dynamics and find that both the nonadiabatic effects and the Coulomb potential play very important roles. The contribution of the nonadiabatic effects manifest in two aspects, i.e., the nonadiabatic ionization rate and the nonzero initial velocities at the tunneling exit. The Coulomb potential has a different impact on the electrons' trajectories for different relative phases between the two pulses.

Atomic-scale diffractive imaging of sub-cycle electron dynamics in condensed matter.

For interaction of light with condensed-matter systems, we show with simulations that ultrafast electron and X-ray diffraction can provide a time-dependent record of charge-density maps with sub-cycle and atomic-scale resolutions. Using graphene as an example material, we predict that diffraction can reveal localised atomic-scale origins of optical and electronic phenomena. In particular, we point out nontrivial relations between microscopic electric current and density in undoped graphene.

Field propagation-induced directionality of carrier-envelope phase-controlled photoemission from nanospheres.

Near-fields of non-resonantly laser-excited nanostructures enable strong localization of ultrashort light fields and have opened novel routes to fundamentally modify and control electronic strong-field processes. Harnessing spatiotemporally tunable near-fields for the steering of sub-cycle electron dynamics may enable ultrafast optoelectronic devices and unprecedented control in the generation of attosecond electron and photon pulses. Here we utilize unsupported sub-wavelength dielectric nanospheres to generate near-fields with adjustable structure and study the resulting strong-field dynamics via photoelectron imaging. We demonstrate field propagation-induced tunability of the emission direction of fast recollision electrons up to a regime, where nonlinear charge interaction effects become dominant in the acceleration process. Our analysis supports that the timing of the recollision process remains controllable with attosecond resolution by the carrier-envelope phase, indicating the possibility to expand near-field-mediated control far into the realm of high-field phenomena.

Time-dependent quantum chemistry of laser driven many-electron molecules.

A Time-Dependent Configuration Interaction approach using multiple Feshbach partitionings, corresponding to multiple ionization stages of a laser-driven molecule, has recently been proposed [T.-T. Nguyen-Dang and J. Viau-Trudel, J. Chem. Phys. 139, 244102 (2013)]. To complete this development toward a fully ab-initio method for the calculation of time-dependent electronic wavefunctions of an N-electron molecule, we describe how tools of multiconfiguration quantum chemistry such as the management of the configuration expansion space using Graphical Unitary Group Approach concepts can be profitably adapted to the new context, that of time-resolved electronic dynamics, as opposed to stationary electronic structure. The method is applied to calculate the detailed, sub-cycle electronic dynamics of BeH2, treated in a 3-21G bound-orbital basis augmented by a set of orthogonalized plane-waves representing continuum-type orbitals, including its ionization under an intense λ = 800 nm or λ = 80 nm continuous-wave laser field. The dynamics is strongly non-linear at the field-intensity considered (I ≃ 10(15) W/cm(2)), featuring important ionization of an inner-shell electron and strong post-ionization bound-electron dynamics.

Strong-field and attosecond physics in solids

We review the status of strong-field and attosecond processes in bulk transparent solids near the Keldysh tunneling limit. For high enough fields and low-frequency excitations, the optical and electronic properties of dielectrics can be transiently and reversibly modified within the applied pulse. In Ghimire et al (2011 Phys. Rev. Lett. 107 167407) non-parabolic band effects were seen in photon-assisted tunneling experiments in ZnO crystals in a strong mid-infrared field. Using the same ZnO crystals, Ghimire et al (2011 Nat. Phys. 7 138–41) reported the first observation of non-pertubative high harmonics, extending well above the bandgap into the vacuum ultraviolet. Recent experiments by Schubert et al (2014 Nat. Photonics 8 119–23) showed a carrier envelope phase dependence in the harmonic spectrum in strong-field 30 THz driven GaSe crystals which is the most direct evidence yet of the role of sub-cycle electron dynamics in solid-state harmonic generation. The harmonic generation mechanism is different from the gas phase owing to the high density and periodicity of the crystal. For example, this results in a linear dependence of the high-energy cutoff with the applied field in contrast to the quadratic dependence in the gas phase. Sub-100 attosecond pulses could become possible if the harmonic spectrum can be extended into the extreme ultraviolet (XUV). Here we report harmonics generated in bulk MgO crystals, extending to eV when driven by ∼35 fs, 800 nm pulses focused to a ∼1 VÅ peak field. The fundamental strong-field and attosecond response also leads to Wannier–Stark localization and reversible semimetallization as seen in the sub-optical cycle behavior of XUV absorption and photocurrent experiments on fused silica by Schiffrin et al (2013 Nature 493 70–4) and Schultze et al (2013 Nature 493 75–8). These studies are advancing our understanding of fundamental strong-field and attosecond physics in solids with potential applications for compact coherent short-wavelength sources and ultra-high speed optoelectronics.

Toward single attosecond pulses using harmonic emission from solid-density plasmas

We report on investigations of high-order harmonic generation from solid surfaces in the coherent wake emission regime with relativistically intense few-cycle (8 fs) laser pulses. Significant spectral broadening compared to previous experiments with many-cycle pulses and the appearance of substructures on the harmonics are observed that strongly fluctuate from shot-to-shot. Measurements in which the linear polarization was rotated or ellipticity of the laser pulse was varied exhibit a strong dependence of the harmonic emission on the polarization state of the incident pulse. We show that the observed spectral features are ultimately connected to the sub-cycle electron dynamics in the laser-solid interaction and thus proof of the few-cycle nature of the observed harmonic emission. Using a simple model we have investigated the factors that play an important role in the shape of the emitted spectrum.