A possible route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal and nanometer spatial resolution is to employ recolliding electrons as `probes'. The recollision process in molecules is, however, very challenging to treat using {\it ab initio} approaches. Even for the simplest diatomic systems, such as H$_2$, today's computational capabilities are not enough to give a complete description of the electron and nuclear dynamics initiated by a strong laser field. As a consequence, approximate qualitative descriptions are called to play an important role. In this contribution we extend the work presented in N. Suárez {\it et al.}, Phys.~Rev. A {\bf 95}, 033415 (2017), to three-center molecular targets. Additionally, we incorporate a more accurate description of the molecular ground state, employing information extracted from quantum chemistry software packages. This step forward allows us to include, in a detailed way, both the molecular symmetries and nodes present in the high-occupied molecular orbital. We are able to, on the one hand, keep our formulation as analytical as in the case of diatomics, and, on the other hand, to still give a complete description of the underlying physics behind the above-threshold ionization process. The application of our approach to complex multicenter - with more than 3 centers, targets appears to be straightforward.
Based on the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in a two-color laser field with infrared (IR) and extreme ultraviolet (XUV) frequencies, where the photon energy of the XUV laser is close to or larger than the atomic ionization threshold. By using the channel analysis, we find that the two laser fields play different roles in an ionization process, where the XUV laser determines the ionization probability by the photon number that the atom absorbs from it, while the IR laser accelerates the ionized electron and hence widens the electr…
The direct above-threshold ionization (ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet (IR+XUV) laser fields is investigated by the frequency-domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ioni…
We report on the observation of discrete structures in the electron energy distribution for strong field double ionization of Argon at 394 nm. The experimental conditions were chosen in order to ensure a non-sequential ejection of both electrons with an intermediate rescattering step. We have found discrete ATI (above-threshold ionization) like peaks in the sum energy of both electrons, as predicted by all quantum mechanical calculations. More surprisingly however is the observation of two ATI combs in the energy distribution of the individual electrons.
We perform a detailed analysis of how high-order harmonic generation (HHG) and above-threshold ionization (ATI) can be controlled by a time-delayed attosecond-pulse train superposed to a strong, near-infrared laser field. In particular we show that the high-harmonic and photoelectron intensities, the high-harmonic plateau structure and cutoff energies, and the ATI angular distributions can be manipulated by changing this delay. This is a direct consequence of the fact that the attosecond pulse train can be employed as a tool for constraining the instant an electronic wave packet is ejected in …
Fully quantum treatment explicitly presents the high harmonic generation as a three-stage process: above threshold ionization (ATI) is followed by the continuum electron propagation in a laser field and subsequent stimulated recombination back into the initial state. The contributions of all ATI channels add up coherently. All three stages of the process are described by simple, mostly analytical expressions. A very good quantitative agreement with the previous calculations on the harmonic generation by H$^-$ ion is demonstrated, thus supplementing the conceptual significance of the theory wit…
Above-threshold ionization (ATI) results from strong field laser-matter interaction and it is one of the fundamental processes that may be used to extract electron structural and dynamical information about the atomic or molecular target. Moreover, it can also be used to characterize the laser field itself. Here, we develop an analytical description of ATI, which extends the theoretical Strong Field Approximation (SFA), for both the direct and re-scattering transition amplitudes in atoms. From a non-local, but separable potential, the bound-free dipole and the re-scattering transition matrix e…
We investigate the physical processes in which an electron, upon return to its parent ion, promotes a second electron to an excited state, from which it subsequently tunnels. Employing the strong-field approximation and saddle-point methods, we perform a detailed analysis of the dynamics of the two electrons, in terms of quantum orbits, and delimit constraints for their momentum components parallel to the laser-field polarization. The kinetic energy of the first electron, upon return, exhibits a cutoff slightly lower than $10U_p$, where $U_p$ is the ponderomotive energy, as in rescattered abov…
We present theoretical studies of above threshold ionization (ATI) produced by spatially inhomogeneous fields. This kind of field appears as a result of the illumination of plasmonic nanostructures and metal nanoparticles with a short laser pulse. We use the time-dependent Schrödinger equation (TDSE) in reduced dimensions to understand and characterize the ATI features in these fields. It is demonstrated that the inhomogeneity of the laser electric field plays an important role in the ATI process and it produces appreciable modifications to the energy-resolved photoelectron spectra. In fact, o…
We present both full quantum mechanical and semiclassical calculations of above threshold ionization (ATI) of a hydrogen atom in the tunneling regime by a few-cycle linearly polarized infrared laser pulse. As a quantum treatment, we applied the direct integration of the time dependent Schrödinger equation (TDSE). In the semiclassical approximation (SCA), it is assumed that wavepacket propagation in the post-tunneling process can be well described within the classical framework. With these two methods, we analyze the similarities and deviations for ionization of the hydrogen atom. We found that…
Quantum calculations of tunneling in strong-field ionization (SFI) predict intricate momentum distributions due to sub-laser-cycle attosecond electron dynamics. These are obscured in most experiments by the dominance of inter-cycle interference patterns which are the hallmark of above-threshold ionization (ATI). Highly controlled 1- to 2-cycle laser pulses produce less inter-cycle interference but cannot accurately recreate the sub-cycle features produced by uniform cycle calculations due to the effect of the carrier envelope of the pulse. We present a simple and effective technique to recover…
We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in Helium prepared in an excited $p$ state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using ab initio B-spline Algebraic Diagrammatic Construction (ADC), and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the Strong-Field Approximation and the Coulomb-Quantum Orbit Strong-Field Approximation (CQSFA), we find that these specific physical mechanisms leave signifi…
Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical…
The collision-ionization mechanism of nonsequential double ionization (NSDI) process in IR+XUV two-color laser fields [\PRA \textbf{93}, 043417 (2016)] has been investigated by us recently. Here we extend this work to study the collision-excitation-ionization (CEI) mechanism of NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the XUV photon energy is smaller than the ionization threshold of the He$^+$ ion, and the momentum spectrum shows complex interference patterns and symmetrical str…
We perform a detailed analysis of above threshold ionization (ATI) in atoms within the strong field approximation (SFA) by considering spatially inhomogeneous monochromatic laser fields. The locally enhanced field induced by resonance plasmons is an example for such inhomogeneous fields. We investigate how the individual pairs of quantum orbits contribute to the photoelectron spectra and the angular electron momentum distributions. We demonstrate that the quantum orbits have a very different behavior in the spatially inhomogeneous field when compared to the homogeneous field. In the case of in…
We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semi-analytical, Coulomb-corrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories, and we identify a set of orbits which, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard S…
Within a semiclassical description of above-threshold ionization (ATI) we identify the interplay between intracycle and intercycle interferences. The former is imprinted as a modulation envelope on the discrete multiphoton peaks formed by the latter. This allows to unravel the complex interference pattern observed for the full solution of the time-dependent Schrödinger equation (TDSE) in terms of diffraction at a grating in the time domain. These modulations can be clearly seen in the dependence of the ATI spectra on the laser wavelength. Shifts in energy modulation result from the effect of t…
We present intensity-resolved above threshold ionization (ATI) spectra of xenon using an intensity scanning and deconvolution technique. Experimental data were obtained with laser pulses of 58 fs and central wavelength of 800 nm from a chirped-pulse amplifier. Applying a deconvolution algorithm, we obtained spectra that have higher contrast and are in excellent agreement with characteristic 2 $U_p$ and 10 $U_p$ cutoff energies contrary to that found for raw data. The retrieved electron ionization probability is consistent with the presence of a second electron from double ionization. This reco…
We report fully differential photoelectron spectra from an {\it ab-inito} coupled channels treatment of CO$_2$. Photoionization by laser pulses centered at 400 nm and 800 nm wavelength are considered, with arbitrary molecular alignment and polarization (linear and elliptic). Calculations reveal significant excited state channel contributions that are, at certain molecular orientations, an order of magnitude larger than the ground state channel in the rescattering plateau. Partial wash out of the multiphoton structure in the ATI spectra and of the nodal features in angle resolved spectra is obs…
Using the frequency-domain theory, the high-order above threshold ionization (HATI) of a molecule is treated as a two-step transition: an above threshold ionization (ATI) followed by a laser-assisted collision (LAC). It is found that the HATI spectrum carries three pieces of information: the fingerprint of the molecular wave function lying in the ATI transition, the geometry structure of the molecule lying in the potential scattering between two plane waves, and the interaction between the ionized electron and the laser field lying in a phase factor in the LAC transition, where the phase facto…
We present results of high-resolution experiments on single ionization of He, Ne and Ar by ultra-short (25 fs, 6 fs) 795 nm laser pulses at intensities 0.15-2.0x10^15 W/cm^2. We show that the ATI-like pattern can survive deep in the tunneling regime and that the atomic structure plays an important role in the formation of the low-energy photoelectron spectra even at high intensities. The absence of ponderomotive shifts, the splitting of the peaks and their degeneration for few-cycle pulses indicate that the observed structures originate from a resonant process.
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam …
The spin polarization of electrons from multiphoton ionization of Xe by 395 nm circularly polarized laser pulses at $6\cdot10^{13}$ W/cm$^2$ has been measured. At this photon energy of 3.14 eV the above threshold ionization peaks connected to Xe$^+$ ions in the ground state ($J=3/2$, ionization potential $I_p=12.1$ eV) and the first exicted state ($J=1/2$, $I_p=13.4$ eV) are clearly separated in the electron energy distribution. These two combs of ATI peaks show opposite spin polarizations. The magnitude of the spin polarization is a factor of two higher for the $J=1/2$ than for the $J=3/2$ fi…
In this paper we report the theoretical results obtained for partial ionization yields and the above-threshold ionization (ATI) spectra of Magnesium in a Ti:sapphire laser field (804 nm) in the range of short pulse duration (20-120 fs). Ionization yield, with linearly polarized light for a 120 fs laser pulse, is obtained as a function of the peak intensity motivated by recent experimental data \cite{gillen:2001}. For this, we have solved the time-dependent Schrödinger equation nonperturbatively on a basis of discretized states obtained with two different methods; one with the two-electron wave…
A theory for the many-electron multi-photon process is presented. It is shown that after single-electron excitation into some level in the continuum (ATI) an inelastic collision of the excited electron with the parent atomic particle can result in an excitation of the ion. It may be the continuum state excitation giving the doubly charged ion or the discrete state which also greatly enhances the doubly charged ion production. The probability of these phenomena greatly exceeds that of the direct ionization of a single-charged ion. The single-electron ATI makes possible the two-electron process …
We study the dynamics of the Potassium atom in the mid-infrared, high intensity, short laser pulse regime. We ascertain numerical convergence by comparing the results obtained by the direct expansion of the time-dependent Schroedinger equation onto B-Splines, to those obtained by the eigenbasis expansion method. We present ionization curves in the 12-, 13-, and 14-photon ionization range for Potassium. The ionization curve of a scaled system, namely Hydrogen starting from the 2s, is compared to the 12-photon results. In the 13-photon regime, a dynamic resonance is found and analyzed in some de…
A versatile semiclassical approximation for intense laser-atom processes is presented. This uniform approximation is no more complicated than the frequently-used multi-dimensional saddle-point approximation and far superior, since it applies for all energies, both close to as well as away from classical cutoffs. In the latter case, it reduces to the standard saddle-point approximation. The uniform approximation agrees accurately with numerical evaluations for potentials, for which these are feasible, and constitutes a practicable method of calculation in general. The method is applied to the c…
Calculations on the dynamics of ions and electrons in near-infrared laser fields at intensities up to $3 \times 10^{23}$ W/cm$^2$ are presented. We explore the acceleration of ions in a laser focus by conservation of canonical momentum during ionization events and by the ponderomotive force in the f/1 focal geometry required to reach such intensity. At intensity exceeding 10$^{23}$ W/cm$^2$, highly charged ions are expelled from the laser focus before they can interact with the laser pulse at peak intensity, decreasing the predicted ionization yields of deeply-bound states. We consider the int…
We analyze the contribution of the quiver kinetic energy acquired by an electron in an oscillating electric field to the energy balance in atomic ionization processes by a short laser pulse. Due to the time dependence of this additional kinetic energy, a temporal average is assumed to maintain a stationary energy conservation rule. This rule is used to predict the position of the peaks observed in the photo electron spectra (PE). For a flat top pulse envelope, the mean value of the quiver energy over the whole pulse leads to the concept of ponderomotive energy $U_{p}$. However for a short puls…
Fully quantum treatment explicitly presents the high harmonic generation as a three-step process: (i) above threshold ionization (ATI) is followed by (ii) electron propagation in a laser-dressed continuum. Subsequently (iii) stimulated (or laser assisted) recombination brings the electron back into the initial state with emission of a high-energy photon. Contributions of all ATI channels add up coherently. All three stages of the process are described by simple, mostly analytical expressions that allow a detailed physical interpretation. A very good quantitative agreement with the previous cal…
Using the recently developed Coulomb Quantum Orbit Strong-Field Approximation (CQSFA), we perform a systematic analysis of several features encountered in above-threshold ionization (ATI) photoelectron angle-resolved distributions (PADs), such as side lobes, and intra- and intercycle interference patterns. The latter include not only the well-known intra-cycle rings and the near-threshold fan-shaped structure, but also previously overlooked patterns. We provide a direct account of how the Coulomb potential distorts different types of interfering trajectories and changes the corresponding phase…
We provide approximate analytic expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions (PADs). These analytic expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit stron…
We analyze interference processes in atomic ionization induced by a two-color laser with fundamental frequency $ω$ and its second harmonic $2ω$. The interplay between inter- and intracycle interference processes give rise to multiphoton peaks which can be named as main or ATI peaks and sidebands, in analogy to the well-known RABBIT (reconstruction of attosecond harmonic beating by interference of two-photon transitions). We use the saddle point approximation (SPA) to extract the complex ionization times of the interfering electron trajectories. Changing the relative phase between the two color…
We investigate the process of phase-controlled high-order above-threshold photoemission from sharp metallic nanotips under bichromatic laser fields. Experimental photoelectron spectra resulting from two-color excitation with a moderately intense near-infrared fundamental field (1560 nm) and its weak second harmonic show a strong sensitivity on the relative phase and clear indications for a plateau-like structure that is attributed to elastic backscattering. To explore the relevant control mechanisms, characteristic features, and particular signatures from near-field inhomogeneity, we performed…
We analyze strong field atomic dynamics semiclassically, based on a full time-dependent description with the Hermann-Kluk propagator. From the properties of the exact classical trajectories, in particular the accumulation of action in time, the prominent features of above threshold ionization (ATI) and higher harmonic generation (HHG) are proven to be interference phenomena. They are reproduced quantitatively in the semiclassical approximation. Moreover, the behavior of the action of the classical trajectories supports the so called strong field approximation which has been devised and postula…
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, Above-Threshold Ionization, and Non-Sequential Multielectron Ionization. "Simple man's models" provide, both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation, and the motivation for …
