The time-dependent Schrödinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the numerical ab initio results with classical orbit theory is facilitated. Integration over position space yields directly the photoelectron spectra so that the various pathways contributing to a certain energy in the photoelectron spectra can be established in an unprecedented direct and transparent way.
Few-cycle pulses of intense 800 nm light are used to probe ionization and dissociation of carbon disulfide in the intensity and temporal regime where rescattering is expected to dominate the laser-molecule interaction. The wavepacket of the rescattered electron destructively interferes with the anti-bonding $π$-orbital of CS$_2^+$ such that rescattering is effectively "switched off". Direct signature of enhanced ionization being "switched off" in the ultrashort domain is also obtained. Consequently, dissociation becomes an almost non-existent channel when few-cycle pulses are used, with only l…
We present the first 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 {\it ab initio} simulation over a wide range of laser intensities and electron energies.
Nonsequential double ionization (NSDI) of helium in an intense few-cycle laser pulse is investigated by applying the three-dimensional semi-classical re-scattering method. It is found that the momentum distribution of He$^{2+}$ shows a single-double-single peak structure as the pulse intensity increases. According to the different mechanisms dominating the NSDI process, the laser intensity can be classified into three regimes where the momentum distribution of He$^{2+}$ exhibits different characteristics. In the relatively high intensity regime, an NSDI mechanism named the "laser-assisted coll…
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 (LES). Here, we demonstrate by combined quantum and classical simulations that a small time-varying spatial dependence in the laser electric field creates a p…
We investigate numerically effects related to ``single-cycle'' ionization of dense matter by an ultra-short laser pulse. The strongly non-adiabatic response of electrons leads to generation of a megagauss steady magnetic field in laser-solid interaction. By using two-beam interference, it is possible to create periodic density structures able to trap light and to generate relativistic ionization fronts
We investigate the interwoven dynamic evolutions of neutral nitrogen molecules together with nitrogen ions created through transient tunnel ionization in an intense laser field. By treating the molecules as open quantum systems, it is found that considering real-time injection of ions and strong couplings among their electronic states, nitrogen molecular ions are primarily populated in the electronically excited states, rather than staying in the ground state as predicted by the well-known tunneling theory. The unexpected result is attributed to sub-cycle switch-on of time-dependent polarizati…
We report on tunnel ionization of Xe by 2-cycle, intense, infrared laser pulses and its dependence on carrier-envelope-phase (CEP). At low values of optical field ($E$), the ionization yield is maximum for cos-like pulses with the dependence becoming stronger for higher charge states. At higher $E$-values, the CEP dependence either washes out or flips. A simple phenomenological model is developed that predicts and confirms the observed results. CEP effects are seen to persist for 8-cycle pulses. Unexpectedly, electron rescattering plays an unimportant role in the observed CEP dependence. Our r…
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 report on the unambiguous observation of the sub-cycle ionization bursts in sequential strong-field double ionization of H$_2$ and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase in combination with multi-particle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state specific Coulomb-distortions on emitted electrons in polyatomic molecules.
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale \emph{inversely} with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both 3D classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schrödinger equation. More surprisingly, t…
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 use classical electron ensembles and the aligned-electron approximation to examine the effect of laser pulse duration on the dynamics of strong-field double ionization. We cover the range of intensities $10^{14}-10^{16} W/cm^2$ for the laser wavelength 780 nm. The classical scenario suggests that the highest rate of recollision occurs early in the pulse and promotes double ionization production in few-cycle pulses. In addition, the purely classical ensemble calculation predicts an exponentially decreasing recollision rate with each subsequent half cycle. We confirm the exponential behavior …
We provide theoretical investigations of the response of the Ar and H atoms to an intense elliptically polarized few-cycle laser pulse, as a function of light ellipticity. The time-dependent Schr{ö}dinger equation describing the least-bound electron is solved numerically, and differential quantities such as the momentum distribution, the electron density in the continuum, and the above-threshold ionization spectra are computed. These quantities provide insight into the ionization dynamics and the electron rescattering process as a function of light ellipticity, and reveal great similarities be…
This paper concerns the theory of non-recollisional ionization or detachment of atoms or ions by intense few-cycle pulses. It is shown that in certain conditions of pulse duration, peak intensity and carrier-envelope phase, the ionization probability integrated over ejection angle varies almost periodically with energy, with a period roughly equal to the photon energy for slow enough outgoing electrons. This modulation is found both in calculations based on the strong field approximation (SFA) and in ab initio time-dependent calculations. It is explained as resulting from the interference betw…
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
The interaction of a short, few-cycle light pulse and an atom which is prepared initially in a superposition of two stationary states is shown to exhibit strong signatures of atomic coherence. For a given waveform of the laser pulse, appropriate quantum mechanical relative phase between the constituents of the initial superposition can increase the ionization probability by a factor of three. A similarly strong effect can be observed when the waveform of the ionizing pulse is changed. These results allow for intuitive explanations, which are in agreement with the numerical integration of the t…
We investigate differential electron distributions in nonsequential double ionization (NSDI) with linearly polarized, few-cycle pulses, using a classical model based on a laser-assisted inelastic $(e^-,2e^-)$ rescattering mechanism. We show that these yields, as functions of the momentum components parallel to the laser polarization, are highly asymmetric, and strongly influenced by the absolute phase, i.e., the phase difference between the carrier oscillation of a few-cycle laser pulse and its envelope. Indeed, around a critical phase, such distributions change their sign in a radical fashion…
Attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions (PMDs). These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfering pairs of electron orbits by performing a differential Fourier analysis on the measured momentum spectrum. We identify electron holograms formed by trajectory pairs whose ionization times are separ…
We report on three-dimensional (3D) electron momentum distributions from single ionization of helium by a laser pulse consisting of two counterrotating circularly polarized fields (390 nm and 780 nm). A pronounced 3D low energy structure and sub-cycle interferences are observed experimentally and reproduced numerically using a trajectory based semi-classical simulation. The orientation of the low energy structure in the polarization plane is verified by numerical simulations solving the time dependent Schrödinger equation.
A three-dimensional semiclassical model is used to study double ionization of Ar when driven by a near-infrared and near-single-cycle laser pulse for intensities ranging from 0.85$\times$10$^{14}$ W/cm$^{2}$ to 5$\times$10$^{14}$ W/cm$^{2}$. Asymmetry parameters, distributions of the sum of the two electron momentum components along the direction of the polarization of the laser field and correlated momenta are computed as a function of intensity and of the carrier envelope phase. A very good agreement is found with recently obtained results in kinematically complete experiments employing near…
We demonstrate sub-cycle control of frustrated double ionization (FDI) in the two-electron triatomic molecule D$_3^+$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We control FDI triggered by a strong near-infrared laser field with a weak mid-infrared laser field. This control as a function of the time delay between the two pulses is demonstrated when the FDI probability and the distribution of the momentum of the escaping electron along the mid-infra…
Joint electron-ion energy spectra for the dissociative ionization of a model H$_2^+$ in few-cycle, infrared laser pulses are calculated via the numerical ab initio solution of the time-dependent Schrödinger equation. A strong, pulse-dependent modulation of the ionization probability for certain values of the protons' kinetic energy (but almost independent of the electron's energy) is observed. With the help of models with frozen ions, this feature---which mistakenly might be attributed to vibrational excitations---is traced back to the transient population of electronically excited states, fol…
Strong-field ionization with few-cycle, mid-infrared laser pulses induces a localized ionization followed by long-lasting charge migration in halogenated organic molecules
In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or non-geometric. The observ…
During multi-photon ionization of an atom it is well understood how the involved photons transfer their energy to the ion and the photoelectron. However, the transfer of the photon linear momentum is still not fully understood. Here, we present a time-resolved measurement of linear momentum transfer along the laser pulse propagation direction. Beyond the limit of the electric dipole approximation we observe a time-dependent momentum transfer. We can show that the time-averaged photon radiation pressure picture is not generally applicable and the linear momentum transfer to the photoelectron de…
We study theoretically the dipole radiation of a hydrogen atom driven by an intense sub-cycle pulse. The time-dependent Schrödinger equation for the system is solved by ab initio calculation to obtain the dipole response. Remarkably, a narrowband emission lasting longer than the driving pulse appears at a frequency just above the ionization threshold. An additional calculation using the strong field approximation also recovers this emission, which suggests that it corresponds to the oscillation of nearly-bound electrons that behave similarly to Rydberg electrons. The predicted phenomenon is un…
We theoretically study dissociative ionization of H$_2^+$ exposed to strong linearly polarized few-cycle visible, near-infrared and midinfrared laser pulses. We find rich energy-sharing structures in the combined electron and nuclear kinetic energy spectra with features that are a priori at odds with simple energy conservation arguments. We explain the structures as interferences between wave packets released during different optical cycles, and during the same optical cycle, respectively. Both inter- and intracycle interference structures are clearly visible in the joint energy spectra. The s…
We perform theoretical investigations of laser-induced nonsequential double ionization with few cycle pulses, with particular emphasis on the dependence of the electron-momentum distributions on the carrier-envelope phase. We focus on the recollision-excitation with subsequent tunneling ionization (RESI) pathway, in which a released electron, upon return to its parent ion, gives part of its kinetic energy to promote a second electron to an excited state. At a subsequent time, the second electron is freed through tunneling ionization. We show that the RESI electron-momentum distributions vary d…
We have investigated the ionization of the H atom by intense few-cycle laser pulses, in particular the intra-pulse interference effects, and their dependence on the carrier-envelope phase (CEP) of the laser pulse. In the final momentum distribution of the continuum electrons the imprint of two types of intra-pulse interference effects can be observed, namely the temporal and spatial interference. During the spatial interference electronic wave packets emitted at the same time, but following different paths interfere leading to an interference pattern measurable in the electron spectra. This ca…
We investigate the carrier-envelope phase and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above-threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750\,nm is varied in a range between $0.7 \times 10^{14}$ and $\unit[5.5 \times 10^{14}]{W/cm^2}$. Our measurements reveal a prominent maximum in the carrier-envelope phase-dependent asymmetry at photoelectron energies of 2\,$U_\mathrm{P}$ ($U_\mathrm{P}$ being the ponderomotive potential), that is persistent over the entire intensity ra…
The sub-cycle dynamics of electrons driven by strong laser fields is central to the emerging field of attosecond science. We demonstrate how the dynamics can be probed through high-order harmonic generation, where different trajectories leading to the same harmonic order are initiated at different times, thereby probing different field strengths. We find large differences between the trajectories with respect to both their sensitivity to driving field ellipticity and resonant enhancement. To accurately describe the ellipticity dependence of the long trajectory harmonics we must include a sub-c…
Elliptically polarized laser pulses (EPLPs) are widely applied in many fields of ultrafast sciences, but the ellipticity~($\varepsilon$) has never been in situ measured in the interaction zone of the laser focus. In this work, we propose and realize a robust scheme to retrieve the $\varepsilon$ by temporally overlapping two identical counter-rotating EPLPs. The combined linearly electric field is coherently controlled to ionize Xe atoms by varying the phase delay between the two EPLPs. The electron spectra of the above-threshold ionization and the ion yield are sensitively modulated by the pha…
The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong-field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved Simpleman model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the photoelectr…
Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model for predicting the bandwidth of ionic states that can be coherently prepared by SFI. This bandwidth is given by the Fourier-transformed sub-cycle SFI rate and decreases considerably with increasing central wavelength of the ionizing pulse. Many-body calculations based on time-dependent configuration-interaction singles (TDCIS) quantitatively support this result and reveal an addit…
Carrier envelope phase (CEP) stabilized 5 fs and 22 fs pulses of intense 800 nm light are used to probe the strong-field ionization dynamics of multielectron entities, xenon and carbon disulfide. We compare ion yields obtained with and without CEP-stabilization: with 8-cycle (22 fs) pulses, Xe$^{6+}$ yields are suppressed (relative to Xe$^+$ yields) by between 30% and 50%, depending on phase, reflecting the phase dependence of non-sequential ionization and its contribution to the formation of higher charge states. On the other hand, ion yields for Xe$^{q+}$ ($q$=2-4) with CEP-stablized pulses …
We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum-mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of "quantum orbits", which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymm…
Electrons in atoms and molecules can not react immediately to the action of intense laser field. A time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum emerges. This lag characterizes the response time of the electronic wave function to the strong-field ionization event and has important effects on subsequent ultrafast dynamics of the ionized electron. The absolute time lag is not accessible in experiments. Here, a calibrated attoclock procedure, which is related to a simple Coulomb-induced temporal correction to electron trajectories, is propo…
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…
Ionization and excitation of water molecules in intense laser pulses is studied theoretically by solving the three-dimensional time-dependent electronic Schrödinger equation within the single-active-electron approximation. The possibility to image orbital densities by measurement of the orientation-dependent ionization of H2O in few-cycle, 800nm linear-polarized laser pulses is investigated. While the highest-occupied molecular orbital 1b1 is found to dominate the overall ionization behavior, contributions from the energetically lower lying 3a1 orbital dominate the ionization yield in the noda…
Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory and experimental analysis: unit-cell averaging and time-filtering data and simulations. Together these suppress ATI rings and enable an unprecedented highly-detailed quantitative match between strong-fi…
When intense laser pulses release correlated electrons, the time delay between the ionizations may last more than one laser cycle. We show that this "Recollision-Excitation with Subsequent Ionization" pathway originates from the inner electron being promoted to a sticky region by a recollision where it is trapped for a long time before ionizing. We identify the mechanism which regulates this region, and predict oscillations in the double ionization yield with laser intensity.
We investigate laser-induced nonsequential double ionization by a polarization-gated laser pulse, constructed employing two counter-rotating circularly polarized few cycle pulses with a time delay $T_{d}$. We address the problem within a classical framework, and mimic the behavior of the quantum-mechanical electronic wave packet by means of an ensemble of classical electron trajectories. These trajectories are initially weighted with the quasi-static tunneling rate, and with suitably chosen distributions for the momentum components parallel and perpendicular to the laser-field polarization, in…
We present the results of the detailed experimental study of multiple ionization of Ne and Ar by 25 and 7 fs laser pulses. For Ne the highly correlated "instantaneous" emission of up to four electrons is triggered by a recollisional electron impact, whereas in multiple ionization of Ar different mechanisms, involving field ionization steps and recollision-induced excitations, play a major role. Using few-cycle pulses we are able to suppress those processes that occur on time scales longer than one laser cycle.
Isolated attosecond pulses (IAPs) produced through laser-driven high-harmonic generation (HHG) hold promise for unprecedented insight into biological processes via attosecond x-ray diffraction with tabletop sources. However, efficient scaling of HHG towards x-ray energies has been hampered by ionization-induced plasma generation impeding the coherent buildup of high-harmonic radiation. Recently, it has been shown that these limitations can be overcome in the so-called 'overdriven regime' where ionization loss and plasma dispersion strongly modify the driving laser pulse over small distances, a…
Chiral molecules ionized by circularly polarized fields produce a photoelectron current orthogonal to the polarization plane. This current has opposite directions for opposite enantiomers and provides an extremely sensitive probe of molecular handedness. Recently, such photoelectron currents have been measured in the strong-field ionization regime, where they may serve as an ultrafast probe of molecular chirality. Here we provide a mechanism for the emergence of such strong-field photoelectron currents in terms of two propensity rules that link the properties of the initial electronic chiral s…
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 1-d 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 …
We present a theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an IR laser with both fields linearly polarized in the same direction. In particular, we study the energy distribution of photoelectrons emitted perpendicularly to the polarization direction. By means of a very simple semiclassical model which considers electron trajectories born at different ionization times, the electron energy spectrum can be interpreted as the interplay of Intra and Intercycle interferences. The intracycle interference pattern stems from the coherent superposition of fo…
Intense attosecond magnetic field pulses are predicted to be produced by intense few cycle circularly polarized UV pulses. Numerical solutions of the time dependent Schrödinger equation for H$_2^+$ are used to study the dynamical process. Spiralling attosecond circular electron wave packets are created with nanometer molecular dimensions, thus generating magnetic fields of several tens of Teslas ($10^5$ Gauss). Simulations show that the induced magnetic field is critically dependent on the pulse wavelength $λ$ and pulse duration $nτ$ ($n$ number of cycle) as predicted by a classical model. For…
We show through simulation that quantum interference in non-sequential double ionization can be used to control the recollision 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 anti-correlated 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 indisting…
We study the ionization of atomic hydrogen in the direction of polarization due to a linearly polarized XUV pulse in the presence a strong field IR. We describe the photoelectron spectra as an interference problem in the time domain. Electron trajectories steming from different optical laser cycles give rise to intercycle interference energy peaks known as sidebands. These sidebands are modulated by a grosser structure coming from the intracycle interference of the two electron trajectories born during the same optical cycle. We make use of a simple semiclassical model which offers the possibi…
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…
Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schr{ö}dinger equation in high-harmonic generation processes from excited states of He$^+$. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He$^+$ ground state and is o…
A theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an IR laser is presented. Well-established theories are usually used to describe the problem of laser assisted photoelectron effect. However, the well-known soft-photon approximation firstly posed by Maquet et al in Journal of Modern Optics 54, 1847 (2007) and Kazansky's theory in Phys. Rev. A 82, 033420 (2010) completely fails to predict the electron emission prependicularly to the polarization direction. Making use of a simple semiclassical model, we study the angle-resolved energy distribution of p…
