Strong-field Ionization Of Atoms Research Articles

Electric Nondipole Effect in Strong-Field Ionization.

Strong-field ionization of atoms by circularly polarized femtosecond laser pulses produces a donut-shaped electron momentum distribution. Within the dipole approximation this distribution is symmetric with respect to the polarization plane. The magnetic component of the light field is known to shift this distribution forward. Here, we show that this magnetic nondipole effect is not the only nondipole effect in strong-field ionization. We find that an electric nondipole effect arises that is due to the position dependence of the electric field and which can be understood in analogy to the Doppler effect. This electric nondipole effect manifests as an increase of the radius of the donut-shaped photoelectron momentum distribution for forward-directed momenta and as a decrease of this radius for backwards-directed electrons. We present experimental data showing this fingerprint of the electric nondipole effect and compare our findings with a classical model and quantum calculations.

InSitu Generation of High-Energy Spin-Polarized Electrons in a Beam-Driven Plasma Wakefield Accelerator.

Insitu generation of a high-energy, high-current, spin-polarized electron beam is an outstanding scientific challenge to the development of plasma-based accelerators for high-energy colliders. In this Letter, we show how such a spin-polarized relativistic beam can be produced by ionization injection of electrons of certain atoms with a circularly polarized laser field into a beam-driven plasma wakefield accelerator, providing a much desired one-step solution to this challenge. Using time-dependent Schrödinger equation (TDSE) simulations, we show the propensity rule of spin-dependent ionization of xenon atoms can be reversed in the strong-field multiphoton regime compared with the non-adiabatic tunneling regime, leading to high total spin polarization. Furthermore, three-dimensional particle-in-cell simulations are incorporated with TDSE simulations, providing start-to-end simulations of spin-dependent strong-field ionization of xenon atoms and subsequent trapping, acceleration, and preservation of electron spin polarization in lithium plasma. We show the generation of a high-current (0.8kA), ultralow-normalized-emittance (∼37 nm), and high-energy (2.7GeV) electron beam within just 11cm distance, with up to ∼31% net spin polarization. Higher current, energy, and net spin-polarization beams are possible by optimizing this concept, thus solving a long-standing problem facing the development of plasma accelerators.

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization.

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.

Species-dependent tunneling ionization of weakly bound atoms in the short-wave infrared regime

We investigate the intensity- and species-dependent strong-field ionization of alkali metal atoms; sodium, potassium, rubidium and caesium; by intense, few-cycle laser pulses in the short-wave infrared (sw-IR) regime at 1800 nm. The low ionization potential, Ip, of these atoms allows us to scale the interaction and study the tunneling regime at sw-IR wavelengths using low intensities and pulse energies. Measurements of above-threshold ionization spectra in the alkali species exhibit distinct differences to rare gas spectra at 800 and 1800 nm. However, pairing the low ionization potential of these atoms with longer wavelengths results in the reemergence of some well-know features of nobel gas spectra in the visible, e.g., the plateau. Our focus lies on the comparison of high-energy rescattered electron yield among the different alkali species. The highly unfavorable plateau scaling known from rare gases at longer wavelengths is successfully circumvented by switching to low-Ip targets. In the investigated parameter range, we identify potassium as the most efficient rescatterer. In addition, this paves the way to a carrier-envelope phasemeter operating in the sw-IR/mid-wave IR regime, employing alkali metal atoms as a target.

Adiabatic theory of strong-field ionization of molecules including nuclear motion

The adiabatic theory of strong-field ionization of molecules with internuclear motion included into consideration is developed. Two adiabatic regimes in terms of the electronic, nuclear, and laser field timescales are considered. In the first regime, field is the slowest; that is, its timescale is much larger than the electronic and nuclear timescales. The corresponding theory generalizes the adiabatic theory of strong-field ionization of atoms and molecules with frozen nuclei [Phys. Rev. A 86, 043417 (2012)] by treating the internuclear motion on equal footing with the electronic motion. In the second regime, the active electron is the fastest; that is, its timescale is much smaller than that of the nuclei and laser field. The corresponding theory naturally involves the Born-Oppenheimer approximation. The two versions of the adiabatic theory are validated by comparing their predictions with accurate numerical results obtained by solving the time-dependent Schr\odinger equation (TDSE) for a model diatomic molecule with one electronic and one internuclear degree of freedom. The adiabatic results are shown to converge to the TDSE results uniformly with respect to the laser field amplitude both in tunneling and over-the-barrier ionization regimes. Two applications of the theory to the analysis of strong-field effects associated with the internuclear motion are discussed.

Pulse-length effects in strong-field ionization of atoms by co-rotating and counter-rotating bicircular laser pulses

We study strong-field ionization of H and selected rare-gas atoms by solving the three-dimensional time-dependent Schr\odinger equation in the single-active-electron approximation with particular attention to the effect of pulse length on the total ionization yields (TIYs) produced by counter-rotating bicircular (CRBC) lasers compared to co-rotating bicircular (COBC) lasers. To this end, TIYs, photoelectron momentum distributions, and above-threshold ionization spectra are presented for various pulse durations and peak intensities. For pulses containing five or more cycles of the fundamental near-infrared laser field, the CRBC/COBC ratio of TIYs is affected due to ionization via excited states and multiphoton ionization channels. For pulses containing less than five cycles, the CRBC/COBC ratio of TIYs depends on both the frequency combination and number of optical cycles: With the $1\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ frequency combination, the ratio of TIYs is enhanced (reduced) for pulses with an odd (even) number of optical cycles. The $1\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ frequency combination was considered for pulses containing two or three optical cycles, and for both pulse lengths the CRBC/COBC ratio of TIYs is less than unity.

Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities.

We present a detailed experimental and theoretical study on the relativistic nondipole effects in strong-field atomic ionization by near-infrared linearly polarized few-cycle laser pulses in the intensity range of 10^{14}-10^{15} W/cm^{2}. We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly abinitio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counterintuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between the experimental results and theoretical predictions.

Manipulating dynamical Rabi-splitting with two-color laser pulses.

We theoretically investigate strong-field ionization of hydrogen atoms by orthogonally polarized two-color (OTC) laser pulses consisting of a fundamental field that is resonant with the 1s - 2p transition and its second harmonic. Numerical simulations are performed by solving the two-dimensional time-dependent Schrödinger equation and recording the photoelectron momentum distribution. In this strong-field resonant ionization, the atom undergoes many Rabi cycles and the electron can be emitted within a completed Rabi-cycle leading to the splitting of the localized momentum distribution. Here, the splitting is attributed to dynamic Rabi-splitting as a result of the dynamic Stark effect. The employed OTC scheme is shown to be efficient for controlling the dynamic Rabi-splitting through the control of quantum-path interferences involved in one-photon and two-photon absorption processes. The control scheme is accomplished by varying the relative ratio intensity and optical phase between the two pulses, and its footprint is mapped in the momentum distribution. This is shown to lead to an asymmetric distribution and suppression of the ionization process. The obtained results suggest the OTC scheme as a tool for coherent control of dynamic Rabi-oscillations via the controlled quantum-path interferences, thus opening new directions towards designing quantum states via the control OTC scheme.

In Memoriam Leonid V. Keldysh

Leonid V. Keldysh – one of the most influential theoretical physicists of the 20th century – passed away in November 2016. L. V. Keldysh is best known for the diagrammatic formulation of real‐time (nonequilibrium) Green functions theory and for the theory of strong field ionization of atoms. Both theories profoundly changed large areas of theoretical physics and stimulated important experiments. Both these discoveries emerged almost simultaneously – like Einstein, also L. V. Keldysh had his annus mirabilis – the year 1964. But the list of his theoretical developments is much broader and is briefly reviewed here.

Quantum effect of laser-induced rescattering from the tunneling barrier

Rescattering mediated by intense laser fields is one of the dominant processes in strong-field physics. It was usually described classically or semiclassically. Recently, laser-induced recollisions with the tunneling barriers have attracted great theoretical interest. However, fully distinguishing the ``quantum'' effect of rescattering with the tunneling barrier on photoelectron energy and momentum distributions is very difficult if using the linearly polarized light field. Here we perform the measurement of photoelectron momentum distributions by strong-field ionization of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. We observe the strong ionization enhancement due to rescattering on two-dimensional momentum distribution, which is in striking disagreement with the predictions by the plain strong-field approximation and the classical-trajectory Monte Carlo simulation. With the help of the analysis on the electron complex trajectories in both sub-barrier and quasicontinuum regions, the enhancement is illustrated to originate from the quantum effect of forward scattering between the tunneling electron and its parent ion. The study shows that the electron probability will be significantly modified when the rescattered electrons excurse in the continuum and the ``classical'' rescattering process needs the quantum description.

Spatially and temporally controlling electron spin polarization in strong-field ionization using orthogonal two-color laser fields

We propose a scheme to produce spatially and temporally controlled spin-polarized photoelectrons by strong-field ionization of atoms. We calculate the momentum-resolved electron spin polarization from two spin-orbit coupled ionic states ($J=1/2$ and $J=3/2$) of krypton atoms in orthogonal two-color laser fields using the strong-field approximation, and obtain the instantaneous spin-polarization degree. With this scheme, the spin-up and -down photoelectrons can be well separated in the space, and the spin polarization is controlled on the sub-laser-cycle timescale. This study illustrates and reveals the mechanism of the generation of spin-polarized photoelectrons with an arbitrary spatially and temporally tailored laser field. We expect this work has implications for controlling the spatiotemporal spin polarization in strong-field physics.

Instantaneous ionization rate as a functional derivative

The notion of the instantaneous ionization rate (IIR) is often employed in the literature for understanding the process of strong field ionization of atoms and molecules. This notion is based on the idea of the ionization event occurring at a given moment of time, which is difficult to reconcile with the conventional quantum mechanics. We describe an approach defining instantaneous ionization rate as a functional derivative of the total ionization probability. The definition is based on physical quantities, such as the total ionization probability and the waveform of an ionizing pulse, which are directly measurable. The definition is, therefore, unambiguous and does not suffer from gauge non-invariance. We compute IIR by numerically solving the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field. In agreement with some previous results using attoclock methodology, the IIR we define does not show measurable delay in strong field tunnel ionization.

Coulomb potential effects in strong-field atomic ionization under elliptical polarization

We experimentally and theoretically investigate strong-field ionization of noble-gas atoms in elliptically polarized laser fields at 2000 nm. The ellipticity dependence of the ion yields has been measured at a series of intensities and compared to various theoretical model predictions [i.e., the Ammosov-Delone-Krainov (ADK), strong-field approximation (SFA), and Coulomb-Volkov distorted-wave approximation (CVA) models]. The SFA and ADK calculations match each other, which alludes to the negligible contribution of nonadiabatic effect. In the meantime, they both deviate significantly from the measurements. On the other hand, the good agreement between CVA calculations and measurements reveals the salient role played by the Coulomb potential in atomic ionization. The Coulomb potential effect is further confirmed by comparison of CVA calculations and measurements at 800 nm. Our work demonstrates the significant Coulomb potential effect on the ionization yields, the experimental evidence of which has rarely been documented.

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.

Photoelectron holography and forward scattering in atomic ionization by elliptically polarized laser pulses.

We report on the scaling of the photoelectron holography with the laser ellipticity in strong-field atomic ionization. We find that the spacing of the holographic fringe gradually decreases with increasing of the ellipticity. In terms of the strong-field approximation, the scaling of the fringe spacing with the laser ellipticity is explained by the effect of the initial transverse momenta at the tunnel exit. With increasing of the laser ellipticity, a ridge structure arising from forward scattering electrons is observed in the low-energy region of the electron momentum distribution. An analytic formula is obtained that demarcates the phase diagram for the observation of the holographic pattern and ridge structure in elliptically polarized laser fields.

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.

Strong-field ionization with twisted laser pulses

We apply quantum trajectory Monte Carlo computations in order to model strong-field ionization of atoms by twisted Bessel pulses and calculate photoelectron momentum distributions (PEMD). Since Bessel beams can be considered as an infinite superposition of circularly polarized plane waves with the same helicity, whose wave vectors lie on a cone, we compared the PEMD of such Bessel pulses to those of a circularly polarized pulse. We focus on the momentum distributions in propagation direction of the pulse and show how these momentum distributions are affected by experimental accessible parameters, such as the opening angle of the beam or the impact parameter of the atom with regard to the beam axis. In particular, we show that we can find higher momenta of the photoelectrons, if the opening angle is increased.

Trajectory-free ionization times in strong-field ionization

Using a purely quantum mechanical approach without trajectories, we are able to compute momentum-resolved ionization times of electrons released by the strong-field ionization of atoms. For the attoclock setting, we show that the dominant emission angle corresponds well to instantaneous ionization at the maximum field if geometrical factors are taken into account appropriately and if the field intensity is small enough to avoid depletion of the bound state.

Impact of Coulomb potential on peak structures arising in momentum and low-energy photoelectron spectra produced in strong-field ionization of laser-irradiated atoms

The phenomenon of pronounced peak structure(s) of longitudinal momentum distributions as well as a spike-like structure of low-energy spectra of photoelectrons emitted from laser-irradiated Ar and Ne atoms in a single ionization process is theoretically studied in the tunneling and multiphoton regimes of ionization. The problem is addressed assuming only the direct above-threshold ionization (ATI) as a physical mechanism underlying the phenomenon under consideration (viz. solely contributing to observed photoelectron momentum distributions (PMD)) and using the Coulomb–Volkov (CV) ansatz within the frame of conventional strong-field approximation (SFA) applied in the length-gauge formulation. The developed CV-SFA approach also incorporates the density functional theory essentially exploited for numerical composition of initial (laser-free) atomic state(s) constructed from atomic orbitals of Gaussian type. Our presented CV-SFA based (and laser focal-volume averaged) calculation results proved to be well reproducing both the pronounced double-peak and/or ATI-like multi-peak structure(s) experimentally observed in longitudinal PMD under conditions of tunneling and/or multiphoton regime, respectively. In addition, our CV-SFA results presented for tunneling regime also suggest and remarkably reproduce a pronounced structure observed in relevant experiments as a ‘spike-like’ enhanced maximum arising in low-energy region (around the value of about 1 eV) of photoelectron spectra. The latter consistency allows to identify and interpret these results as the so-called low-energy structure (LES) since the phenomenon proved to appear as the most prominent if the influence of Coulomb potential on photoelectron continuum states is maximally taken into account under calculations (viz. if the parameter Z in CV’s functions is put equal to 1). Moreover, the calculated LES proved to correspond (viz., established as closely related) to the mentioned double-peak structure arising in the low-momentum region ( a.u.) of longitudinal PMDs calculated under condition of the tunneling regime. Thus, the phenomena under consideration can be well understood and adequately interpreted beyond the terms and/or concepts of various different alternative strong-field approaches and models (such as e.g., extensively invoked and exploited nowadays though, more sophisticated SFA-based ‘rescattering’ mechanism) compared to which, the currently applied CV-SFA model (through the same underlying physical mechanism of solely direct ATI suggested) is additionally able to provide and reveal an intimate and transparent interrelation between the phenomena of LES and double-peak structure arising in PMDs observed in the tunneling regime.

Dynamics of tunneling ionization using Bohmian mechanics

Recent attoclock experiments and theoretical studies regarding the strong-field ionization of atoms by few-cycle infrared pulses revealed new features that have attracted much attention. Here we investigate tunneling ionization and the dynamics of the electron probability using Bohmian Mechanics. We consider a one-dimensional problem to illustrate the underlying mechanisms of the ionization process. It is revealed that in the major part of the below-the-barrier ionization regime, in an intense and short infrared pulse, the electron does not tunnel \through" the entire barrier, but rather already starts from the classically forbidden region. Moreover, we highlight the correspondence between the probability of locating the electron at a particular initial position and its asymptotic momentum. Bohmian Mechanics also provides a natural definition of mean tunneling time and exit position, taking account of the time dependence of the barrier. Finally, we find that the electron can exit the barrier with significant kinetic energy, thereby corroborating the results of a recent study [Camus et al., Phys. Rev. Lett. 119 (2017) 023201].