Correlated multielectron dynamics in ultrafast laser pulse interactions with atoms

Classical multielectron model atoms with optimized ionization energies

We propose a method to build stable classical multielectron model atoms with the ionization energies optimized to experimental values. Based on the work of Kirschbaum and Wilets [Phys. Rev. A21, 834 (1980)10.1103/PhysRevA.21.834], which introduces auxiliary potentials to simulate quantum mechanical effects, we implement a genetic algorithm to optimize the related parameters such that the model atoms yield correct (first few) ionization energies. Ionization-energy optimized model atoms automatically show separated electron shells, consistent to normal expectations. Numerical examples are given to demonstrate the importance of correct ionization energies, as well as new perspectives to double ionization processes.

Spatially homogeneous few-cycle compression of Yb lasers via all-solid-state free-space soliton management

The high power and variable repetition-rate of Yb femtosecond lasers makes them very attractive for ultrafast science. However, for capturing sub-200 fs dynamics, efficient, high-fidelity and high-stability pulse compression techniques are essential. Spectral broadening using an all-solid-state free-space geometry is particularly attractive, as it is simple, robust and low-cost. However, spatial and temporal losses caused by spatio-spectral inhomogeneities have been a major challenge to date, due to coupled space-time dynamics associated with unguided nonlinear propagation. In this work, we use all-solid-state free-space compressors to demonstrate compression of 170 fs pulses at a wavelength of 1030nm from a Yb:KGW laser to ∼9.2 fs, with a highly spatially homogeneous mode. This is achieved by ensuring that the nonlinear beam propagation in periodic layered Kerr media occurs in spatial soliton modes, and by confining the nonlinear phase through each material layer to less than 1.0 rad. A remarkable spatio-spectral homogeneity of ∼0.87 can be realized, which yields a high efficiency of >50% for few-cycle compression. The universality of the method is demonstrated by implementing high-quality pulse compression under a wide range of laser conditions. The high spatiotemporal quality and the exceptional stability of the compressed pulses are further verified by high-harmonic generation. Our predictive method offers a compact and cost-effective solution for high-quality few-cycle-pulse generation from Yb femtosecond lasers, and will enable broad applications in ultrafast science and extreme nonlinear optics.

Laser-Induced Electron Transfer in the Dissociative Multiple Ionization of Argon Dimers

We report on an experimental and theoretical study of the ionization-fragmentation dynamics of argon dimers in intense few-cycle laser pulses with a tagged carrier-envelope phase. We find that a field-driven electron transfer process from one argon atom across the system boundary to the other argon atom triggers subcycle electron-electron interaction dynamics in the neighboring atom. This attosecond electron-transfer process between distant entities and its implications manifests itself as a distinct phase-shift between the measured asymmetry of electron emission curves of the Ar^{+}+Ar^{2+} and Ar^{2+}+Ar^{2+} fragmentation channels. This letter discloses a strong-field route to controlling the dynamics in molecular compounds through the excitation of electronic dynamics on a distant molecule by driving intermolecular electron-transfer processes.

Nonsequential double ionization of alkaline-earth metal atoms by intense mid-infrared femtosecond pulses

A systematic study of nonsequential double ionization (NSDI) of alkaline-earth metal atoms with mid-infrared femtosecond pulses is reported. We find that the measured NSDI yield shows a strong target dependence and it is more suppressed for alkaline-earth metal with higher ionization potential. The observation is attributed to the differences in the recollision induced excitation and ionization cross sections of alkaline-earth metals. This work indicates that NSDI of alkaline-earth metals can be generally understood within recollision picture and sheds light on ultrafast control of electron correlation and dynamics of ionic excited states during NSDI of atoms with complex structures.

Intensity dependence in nonsequential double ionization of helium

Using the quantitative rescattering model, we simulate the correlated two-electron momentum distributions for nonsequential double ionization of helium by 800 nm laser pulses at intensities in the range of (2 - 15) × 10¹⁴ W/cm². The experimentally observed V-shaped structure at high intensities [A. Rudenko et al., Phys. Rev. Lett. 99, 263003 (2007)] is attributed to the strong forward scattering in laser-induced recollision excitation and the asymmetric momentum distribution of electrons that are tunneling-ionized from the excited states. The final-state electron repulsion also plays an important role in forming the V-shaped structure.

Fingerprints of slingshot non-sequential double ionization on two-electron probability distributions

We study double ionization of He driven by near-single-cycle laser pulses at low intensities at 400 nm. Using a three-dimensional semiclassical model, we identify the pathways that prevail non-sequential double ionization (NSDI). We focus mostly on the delayed pathway, where one electron ionizes with a time-delay after recollision. We have recently shown that the mechanism that prevails the delayed pathway depends on intensity. For low intensities slingshot-NSDI is the dominant mechanism. Here, we identify the differences in two-electron probability distributions of the prevailing NSDI pathways. This allows us to identify properties of the two-electron escape and thus gain significant insight into slingshot-NSDI. Interestingly, we find that an observable fingerpint of slingshot-NSDI is the two electrons escaping with large and roughly equal energies.

Internal collision induced strong-field nonsequential double ionization in molecules

Using the classical ensemble method, we have investigated the alignment dependence of the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) of diatomic molecules driven by linearly polarized laser pulses. Our numerical results show that the correlated electron pairs are more likely to emit into the same hemisphere (side-by-side emission) for the parallel aligned molecules at the small internuclear distance, in agreement with previous experimental results. Surprisingly, as the internuclear distance increases, this side-by-side emission is more prevalent for the perpendicularly aligned molecules. Back analyzing of the classical trajectories shows that a considerable part of the NSDI events for the parallel aligned molecules at the large internuclear distances occur through an internal collision, not the well-known recollision. In the internal collision induced NSDI, the first electron tunnels through the inner barrier from the up-field core, moves directly towards the other core, and kicks out the second electron. For this type of NSDI events, the electron pairs are more likely to emit into the opposite hemispheres and thus the correlated electron momentum spectrum exhibits a more dominant back-to-back behavior in the parallel aligned molecules.

Timing the release of the correlated electrons in strong-field nonsequential double ionization by circularly polarized two-color laser fields

With the semiclassical ensemble model, we systematically investigate the correlated electron dynamics in strong-field nonsequential double ionization (NSDI) by the counter-rotating circularly polarized two-color (CPTC) laser pulses. Our results show that the angular distributions of the electrons in NSDI sensitively depend on the intensity ratio of the CPTC laser fields. At the small ratio, the electron pairs emit with a relative angle of about 120°, and this angle shifts to 40° as the ratio increases and finally it exhibits a wide range distribution as the intensity ratio further increases. Back analysis of the NSDI trajectories shows that this behavior results from the relative-intensity-dependence of the release time of the electron pairs in the CPTC laser fields. The release times of the electron pairs are directly mapped to the angular distribution. Our results indicate that the emission times of the correlated electrons in NSDI can be controlled with the CPTC laser fields.

Slingshot Nonsequential Double Ionization as a Gate to Anticorrelated Two-Electron Escape

At intensities below the recollision threshold, we show that recollision-induced excitation with one electron escaping fast after recollision and the other electron escaping with a time delay via a Coulomb slingshot motion is one of the most important mechanisms of nonsequential double ionization (NSDI), for strongly driven He at 400 nm. Slingshot NSDI is a general mechanism present for a wide range of low intensities and pulse durations. Anticorrelated two-electron escape is its striking hallmark. This mechanism offers an alternative explanation of anticorrelated two-electron escape obtained in previous studies.

Steering electron correlation time by elliptically polarized femtosecond laser pulses

Electron correlation is ubiquitous across diverse physical systems from atoms and molecules to condensed matter. Observing and controlling dynamical electron correlation in photoinduced processes paves the way to the coherent control of chemical reactionsand photobiological processes. Here, we experimentally investigate dynamics of electron correlation in double ionization of neon irradiated by intense elliptically polarized laser pulses. We find a characteristic, ellipticity-dependent, correlated electron emission along the minor axis of the elliptically polarized light. This observation is well reproduced by a semi-classical ensemble model simulation. By tracing back the corresponding electron trajectories, we find that the dynamical energy sharing during the electron emission process is modified by the ellipticity of the laser light. Thus, our work provides evidence for a possible ultrafast control of the energy sharing between the correlated electrons by varying the light ellipticity.

Correlated electron dynamics in strong-field nonsequential double ionization of Mg

Using the classical ensemble model, we systematically investigate strong-field nonsequential double ionization (NSDI) of Mg by intense elliptically polarized laser pulses with different wavelengths. Different from the noble atoms, NSDI occurs for Mg driven by elliptically and circularly polarized laser fields. Our results show that in elliptically and circularly polarized laser fields, the NSDI yield is sharply suppressed as the wavelength increases. Interestingly, the correlated behavior in the electron momentum spectra depends sensitively on the wavelengths. The corresponding electron dynamics is revealed by back tracing the classical trajectory.

Intense-Field Multiple-Detachment of F2¯: Competition with Photodissociation

The competition of intense-field multiple-detachment with efficient photodissociation of F₂¯ is studied as a function of laser peak intensity. The main product channels are disentangled and characterized by 3D coincidence fragment imaging. The presented kinetic energy release spectra, angular distributions, as well as two-color pump-probe measurements allow identification of competing sequential and nonsequential mechanisms. Dissociative detachment, producing two neutral atoms (F + F), is found to be dominated by a sequential mechanism of photodissociation (F¯ + F), followed by detachment of the atomic anion fragment. In contrast, dissociative ionization (F + F⁺) shows competing contributions of both a sequential two-step mechanism as well as a nonsequential double-detachment of the molecular anion, which are distinguished by the kinetic energy released in the dissociation. Triple-detachment is found to be nonsequential in nature and results in Coulomb explosion (F⁺ + F⁺). Furthermore, the measured kinetic energy release for dissociation on the ²Σ_g⁺ state provides a direct measurement of the F₂¯ dissociation energy, D₀ = 1.26 ± 0.03 eV.

Dissection of electron correlation in strong-field sequential double ionization using a classical model

Recent experiments on strong-field sequential double ionization (SDI) have reported several observations which are regarded as evidence of electron correlation, querying the validity of the standard independent electron approximation for SDI. Here we theoretically study SDI with a classical ensemble model. The experimental results are well reproduced with this model. Back tracing of the ionization process shows that these results are ascribed to the subcycle ionization dynamics of the two electrons, not the evidences of the electron correlation in SDI. Thus, the previously reported observations are not enough to claim the breakdown of the independent electron approximation in SDI.

Order of Magnitude Dissociative Ionization Enhancement Observed for Pulses with High Order Dispersion

While the interaction of atoms in strong fields is well understood, the same cannot be said about molecules. We consider how dissociative ionization of molecules depends on the quality of the femtosecond laser pulses, in particular, the presence of third- and fourth-order dispersion. We find that high-order dispersion (HOD) unexpectedly results in order-of-magnitude enhanced ion yields, along with the factor of 3 greater kinetic energy release compared to transform-limited pulses with equal peak intensities. The magnitude of these effects is not caused by increased pulse duration. We evaluate the role of pulse pedestals produced by HOD and other pulse shaping approaches, for a number of molecules including acetylene, methanol, methylene chloride, acetonitrile, toluene, and o-nitrotoluene, and discuss our findings in terms of processes such as prealignment, preionization, and bond softening. We conclude, based on the quasi-symmetric temporal dependence of the observed enhancements that cascade ionization is likely responsible for the large accumulation of charge prior to the ejection of energetic fragments along the laser polarization axis.

The interaction of excited atoms and few-cycle laser pulses

This work describes the first observations of the ionisation of neon in a metastable atomic state utilising a strong-field, few-cycle light pulse. We compare the observations to theoretical predictions based on the Ammosov-Delone-Krainov (ADK) theory and a solution to the time-dependent Schrödinger equation (TDSE). The TDSE provides better agreement with the experimental data than the ADK theory. We optically pump the target atomic species and measure the ionisation rate as the a function of different steady-state populations in the fine structure of the target state which shows significant ionisation rate dependence on populations of spin-polarised states. The physical mechanism for this effect is unknown.

Criterion for Distinguishing Sequential from Nonsequential Contributions to the Double Ionization of Helium in Ultrashort Extreme-Ultraviolet Pulses

We quantify sequential and nonsequential contributions in two-photon double ionization of helium atoms by intense ultrashort extreme-ultraviolet pulses with central photon energies ℏω_{ctr} near the sequential double-ionization threshold. If the spectrum of such pulses overlaps both the sequential (ℏω>54.4 eV) and nonsequential (ℏω<54.4 eV) double-ionization regimes, the sequential and nonsequential double-ionization mechanisms are difficult to distinguish. By tracking the double-ionization asymmetry in joint photoelectron angular distributions, we introduce the two-electron forward-backward-emission asymmetry as a measure that allows the distinction of sequential and nonsequential contributions. Specifically, for ℏω_{ctr}=50 eV pulses with a sine-squared temporal profile, we find that the sequential double-ionization contribution is the largest at a pulse length of 650 as, due to competing temporal and spectral constraints. In addition, we validate a simple heuristic expression for the sequential double-ionization contribution in comparison with ab initio calculations.

Boosting photoabsorption by attosecond control of electron correlation

Electron correlation plays an essential role in a wide range of fundamentally important many-body phenomena in modern physics and chemistry. An example is the importance of electron-electron correlation in multiple ionization of multielectron atoms and molecules exposed to intense laser pulses. Manipulating the dynamic electron correlation in such photoinduced processes is a crucial step toward the coherent control of chemical reactions and photobiological processes. The generation of an attosecond extreme ultraviolet (EUV) pulse may enable such controls. Here, we show for the first time, from full-dimensional ab initio calculations of double ionization of helium in intense laser pulses (λ = 780 nm), that the electron-electron interactions can be instantaneously tuned using a time-delayed attosecond EUV pulse. Consequently, the probability of producing energetic electrons from excessive photoabsorption can be enhanced by an order of magnitude, by the attosecond control of electron-electron correlation.

Correlated multielectron dynamics in mid-infrared laser pulse interactions with neon atoms

The multielectron dynamics in nonsequential triple ionization (NSTI) of neon atoms driven by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. In consistent with the experimental result, our numerical result shows that in the MIR regime, the triply charged ion longitudinal momentum spectrum exhibits a pronounced double-hump structure at low laser intensity. Back analysis reveals that as the intensity increases, the responsible triple ionization channels transform from direct (e, 3e) channel to the various mixed channels. This transformation of the NSTI channels leads to the results that the shape of ion momentum spectra becomes narrow and the distinct maxima shift towards low momenta with the increase of the laser intensity. By tracing the triply ionized trajectories, the various ionization channels at different laser intensities are clearly identified and these results provide an insight into the complex dynamics of the correlated three electrons in NSTI.

Attosecond-recollision-controlled selective fragmentation of polyatomic molecules

Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wave packets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of predetermining fragmentation and isomerization reactions in polyatomic molecules on subfemtosecond time scales.

Delayed double ionization as a signature of Hamiltonian chaos

We analyze the dynamical processes behind delayed double ionization of atoms subjected to strong laser pulses. Using reduced models, we show that these processes are a signature of Hamiltonian chaos which results from the competition between the laser field and the Coulomb attraction to the nucleus. In particular, we exhibit the paramount role of the unstable manifold of selected periodic orbits which lead to a delay in these double ionizations. Among delayed double ionizations, we consider the case of recollision excitation with subsequent ionization (RESI) and, as a hallmark of this mechanism, we predict oscillations in the ratio of RESI to double ionization yields versus laser intensity. We discuss the significance of the dimensionality of the reduced models for the analysis of the dynamical processes behind delayed double ionization.

Revealing the multi-electron effects in sequential double ionization using classical simulations

We theoretically investigated sequential double ionization (SDI) of Ar by the nearly circularly polarized laser pulses with a fully correlated classical ensemble model. The ion momentum distributions of our numerical results at various laser intensities and pulse durations agree well with the experimental results. The experimentally observed multi-electron effects embodied in the joint momentum spectrum of the two electrons is also reproduced by our correlated classical calculations. Interestingly, our calculations show that the angular distribution of the first photoelectron from the trajectories which eventually suffer SDI differs from the distribution of the photoelectrons from above-threshold ionization trajectories. This observation provides additional evidence of multi-electron effects in strong field SDI.

Correlated electron dynamics in nonsequential double ionization of molecules by mid-infrared fields

The electron dynamics in strong field nonsequential double ionization (NSDI) of nitrogen molecules by mid-infrared (MIR) laser pulses is investigated with the three-dimensional classical ensemble model. The numerical results show that in the MIR regime, the correlated behavior of the two electrons from NSDI is independent on the molecular alignment, contrary to the case in the near-infrared (NIR) regime where the electron correlations exhibit a strong alignment dependence. In consistent with the experimental results, our numerical results show that the longitudinal momentum spectrum of the doubly charged ion evolves from a wide single-hump structure at NIR regime into a double-hump structure when wavelength enters the MIR regime. This double-hump structure becomes more pronounced as the wavelength further increases. The responsible microscopic electron dynamics of NSDI at the MIR regime is explored by back analysis of the classical trajectories.

Classical simulations including electron correlations for sequential double ionization

With a classical ensemble model that includes electron correlations during the whole ionization process, we investigate strong-field sequential double ionization of Ar by elliptically polarized pulses at the quantitative level. The experimentally observed intensity-dependent three-band or four-band structures in the ion momentum distributions are well reproduced with this classical model. More importantly, the experimentally measured ionization time of the second electrons by A. N. Pfeiffer et al. [Nature Phys. 7, 428 (2011)], which cannot be predicted by the standard independent-electron model, is quantitatively reproduced by this fully classical correlated model. The success of our work encourages classical descriptions and interpretations of the complex multielectron effects in strong-field ionization where nonperturbative quantum approaches are currently not feasible.

Mechanism of delayed double ionization in a strong laser field

When intense laser pulses release electrons nonsequentially, the time delay between the last recollision and the subsequent ionization may last longer than what is expected from a direct impact scenario [recollision excitation with subsequent ionization (RESI)]. We show that the resulting delayed ionization stems from the inner electron being promoted to a sticky region. We identify the mechanism that traps and releases the electron from this region. As a signature of this mechanism, we predict oscillations in the ratio of RESI to double ionization yields versus laser intensity.

Experimental ionization of atomic hydrogen with few-cycle pulses

We present experimental data on strong-field ionization of atomic hydrogen by few-cycle laser pulses. We obtain quantitative agreement at the 10% level between the data and an ab initio simulation over a wide range of laser intensities and electron energies.

Probing angular correlations in sequential double ionization

We study electron correlation in sequential double ionization of noble gas atoms and HCl in intense, femtosecond laser pulses. We measure the photoelectron angular distributions of Ne+ relative to the first electron in a pump-probe experiment with 8 fs, 800 nm, circularly polarized laser pulses at a peak intensity of a few 10(15)  W/cm2. Using a linear-linear pump-probe setup, we further study He, Ar, and HCl. We find a clear angular correlation between the two ionization steps in the sequential double ionization intensity regime.

High energy proton ejection from hydrocarbon molecules driven by highly efficient field ionization

We investigated the ejection of energetic protons from a series of polyatomic hydrocarbon molecules exposed to 790 nm 27 fs laser pulses. Using multiparticle coincidence imaging we were able to decompose the observed proton energy spectra into the contributions of individual fragmentation channels. It is shown that the molecules can completely fragment already at relatively low peak intensities of a few 10(14)  W/cm(2), and that the protons are ejected in a concerted Coulomb explosion from unexpectedly high charge states. The observations are in agreement with enhanced ionization taking place at many C-H bonds in parallel.

Complex sub-laser-cycle electron dynamics in strong-field nonsequential triple ionization

Using the full three-dimensional classical ensemble model, we have investigated nonsequential triple ionization (NSTI) of Ne by intense linearly polarized laser fields systematically. Trajectory back analysis enables us to identify the various NSTI channels at different intensities in an intuitive way. The momentum distributions of the triply ionized ions calculated by this model agree well with the experimental results over a wide range of laser intensities [J. Phys. B 41, 081006 (2008)]. With this classical model we achieve insight into the complex sub-laser-cycle dynamics of the correlated three electrons in NSTI.

Multiphoton double ionization of Ar and Ne close to threshold

In kinematically complete studies we explore double ionization (DI) of Ne and Ar in the threshold regime (I>3x10{13} W/cm{2}) for 800 nm, 45 fs pulses. The basic differences are found in the two-electron momentum distributions-"correlation" (CO) for Ne and "anticorrelation" (ACO) for Ar-that can be partially explained theoretically within a 3D classical model including tunneling. Transverse electron momentum spectra provide insight into "Coulomb focusing" and point to correlated nonclassical dynamics. Finally, DI threshold intensities, CO as well as ACO regimes are predicted for both targets.

From recollisions to the knee: a road map for double ionization in intense laser fields

We examine the nature and statistical properties of electron-electron collisions in the recollision process in a strong laser field. The separation of the double ionization yield into sequential and nonsequential components leads to a bell-shaped curve for the nonsequential probability and a monotonically rising one for the sequential process. We identify key features of the nonsequential process and connect our findings in a simplified model which reproduces the knee shape for the probability of double ionization with laser intensity and associated trends.

Controlling nonsequential double ionization via two-color few-cycle pulses

Using the classical three-dimensional ensembles, we have demonstrated the controlling of dynamics in nonsequential double ionization (NSDI) of helium by two-color few-cycle pulses. By changing the relative phase of the two pulses, recollisions leading to NSDI can be restricted in a time interval of several hundreds attosecond nearly before the field extremum and as a result, the correlated electron momentum distribution exhibits a so-far unobserved narrow arc-like structure. This structure reveals a novel energy correlation between the two electrons from NSDI by two-color few-cycle pulses.

Strong-field double ionization of Ar below the recollision threshold

Nonsequential double ionization of Ar by 45 fs laser pulses (800 nm) at (4-7)x10;{13} W/cm;{2} was explored in fully differential measurements. Well below the field-modified recollision threshold we enter the multiphoton regime. Strongly correlated back-to-back emission of the electrons along the polarization direction is observed to dominate in striking contrast to all previous data. No effect of Coulomb repulsion can be found, the predicted cutoff in the sum-energy spectra of two emitted electrons is confirmed, and the potential importance of multiple recollisions is discussed.

Two-electron photodetachment of negative ions in a strong laser field

We study the photodetachment of H-, F-, and Br- in a short laser pulse of 800 nm wavelength and 6 x 10(14) W/cm2 peak intensity. Photoelectron spectra, recorded with the use of an imaging technique, reveal a substantial contribution from the sequential process of double detachment of halogen negative ions. The saturation effect is shown to play a crucial role in this process. The role of the alignment of atoms produced by photodetachment is discussed.

Time-resolved quantum dynamics of double ionization in strong laser fields

Quantum calculations of a (1+1)-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two-electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1D coordinates for the electrons. The time-resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration and reveal the relative importance of sequential and nonsequential double ionization, even when ionization takes place during the same field cycle.

Attosecond temporal gating with elliptically polarized light

Temporal gating allows high accuracy time-resolved measurements of a broad range of ultrafast processes. By manipulating the interaction between an atom and an intense laser field, we extend gating into the nonlinear medium in which attosecond optical and electron pulses are generated. Our gate is an amplitude gate induced by ellipticity of the fundamental pulse. The gate modulates the spectrum of the high harmonic emission and we use the measured modulation to characterize the sub-laser-cycle dynamics of the recollision electron wave packet.

In-plane theory of nonsequential triple ionization

We describe first-principles in-plane calculations of nonsequential triple ionization of atoms in a linearly polarized intense laser pulse. In a fully classically correlated description, all three electrons respond dynamically to the nuclear attraction, the pairwise e-e repulsions, and the laser force throughout the duration of a 780 nm laser pulse. Nonsequential ejection is shown to occur in a multielectron, possibly multicycle and multidimensional, rescattering sequence that is coordinated by a number of sharp transverse recollimation impacts.

Theoretical studies on tunneling ionizations of helium atom in intense laser fields

Our generalized Keldysh theory is applied to the simplest many-electron atom, helium atom. For the single ionization (He-->He(+)+e) we derive a compact rate formula, which does not contain any series summation or integral and thus is as simple as the Ammosov-Delone-Krainov ionization rates. In addition to its simplicity, our formula can explicitly show the wavelength dependence. Furthermore a simple form of the angular distribution of the photoelectron is available. Our compact formula agrees well with both the exact numerical calculations [A. Scrinzi et al., Phys. Rev. Lett. 83, 706 (1999)] and experimental data [B. Walker et al., Phys. Rev. Lett. 73, 1227 (1994)] in the intensity range of I<5x10(15) Wcm(2). In higher intensity regions, we suggest to utilize another simple formula which is valid in the tunneling limit.

Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold

We analyze the two-dimensional momentum distribution of electrons ionized by few-cycle laser pulses in the transition regime from multiphoton absorption to tunneling by solving the time-dependent Schrödinger equation and by a classical-trajectory Monte-Carlo simulation with tunneling (CTMC-T). We find a complex two-dimensional interference pattern that resembles above threshold ionization (ATI) rings at higher energies and displays Ramsauer-Townsend-type diffraction oscillations in the angular distribution near threshold. CTMC-T calculations provide a semiclassical explanation for the dominance of selected partial waves. While the present calculation pertains to hydrogen, we find surprising qualitative agreement with recent experimental data for rare gases [A. Rudenko, J. Phys. B 37, L407 (2004)].