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

Observation of Attosecond Time Delays in Above-Threshold Ionization

Attosecond-scale temporal characterization of photoionization is essential in understanding how light and matter interact on the most fundamental level. However, characterizing the temporal property of strong-field above-threshold ionization has remained unreached. Here, we propose a novel photoelectron interferometric method to disentangle the contribution of Coulomb effect from an attoclock, allowing us to clock energy-resolved time delays of strong-field above-threshold ionization. We disentangle two types of Coulomb effects for the attoclock, i.e., one arising from the Coulomb disturbance of a single electron trajectory and the second effect arising from the photoelectron phase space distortion due to the Coulomb field. We find that the second Coulomb effect manifests itself as an energy-resolved attosecond time delay in the electron emission, which is relevant to the effect of nonadiabatic initial longitudinal momentum at the tunnel exit. Our study further indicates a sensitivity of the time delay to the temporal profile of the released electron wave packet within one half laser cycle. The temporal width of the released electron wave packet is found to increase with energy, which contradicts the common assumption in the adiabatic picture.

Sub-cycle strong-field tunneling dynamics in solids

Tunneling ionization is a crucial process in the interaction between strong laser fields and matter which initiates numerous nonlinear phenomena including high-order harmonic generation, photoelectron holography, etc. Both adiabatic and nonadiabatic tunneling ionization are well understood in atomic systems. However, the tunneling dynamics in solids, especially nonadiabatic tunneling, has not yet been fully understood. Here, we study the sub-cycle resolved strong-field tunneling dynamics in solids via a complex saddle-point method. We compare the instantaneous momentum at the moment of tunneling and the tunneling distances over a range of Keldysh parameters. Our results demonstrate that for nonadiabatic tunneling, tunneling ionization away from Γ point is possible. When this happens the electron has a nonzero initial velocity when it emerges in the conduction band. Moreover, consistent with atomic tunneling, a reduced tunneling distance as compared to the quasi-static case is found. Our results provide remarkable insight into the basic physics governing the sub-cycle electron tunneling dynamics with significant implications for understanding subsequent strong-field nonlinear phenomena in solids.

Response time of an electron inside a molecule to light in strong-field ionization

We study ionization of aligned H2+ in strong elliptically polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Coulomb potentials, we are able to quantitatively reproduce this angle difference between the molecule and the atom. Further analyses based on this model show that the response time of electron to light which is encoded in the offset angle and is manifested as the time spent in tunneling ionization, is about 15 attoseconds longer for the molecule than the atom. This time difference is further enlarged when increasing the internuclear distance of the molecule.

Tunnelling of electrons via the neighboring atom

As compared to the intuitive process that the electron emits straight to the continuum from its parent ion, there is an alternative route that the electron may transfer to and be trapped by a neighboring ionic core before the eventual release. Here, we demonstrate that electron tunnelling via the neighboring atomic core is a pronounced process in light-induced tunnelling ionization of molecules by absorbing multiple near-infrared photons. We devised a site-resolved tunnelling experiment using an Ar-Kr+ ion as a prototype system to track the electron tunnelling dynamics from the Ar atom towards the neighboring Kr+ by monitoring its transverse momentum distribution, which is temporally captured into the resonant excited states of the Ar-Kr+ before its eventual releasing. The influence of the Coulomb potential of neighboring ionic cores promises new insights into the understanding and controlling of tunnelling dynamics in complex molecules or environment.

Strong-Field Ionization of Hydrogen Atoms with Quantum Light

We study the strong-field ionization driven by quantum lights. Developing a quantum-optical-corrected strong-field approximation model, we simulate the photoelectron momentum distribution with squeezed-state light, which manifests as notably different interference structures from that with coherent-state (classical) light. With the saddle-point method, we analyze the electron dynamics and reveal that the photon statistics of squeezed-state light fields endows the tunneling electron wave packets with a time-varying phase uncertainty and modulates the photoelectron intracycle and intercycle interferences. Moreover, it is found the fluctuation of quantum light imprints significant influence on the propagation of tunneling electron wave packets, in which the ionization probability of electrons is considerably modified in time domain.

Two-color attosecond chronoscope

We study ionization of atoms in strong orthogonal two-color (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like one and a shoulder-like one, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived. Through these mappings, we are able to establish a two-color attosecond chronoscope for timing electron emission, which is essential for OTC-based precise manipulation.

Coulomb potential determining terahertz polarization in a two-color laser field

The orientation and ellipticity of terahertz (THz) polarization generated by a two-color strong field not only casts light on underlying mechanisms of laser-matter interaction, but also plays an important role for various applications. We develop the Coulomb-corrected classical trajectory Monte Carlo (CTMC) method to well reproduce the joint measurements, that the THz polarization generated by the linearly polarized 800 nm and circularly polarized 400 nm fields is independent on two-color phase delay. The trajectory analysis shows that the Coulomb potential twists the THz polarization by deflecting the orientation of asymptotic momentum of electron trajectories. Further, the CTMC calculations predict that, the two-color mid-infrared field can effectively accelerate the electron rapidly away from the parent core to relieve the disturbance of Coulomb potential, and simultaneously create large transverse acceleration of trajectories, leading to the circularly polarized THz radiation.

Trajectory analysis for low-order harmonic generation in two-color strong laser fields

Focusing two-color laser fields in gas-phase medium produces ultrashort ultra-broadband low-order harmonics spanning from terahertz to extreme ultraviolet regime. The low-order harmonic generation can be explained by both macroscopic photocurrent model and microscopic strong field approximation theory. Here, we analytically build a bridge between the macroscopic and microscopic theories by means of the trajectory method, which manifests correspondences between macroscopic and microscopic theories. And we demonstrate the trajectory analysis to explain phase-dependent terahertz and third-harmonic generations, and contribute the phase-dependent yields and spectral shapes to the coherent superposition of electron trajectories released at distinct ionization instants, reflecting electron interfering with itself in radiation process. The trajectory method readily connects the low-order harmonics characteristics and behaviors of electron wavepacket, which has potential for reconstructing ultrafast electron dynamics by means of low-harmonics observations.

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.

Probing Resonant Photoionization Time Delay by Self-Referenced Molecular Attoclock

Attosecond time-resolved electron tunneling dynamics have been investigated by using attosecond angular streaking spectroscopy, where a clock reference to the laser field vector is required in atomic strong-field ionization and the situation becomes complicated in molecules. Here we reveal a resonant ionization process via a transient state by developing an electron-tunneling-site-resolved molecular attoclock in Ar-Kr^{+}. Two distinct deflection angles are observed in the photoelectron angular distribution in the molecular frame, corresponding to the direct and resonant ionization pathways. We find the electron is temporally trapped in the Coulomb potential wells of the Ar-Kr^{+} before finally releasing into the continuum when the electron tunnels through the internal barrier. By utilizing the direct tunneling ionization as a self-referenced arm of the attoclock, the time delay of the electron trapped in the resonant state is revealed to be 3.50±0.04  fs. Our results give an impetus to exploring the ultrafast electron dynamics in complex systems and also endow a semiclassical presentation of the electron trapping dynamics in a quantum resonant state.

Identifying the complexity of the holographic structures in strong field ionization

We present numerical investigations of the strong-field attosecond photoelectron holography by analyzing the holographic interference structures in the two-dimensional photoelectron momentum distribution (PMD) in hydrogen atom target induced by a strong infrared laser pulse. The PMDs are calculated by solving the full-dimensional time-dependent Schrödinger equation. The effect of the number of optical cycles on the PMD is considered and analyzed. We show how the complex interference patterns are formed from a single-cycle pulse to multi-cycle pulses. Furthermore, snapshots of the PMD during the time evolution are presented for a single-cycle pulse in order to track the formation of the so-called fish-bone like holographic structure. The spider- and fan-like holographic structures are also identified and investigated. We found that the fan-like structure could only be identified clearly for pulses with three or more optical cycles and its symmetry depends closely on the number of optical cycles. In addition, we found that the intensity and wavelength of the laser pulse affect the density of interference fringes in the holographic patterns. We show that the longer the wavelength, the more the holographic structures are confined to the polarization axis.

Analyzing the electron trajectories in strong-field tunneling ionization with the phase-of-the-phase spectroscopy

By numerically solving the time-dependent Schrödinger equation, we theoretically study strong-field tunneling ionization of Ar atom in the parallel two-color field which consists of a strong fundamental pulse and a much weaker second harmonic component. Based on the quantum orbits concept, we analyzed the photoelectron momentum distributions with the phase-of-the-phase spectroscopy, and the relative contributions of the two parts of the photoelectrons produced during the rising and falling edges of the adjacent quarters of the laser cycle are identified successfully. Our results show that the relative contributions of these two parts depend on both of the transverse and longitude momenta. By comparing the results from model atoms with Coulomb potential and short-range potential, the role of the long-range Coulomb interaction on the relative contributions of these two parts of electrons is revealed. Additionally, we show that the effects of Coulomb interaction on ionization time are vital for identifying their relative contributions.

Quantum battles in attoscience: tunnelling

ABSTRACT

What is the nature of tunnelling? This yet unanswered question is as pertinent today as it was at the dawn of quantum mechanics. This article presents a cross section of current perspectives on the interpretation, computational modelling, and numerical investigation of tunnelling processes in attosecond physics as debated in the Quantum Battles in Attoscience virtual workshop 2020.

GRAPHIC ABSTRACT

Direct measurement of Coulomb-laser coupling

The Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

Coulomb-induced ionization time lag after electrons tunnel out of a barrier

After electrons tunnel out of a laser-Coulomb-formed barrier, the movement of the tunneling electron can be affected by the Coulomb potential. We show that this Coulomb effect induces a large time difference (longer than a hundred attoseconds) between the tunneling-out time at which the electron exits the barrier and the ionization time at which the electron is free. This large time difference has important influences on strong-field processes such as above-threshold ionization and high-harmonic generation, with remarkably changing time-frequency properties of electron trajectories. Some semi-quantitative evaluations on these influences are addressed, which provide new insight into strong-field processes and give suggestions on attosecond measurements.

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.

Deep Learning for Feynman's Path Integral in Strong-Field Time-Dependent Dynamics

Feynman's path integral approach is to sum over all possible spatiotemporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in the classical view. However, the complete characterization of the quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose a deep-learning-performed strong-field Feynman's formulation with a preclassification scheme that can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build a bridge between deep learning and strong-field physics through Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science and shed new light on the quantum-classical correspondence.

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.

Coulomb focusing in retrapped ionization with near-circularly polarized laser field

The full three-dimensional photoelectron momentum distributions of argon are measured in intense near-circularly polarized laser fields. We observed that the transverse momentum distribution of ejected electrons by 410-nm near-circularly polarized field is unexpectedly narrowed with increasing laser intensity, which is contrary to the conventional rules predicted by adiabatic theory. By analyzing the momentum-resolved angular momentum distribution measured experimentally and the corresponding trajectories of ejected electrons semiclassically, the narrowing can be attributed to a temporary trapping and thereby focusing of a photoelectron by the atomic potential in a quasibound state. With the near-circularly polarized laser field, the strong Coulomb interaction with the rescattering electrons is avoided, thus the Coulomb focusing in the retrapped process is highlighted. We believe that these findings will facilitate understanding and steering electron dynamics in the Coulomb coupled system.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Unifying Tunneling Pictures of Strong-Field Ionization with an Improved Attoclock

We demonstrate a novel attoclock, in which we add a perturbative linearly polarized light field at 400 nm to calibrate the attoclock constructed by an intense circularly polarized field at 800 nm. This approach can be directly implemented to analyze the recent hot and controversial topics involving strong-field tunneling ionization. The generally accepted picture is that tunneling ionization is instantaneous and that the tunneling probability synchronizes with the laser electric field. Alternatively, recently it was described in the Wigner picture that tunneling ionization would occur with a certain of time delay. We unify the two seemingly opposite viewpoints within one theoretical framework, i.e., the strong-field approximation (SFA). We illustrate that both the instantaneous tunneling picture and the Wigner time delay picture that are derived from the SFA can interpret the measurement well. Our results show that the finite tunneling delay will accompany nonzero exit longitudinal momenta. This is not the case for the instantaneous tunneling picture, where the most probable exit longitudinal momentum would be zero.

High-Harmonic and Terahertz Spectroscopy (HATS): Methods and Applications

Electrons driven from atom or molecule by intense dual-color laser fields can coherently radiate high harmonics from extreme ultraviolet to soft X-ray, as well as an intense terahertz (THz) wave from millimeter to sub-millimeter wavelength. The joint measurement of high-harmonic and terahertz spectroscopy (HATS) was established and further developed as a unique tool for monitoring electron dynamics of argon from picoseconds to attoseconds and for studying the molecular structures of nitrogen. More insights on the rescattering process could be gained by correlating the fast and slow electron motions via observing and manipulating the HATS from atoms and molecules. We also propose the potential investigations of HATS of polar molecules, and solid and liquid sources.

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.

Quantum Interference of Glory Rescattering in Strong-Field Atomic Ionization

During the ionization of atoms irradiated by linearly polarized intense laser fields, we find for the first time that the transverse momentum distribution of photoelectrons can be well fitted by a squared zeroth-order Bessel function because of the quantum interference effect of glory rescattering. The characteristic of the Bessel function is determined by the common angular momentum of a number of semiclassical paths termed as glory trajectories, which are launched with different nonzero initial transverse momenta distributed on a specific circle in the momentum plane and finally deflected to the same asymptotic momentum, which is along the polarization direction, through post-tunneling rescattering. Glory rescattering theory based on the semiclassical path-integral formalism is developed to address this effect quantitatively. Our theory can resolve the long-standing discrepancies between existing theories and experiments on the fringe location, predict the sudden transition of the fringe structure in holographic patterns, and shed light on the quantum interference aspects of low-energy structures in strong-field atomic ionization.

Low-Energy Electron Emission in the Strong-Field Ionization of Rare Gas Clusters

Clusters and nanoparticles have been widely investigated to determine how plasmonic near fields influence the strong-field induced energetic electron emission from finite systems. We focus on the contrary, i.e., the slow electrons, and discuss a hitherto unidentified low-energy structure (LES) in the photoemission spectra of rare gas clusters in intense near-infrared laser pulses. For Ar and Kr clusters we find, besides field-driven fast electrons, a robust and nearly isotropic emission of electrons with <4  eV kinetic energies that dominates the total yield. Molecular dynamics simulations reveal a correlated few-body decay process involving quasifree electrons and multiply excited ions in the nonequilibrium nanoplasma that results in a dominant LES feature. Our results indicate that the LES emission occurs after significant nanoplasma expansion, and that it is a generic phenomenon in intense laser nanoparticle interactions, which is likely to influence the formation of highly charged ions.

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.

Resonance-like enhancement in high-order above threshold ionization of atoms and molecules in intense laser fields

We investigate the high-order above-threshold ionization (HATI) of atoms (Ar and Xe) and molecules (N₂ and O₂) subjected to strong laser fields by numerically solving time-dependent Schrödinger equation. It is demonstrated that resonance-like enhancement of groups of adjacent peaks in photoelectron spectrum of HATI is observed for Ar, Xe, and N₂, while this peculiar phenomenon is absent for O₂, which is in agreement with experimental observation [ Phys. Rev. A88, 021401 (2013)]. In addition, analysis indicates that resonance-like enhancement in HATI spectra of atoms and molecules is closely related to excitation of the high-lying excited states.

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.

Revealing the Sub-Barrier Phase using a Spatiotemporal Interferometer with Orthogonal Two-Color Laser Fields of Comparable Intensity

We measure photoelectron momentum distributions of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. The synthesized laser field is used to manipulate the oscillating tunneling barrier and the subsequent motion of electrons onto two spatial dimensions. The subcycle structures associated with the temporal double-slit interference are spatially separated and enhanced. We use such a spatiotemporal interferometer to reveal sub-barrier phase of strong-field tunneling ionization. This study shows that the tunneling process transfers the initial phase onto momentum distribution. Our work has the implication that the sub-barrier phase plays an indispensable role in photoelectron interference processes.

Emergence of a Higher Energy Structure in Strong Field Ionization with Inhomogeneous Electric Fields

Studies of strong field ionization have historically relied on the strong field approximation, which neglects all spatial dependence in the forces experienced by the electron after ionization. More recently, the small spatial inhomogeneity introduced by the long-range Coulomb potential has been linked to a number of important features in the photoelectron spectrum, such as Coulomb asymmetry, Coulomb focusing, and the low energy structure. Here, we demonstrate using midinfrared laser wavelength that a time-varying spatial dependence in the laser electric field, such as that produced in the vicinity of a nanostructure, creates a prominent higher energy peak. This higher energy structure (HES) originates from direct electrons ionized near the peak of a single half-cycle of the laser pulse. The HES is separated from all other ionization events, with its location and width highly dependent on the strength of spatial inhomogeneity. Hence, the HES can be used as a sensitive tool for near-field characterization in the "intermediate regime," where the electron's quiver amplitude is comparable to the field decay length. Moreover, the large accumulation of electrons with tuneable energy suggests a promising method for creating a localized source of electron pulses of attosecond duration using tabletop laser technology.

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.

Recollision dynamics in nonsequential double ionization of atoms by long-wavelength pulses

Recollision dynamics and electron correlation behavior are investigated for several long laser wavelengths (1200-3000 nm) in nonsequential double ionization (NSDI) of helium using three-dimensional classical ensembles. Numerical results show that for these long wavelengths NSDI events are mainly from the multiple-return trajectory which is different from the case of 800 nm. Moreover, with increasing laser wavelength NSDI events move from the diagonal to the two axes in the correlated electron momentum distributions, and finally form an experimentally observed prominent V-shaped structure [Phys. Rev. X 5, 021034 (2015)] in the first and third quadrants. Back analysis indicates that the asymmetric energy sharing between the two electrons at recollision is responsible for the formation of the prominent V-shaped structure of 3000 nm.

Laser-Driven Recollisions under the Coulomb Barrier

Photoelectron spectra obtained from the ab initio solution of the time-dependent Schrödinger equation can be in striking disagreement with predictions by the strong-field approximation (SFA), not only at low energy but also around twice the ponderomotive energy where the transition from the direct to the rescattered electrons is expected. In fact, the relative enhancement of the ionization probability compared to the SFA in this regime can be several orders of magnitude. We show for which laser and target parameters such an enhancement occurs and for which the SFA prediction is qualitatively good. The enhancement is analyzed in terms of the Coulomb-corrected action along analytic quantum orbits in the complex-time plane, taking soft recollisions under the Coulomb barrier into account. These recollisions in complex time and space prevent a separation into sub-barrier motion up to the "tunnel exit" and subsequent classical dynamics. Instead, the entire quantum path up to the detector determines the ionization probability.

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.

Unraveling nonadiabatic ionization and Coulomb potential effect in strong-field photoelectron holography

Strong field photoelectron holography has been proposed as a means for interrogating the spatial and temporal information of electrons and ions in a dynamic system. After ionization, part of the electron wave packet may directly go to the detector (the reference wave), while another part may be driven back and scatters off the ion(the signal wave). The interference hologram of the two waves may be used to extract target information embedded in the collision process. Unlike conventional optical holography, however, propagation of the electron wave packet is affected by the Coulomb potential as well as by the laser field. In addition, electrons are emitted over the whole laser pulse duration, thus multiple interferences may occur. In this work, we used a generalized quantum-trajectory Monte Carlo method to investigate the effect of Coulomb potential and the nonadiabatic subcycle ionization on the photoelectron hologram. We showed that photoelectron hologram can be well described only when the effect of nonadiabatic ionization is accounted for, and Coulomb potential can be neglected only in the tunnel ionization regime. Our results help paving the way for establishing photoelectron holography for probing spatial and dynamic properties of atoms and molecules.

Long-Range Coulomb Effect in Intense Laser-Driven Photoelectron Dynamics

In strong field atomic physics community, long-range Coulomb interaction has for a long time been overlooked and its significant role in intense laser-driven photoelectron dynamics eluded experimental observations. Here we report an experimental investigation of the effect of long-range Coulomb potential on the dynamics of near-zero-momentum photoelectrons produced in photo-ionization process of noble gas atoms in intense midinfrared laser pulses. By exploring the dependence of photoelectron distributions near zero momentum on laser intensity and wavelength, we unambiguously demonstrate that the long-range tail of the Coulomb potential (i.e., up to several hundreds atomic units) plays an important role in determining the photoelectron dynamics after the pulse ends.

Controlling Below-Threshold Nonsequential Double Ionization via Quantum Interference

We show through simulation that quantum interference in nonsequential double ionization can be used to control the recollision excitation with subsequent ionization (RESI) mechanism. This includes the shape, localization, and symmetry of RESI electron-momentum distributions, which may be shifted from a correlated to an anticorrelated distribution or vice versa, far below the direct ionization threshold intensity. As a testing ground, we reproduce recent experimental results by employing specific coherent superpositions of excitation channels. We examine two types of interference, from electron indistinguishability and intracycle events, and from different excitation channels. These effects survive focal averaging and transverse-momentum integration.

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 Monte Carlo 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.

Two-Color Strong-Field Photoelectron Spectroscopy and the Phase of the Phase

The presence of a weak second-harmonic field in an intense-laser ionization experiment affects the momentum-resolved electron yield, depending on the relative phase between the ω and the 2ω component. The proposed two-color "phase-of-the-phase spectroscopy" quantifies for each final electron momentum a relative-phase contrast (RPC) and a phase of the phase (PP) describing how much and with which phase lag, respectively, the yield changes as a function of the relative phase. Experimental results for RPC and PP spectra for rare gas atoms and CO_{2} are presented. The spectra demonstrate a rather universal structure that is analyzed with the help of a simple model based on electron trajectories, wave-packet spreading, and (multiple) rescattering. Details in the PP and RPC spectra are target sensitive and, thus, may be used to extract structural (or even dynamical) information with high accuracy.

Momentum Distribution of Near-Zero-Energy Photoelectrons in the Strong-Field Tunneling Ionization in the Long Wavelength Limit

We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a “V”-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at an extremely large distance. Tracing back classical trajectories, we find the tunneling electrons born in a certain window of the field phase and transverse velocity are responsible for the striking accumulation. Our theoretical results are consistent with recent meV-resolved high-precision measurements.

Strong-field excitation of helium: bound state distribution and spin effects

Using field ionization combined with the direct detection of excited neutral atoms we measured the distribution of principal quantum number n of excited He Rydberg states after strong-field excitation at laser intensities well in the tunneling regime. Our results confirm theoretical predictions from semiclassical and quantum mechanical calculations and simultaneously underpin the validity of the semiclassical frustrated tunneling ionization model. Moreover, since our experimental detection scheme is spin sensitive in the case of He atoms, we show that strong-field excitation leads to strong population of triplet states. The origin of it lies in the fact that high angular momentum states are accessible in strong-field excitation. Thus, singlet-triplet transitions become possible due to the increased importance of spin-orbit interaction rather than due to direct laser induced spin-flip processes.

Low-energy photoelectrons in strong-field ionization by laser pulses with large ellipticity

The 3D photoelectron momentum distributions created by the strong-field ionization of argon atoms and naphthalene molecules with intense, large ellipticity (∼0.7) femtosecond laser pulses are studied. The experiment reveals the presence of low-energy electrons for randomly oriented naphthalene, but not for argon. Our theory shows that the induced dipole part of the cationic potential facilitates the creation of the low-energy electrons. We establish the conditions in terms of laser pulse parameters and molecular properties for which this type of low-energy electrons can be observed and point to applications thereof.

Classical-quantum correspondence for above-threshold ionization

We measure high resolution photoelectron angular distributions (PADs) for above-threshold ionization of xenon atoms in infrared laser fields. Based on the Ammosov-Delone-Krainov theory, we develop an intuitive quantum-trajectory Monte Carlo model encoded with Feynman's path-integral approach, in which the Coulomb effect on electron trajectories and interference patterns are fully considered. We achieve a good agreement with the measured PADs of atoms for above-threshold ionization. The quantum-trajectory Monte Carlo theory sheds light on the role of ionic potential on PADs along the longitudinal and transverse direction with respect to the laser polarization, allowing us to unravel the classical coordinates (i.e., tunneling phase and initial momentum) at the tunnel exit for all of the photoelectrons of the PADs. We study the classical-quantum correspondence and build a bridge between the above-threshold ionization and the tunneling theory.

Ionization with low-frequency fields in the tunneling regime

Strong-field ionisation surprises with richness beyond current understanding despite decade long investigations. Ionisation with mid-IR light has promptly revealed unexpected kinetic energy structures that seem related to unanticipated quantum trajectories of the electrons. We measure first 3D momentum distributions in the deep tunneling regime (γ = 0.3) and observe surprising new electron dynamics of near-zero momentum electrons and extremely low momentum structures, below the eV, despite very high quiver energies of 95 eV. Such level of high-precision measurements at only 1 meV above the threshold, despite 5 orders higher ponderomotive energies, has now become possible with a specifically developed ultrafast mid-IR light source in combination with a reaction microscope, thereby permitting a new level of investigations into mid-IR recollision physics.

Trajectory-resolved Coulomb focusing in tunnel ionization of atoms with intense, elliptically polarized laser pulses

In strong-field light-matter interactions, the strong laser field dominates the dynamics. However, recent experiments indicate that the Coulomb force can play an important role as well. In this Letter, we have studied the photoelectron momentum distributions produced from noble gases in elliptically polarized, 800 nm laser light. By performing a complete mapping of the three-dimensional electron momentum, we find that Coulomb focusing significantly narrows the lateral momentum spread. We find a surprisingly sensitive dependence of Coulomb focusing on the initial transverse momentum distribution, i.e., the momentum at the moment of birth of the photoelectron. We also observe a strong signature of the low-energy structure in the above threshold ionization spectrum.

Scaling of the low-energy structure in above-threshold ionization in the tunneling regime: theory and experiment

A calculation of the second-order (rescattering) term in the S-matrix expansion of above-threshold ionization is presented for the case when the binding potential is the unscreened Coulomb potential. Technical problems related to the divergence of the Coulomb scattering amplitude are avoided in the theory by considering the depletion of the atomic ground state due to the applied laser field, which is well defined and does not require the introduction of a screening constant. We focus on the low-energy structure, which was observed in recent experiments with a midinfrared wavelength laser field. Both the spectra and, in particular, the observed scaling versus the Keldysh parameter and the ponderomotive energy are reproduced. The theory provides evidence that the origin of the structure lies in the long-range Coulomb interaction.

Enhancement of vibrational excitation and dissociation of H2(+) in infrared laser pulses

We study vibrational excitations, dissociation, and ionization of H(2)(+) in few-cycle laser pulses over a broad wavelength regime. Our results of numerical simulations supported by model calculations show a many orders-of-magnitude enhancement of vibrational excitation and dissociation (over ionization) of the molecular ion at infrared wavelengths. The enhancement occurs without any chirping of the pulse, which was previously applied to take account of the anharmonicity of the molecular vibrations. The effect is related to strong-field two- and higher-order photon transitions between different vibrational states.