Sub-cycle Dynamics Research Articles

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.

Laser waveform control of extreme ultraviolet high harmonics from solids.

Solid-state high-harmonic sources offer the possibility of compact, high-repetition-rate attosecond light emitters. However, the time structure of high harmonics must be characterized at the sub-cycle level. We use strong two-cycle laser pulses to directly control the time-dependent nonlinear current in single-crystal MgO, leading to the generation of extreme ultraviolet harmonics. We find that harmonics are delayed with respect to each other, yielding an atto-chirp, the value of which depends on the laser field strength. Our results provide the foundation for attosecond pulse metrology based on solid-state harmonics and a new approach to studying sub-cycle dynamics in solids.

Coulomb rescattering in nondipole interaction of atoms with intense laser fields

We investigate the ionization dynamics of atoms irradiated by an intense laser field using a semiclassical model that includes magnetic Lorentz force in the rescattering process. We find that, the electrons tunneled with different initial transverse momenta (i.e., perpendicular to the instantaneous electric field direction) distributed on a specific circle in the momentum plane can finally converge to the same transverse momentum after experiencing Coulomb forward scattering. These electron trajectories lead to a bright spot structure in the 2D transverse momentum distribution, and particularly in the long-wavelength limit, a nonzero momentum peak in the direction antiparallel to the laser propagation (or radiation pressure) direction. Making analysis of the subcycle dynamics of rescattering trajectories, we unveil the underlying mechanism of the anti-intuitive peak. Beyond the strong field approximation and the dipole approximation, we quantitatively predict the spot center and the peak position. Our results are compared with a recent experiment and some theoretical predictions are given.

Sub-cycle ionization dynamics revealed by trajectory resolved, elliptically-driven high-order harmonic generation.

The sub-cycle dynamics of electrons driven by strong laser fields is central to the emerging field of attosecond science. We demonstrate how the dynamics can be probed through high-order harmonic generation, where different trajectories leading to the same harmonic order are initiated at different times, thereby probing different field strengths. We find large differences between the trajectories with respect to both their sensitivity to driving field ellipticity and resonant enhancement. To accurately describe the ellipticity dependence of the long trajectory harmonics we must include a sub-cycle change of the initial velocity distribution of the electron and its excursion time. The resonant enhancement is observed only for the long trajectory contribution of a particular harmonic when a window resonance in argon, which is off-resonant in the field-free case, is shifted into resonance due to a large dynamic Stark shift.

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.

Subcycle nonadiabatic strong-field tunneling ionization

We present a subcycle nonadiabatic strong-field tunneling theory and derive the position of tunnel exit, the transverse and longitudinal momentum distributions at the tunnel exit, and the ionization rate in an instantaneous laser field. These tunneling coordinates are shown to nonadiabatically couple with each other in an instantaneous laser field when the electron tunnels through the barrier. We have further incorporated the nonadiabatic tunneling theory with the quantum-trajectory Monte Carlo approach to investigate the nonadiabatic effect on the photoelectron angular distributions. The simulated photoelectron angular distributions with the nonadiabatic corrections have been validated by comparison with the ab initio results through numerically solving the time-dependent Schr\odinger equation. The nonadiabatic coordinates at the tunnel exit play important roles in both the direct ionization and rescattering process. The nonadiabatic tunneling theory provides an intuitive understanding on subcycle dynamics of tunneling ionization.

Channel-resolved subcycle interferences of electron wave packets emitted from in two-color laser fields

We report on the observation of subcycle interferences of electron wave packets released during strong field ionization of $\text{H}_{2}$ with cycle-shaped two-color laser fields. With a reaction microscope we measure three-dimensional momentum distributions of photoelectrons correlated with either $\text{H}_{2}^{+}$ or protons within different energy ranges generated by dissociation of $\text{H}_{2}^{+}$ . We refer to these different types of photoelectrons as channels. Our results show that the subcycle interference structures of electron wave packets are very sensitive to the cycle shape of the two-color laser field. We explain this behavior by the dependence of the ionization time within an optical cycle on the shape of the laser field cycle. The subcycle interference structures can be further used to obtain insight into the subcycle dynamics of molecules during strong field interaction.

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.

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.

Subcycle dynamics of high-harmonic generation in valence-shell and virtual states of Ar atoms: A self-interaction-free time-dependent density-functional-theory approach

We perform an ab initio all-electron study of the subcycle structure, dynamics, and spectra of high harmonic generation (HHG) processes of Ar atoms in the presence of extreme ultraviolet (XUV) attosecond pulses and near-infrared (NIR) laser fields by means of the self-interaction-free time-dependent density functional theory (TDDFT). The TDDFT equations are solved accurately and efficiently via the time-dependent generalized pseudospectral (TDGPS) method. We focus on the subcycle (with respect to NIR field) temporal behavior of the level shift of the excited energy levels and related dynamics of harmonic photon emission. We observe and identify the subcycle shifts in the harmonic emission spectrum as a function of the time delay between the XUV and NIR pulses. In the region where the two pulses overlap, the photon emission peaks have an oscillatory structure with a period of $\ensuremath{\sim}1.3$ fs, which is half of the NIR laser optical cycle. We present and analyze the harmonic emission spectra from $3sn{p}_{0},3{p}_{0}ns,3{p}_{1}n{d}_{1},3{p}_{1}n{p}_{1},3{p}_{0}n{d}_{0},3{p}_{0}n{p}_{0}$, and $3{p}_{0}ns$ excited states and the $3{p}_{0}4{p}_{0}^{\ensuremath{-}}$ virtual state as functions of the time delay. In addition, we explore the subcycle a.c. Stark shift phenomenon in NIR fields and its influence on the harmonic emission process. Our analysis reveals several features of the subcycle HHG dynamics and spectra as well as a temporal energy level shift.

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.

Subcycle dynamics of high-order-harmonic generation of He atoms excited by attosecond pulses and driven by near-infrared laser fields: A self-interaction-free time-dependent density-functional-theory approach

In the framework of the self-interaction-free time-dependent density-functional theory, we have performed three-dimensional (3D) ab initio calculations of He atoms in near-infrared (NIR) laser fields subject to excitation by a single extreme ultraviolet (XUV) attosecond pulse (SAP). We have explored the dynamical behavior of the subcycle high harmonic generation (HHG) for transitions from the excited states to the ground state and found oscillation structures with respect to the time delay between the SAP and NIR fields. The oscillatory pattern in the photon emission spectra has a period of $\ensuremath{\sim}$$1.3$ fs which is half of the NIR laser optical cycle, similar to that recently measured in the experiments on transient absorption of He [M. Chini et al., Sci. Rep. 3, 1105 (2013)]. We present the photon emission spectra from $1s2p$, $1s3p$, $1s4p$, $1s5p$, and $1s6p$ excited states as functions of the time delay. We explore the subcycle Stark shift phenomenon in NIR fields and its influence on the photon emission process. Our analysis reveals several interesting features of the subcycle HHG dynamics and we identify the mechanisms responsible for the observed peak splitting in the photon emission spectra.

Subcycle Dynamics of Coulomb Asymmetry in Strong Elliptical Laser Fields

We measure photoelectron angular distributions of noble gases in intense elliptically polarized laser fields, which indicate strong structure-dependent Coulomb asymmetry. Using a dedicated semiclassical model, we have disentangled the contribution of direct ionization and multiple forward scattering on Coulomb asymmetry in elliptical laser fields. Our theory quantifies the roles of the ionic potential and initial transverse momentum on Coulomb asymmetry, proving that the small lobes of asymmetry are induced by direct ionization and the strong asymmetry is induced by multiple forward scattering in the ionic potential. Both processes are distorted by the Coulomb force acting on the electrons after tunneling. Lowering the ionization potential, the relative contribution of direct ionization on Coulomb asymmetry substantially decreases and Coulomb focusing on multiple rescattering is more important. We do not observe evident initial longitudinal momentum spread at the tunnel exit according to our simulation.

Role of subcycle transition dynamics in high-order-harmonic generation in periodic structures

In this paper a method is presented for calculating the subcycle rate for transitions of electrons between two bands of a sinusoidal band structure. A simple closed-form expression for the rate is derived. We show that transition dynamics are sensitive to the shape of the band structure away from the minima of the conduction band. A model of high-order-harmonic generation in periodic solids that incorporates the subcycle dynamics of transitions across the band gap is described. Harmonic emission is found to be highly sensitive to the temporal shape of the transition rate. Destructive interference of electron currents in the conduction band due to subcycle transition dynamics is described.

Intensity-dependent dynamics of the correlated electrons in molecular double ionization driven by mid-infrared laser pulses

With the three-dimensional classical ensemble model, we have investigated the complex electron correlations in N2 double ionization by the mid-infrared laser pulses over a wide range of laser intensities. Our numerical results show that the correlated longitudinal electron momentum spectra exhibit rich correlated patterns with the increase of the laser intensity. At the low and high laser intensities, the correlated electron momentum spectra display an obvious finger-like structure, while at the moderate laser intensity the finger-like structure is not observed and there is a certain contribution from the back-to-back emission. By back-analyzing the classical trajectories, the subcycle dynamics of the molecular double ionization in the long-wavelength regime are revealed and the complex electron correlations are explained.

Coulomb effects in photon-momentum partitioning during atomic ionization by intense linearly polarized light

Partitioning of photon momenta between the ion and electron in photoionization and the involved subcycle dynamics are investigated using an extended semiclassical model, where momentum transfer from the photon to the electron-ion system via the (magnetic) Lorentz force is taken into account. It is found that in both the tunneling and rescattering processes, Coulomb attraction between the ion and electron plays a role in the momentum partitioning. The effect is especially important for linearly polarized light since the photons that lift the electron out of the bound state do not always contribute to the forward ion momentum. The present results can have important implications in the generation of terahertz radiation and the calibration of tunnel exit by measuring final ion longitudinal momentum.

Classical-trajectory simulation of accelerating neutral atoms with polarized intense laser pulses

In the present paper, we perform the classical trajectory Monte Carlo simulation of the complex dynamics of accelerating neutral atoms with linearly or circularly polarized intense laser pulses. Our simulations involve the ion motion as well as the tunneling ionization and the scattering dynamics of valence electron in the combined Coulomb and electromagnetic fields, for both helium (He) and magnesium (Mg). We show that for He atoms, only linearly polarized lasers can effectively accelerate the atoms, while for Mg atoms, we find that both linearly and circularly polarized lasers can successively accelerate the atoms. The underlying mechanism is discussed and the subcycle dynamics of accelerating trajectories is investigated. We have compared our theoretical results with a recent experiment [Eichmann Nature (London) 461, 1261 (2009)].