The limit of decreasing laser frequency can not be considered independently from nondipole effects due to increase in the laser-induced continuum electron speed in this limit. Therefore, in this work, tunneling ionization in the adiabatic limit is considered for an effective field that includes effects beyond the electric-dipole term to first order in $1/c$, with $c$ the speed of light. The nondipole term describes the interaction resulting from the electric dipole-induced velocity of the electron and the magnetic field component of the laser. The impact of this term on the ionization rate, tunnel exit point, momentum at the tunnel exit and electron dynamics is discussed. In the appropriate limit, the results of a nondipole strong-field approximation approach and those of the strict adiabatic limit, where time and field strength are parameters, are consistent. The nondipole strong-field approximation approach is used to identify nonadiabatic modifications of the initial conditions. The results open up an avenue to include nondipole effects in the initial tunneling ionization step in semiclassical models of strong-field and attosecond physics.
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…
The nondipole under-the-barrier dynamics of the electron during strong-field tunneling ionization is investigated, examining the role of the Coulomb field of the atomic core. The common analysis in the strong field approximation is consequently generalised to include the leading light-front non-dipole Coulomb corrections and demonstrates the counter-intuitive impact of the sub-barrier Coulomb field. Despite its attractive nature, the sub-barrier Coulomb field increases the photoelectron nondipole momentum shift along the laser propagation direction, involving a strong dependence on the laser f…
We consider atomic strong-field ionization in the long-pulse limit for linearly polarized infrared laser fields. We show how nondipole effects in the plane formed by the propagation and polarization directions lead to (i) a shift of the origin of the rings describing the energetically allowed final electron momenta for individual above-threshold ionization channels and (ii) a redistribution in the continuum population on each ring.
We employ a recently developed three-dimensional semiclassical model to identify nondipole effects in triple ionization of Ne driven by infrared laser pulses at intensities where electron-electron correlation prevails. This model fully accounts for the Coulomb interaction of each electron with the core and avoids artificial autoionization by employing effective Coulomb potentials to describe the interaction between bound electrons (ECBB). Using the ECBB model, we identify a prominent signature of nondipole effects. Namely, the component along the direction of light propagation of the average s…
We investigate the ionization dynamics of atoms irradiated by an intense laser field using a semiclassical model that includes magnetic Lorentz force in the rescattering process. We find that, the electrons tunneled with different initial transverse momenta (i.e., perpendicular to the instantaneous electric field direction) distributed on a specific circle in the momentum plane can finally converge to the same transverse momentum after experiencing Coulomb forward scattering. These electron trajectories lead to a bright spot structure in the 2D transverse momentum distribution, and particularl…
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 non-dipole effect is not the only non-dipole effect in strong-field ionization. We find that an electric non-dipole effect arises that is due to the position dependence of the electric field and which can be understood in analogy to the Do…
The double-slit interference in single-photon ionization of the diatomic molecular ion $\mathrm{H}_2^+$ is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned $\mathrm{H}_2^+$ and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from $\mathrm{H}_2^+$: (i) the photon-momentum transfer and (ii) the finite speed of light. While both effects could modify the maxima of the interference fringes, we show tha…
A general method for solving numerically the time-dependent Schrödinger equation, that is based on the Suzuki-Trotter scheme with the split-step Fourier approach, is introduced. The method relies on a Hamiltonian decomposition, where except of the components depending exclusively on the momentum or on the position operators, there are also terms depending on both momentum and position operators in particular configurations. We demonstrate that, for as long as the latter does not depend on noncommuting coordinates of the momentum and position operators, nondipole effects in laser-matter interac…
The exact nondipole minimal-coupling Hamiltonian for an atom interacting with an explicitly time- and space-dependent laser field is transformed into the rest frame of a classical free electron in the laser field, i.e., into the Kramers-Henneberger frame. The new form of the Hamiltonian is used to study nondipole effects in the high-intensity, high-frequency regime. Fully three dimensional nondipole {\it ab initio} wavepacket calculations show that the ionization probability may decrease for increasing field strength. We identify a unique signature for the onset of this dynamical stabilization…
Nondipole effects are ubiquitous and crucial in light-matter interaction. However, they are too weak to be directly observed. In strong-field physics, motion of electrons is mainly confined in transverse plane of light fields, which suppresses the significance of nondipole effects. Here, we present a theoretical study on enhancing and controlling the nondipole effect by using the synthesized two perpendicularly propagating laser fields. We calculate the three-dimensional photoelectron momentum distributions of strong-field tunneling ionization of hydrogen atoms using the classical trajectory M…
We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the classical cutoff is found to be vastly different from that below the cutoff. A V-shape structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analy…
The magnetic-field effect of the laser pulse is investigated in laser-assisted XUV ionization. By numerically solving the three-dimensional time-dependent Schrödinger equation, we find that the photoelectron momentum distribution is distorted by the magnetic-field effect of the IR streaking field. It results in a transverse-momentum- and time-delay-dependent longitudinal photoelectron momentum shift, which is further analytically confirmed by employing the nondipole corrected strong field approximation. We also demonstrate that the magnetic field does not affect the time shift retrieved from t…
We investigate the influence of relativistic nondipole effects on the photoelectron spectra of argon, particularly in the low kinetic energy region (0 eV - 5 eV). In our experiment, we use intense linearly polarised 800 nm laser pulse to ionise Ar from a jet and we record photoelectron energy and momentum distributions using a reaction microscope (REMI). Our measurements show that nondipole effect can cause an energy-dependent asymmetry along the laser propagation direction in the photoelectron energy and momentum spectra. Model simulation based on time-dependent Dirac equation (TDDE) can repr…
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…
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. Linear momentum transfer is a unique signature of the laser-atom interaction beyond its dipolar limit. Here, we present a decomposition of the subcycle time-resolved linear momentum transfer in term of its multipolar components. We show that the magnetic dipole contribution dominates the linear momentum transfer durin…
The analytical R-matrix (ARM) theory has been known for an efficient description of the Coulomb effects of the atomic core in strong-field ionization in the nonrelativistic regime. We generalize the ARM theory into the relativistic domain aiming at the application to strong-field ionization of highly-charged ions in ultrastrong laser fields. Comparison with the relativistic Coulomb-corrected strong field approximations (SFA) is provided, highlighting the advantages and disadvantages. The weakly relativistic asymptotics and its accordance with the nondipole Coulomb-corrected SFA are examined. A…
A motion of a classical free charge in an electromagnetic plane wave can be found exactly in a fully relativistic case. We have found an approximate non-parameter form of the suitable equations of motion. In a linearly polarized wave, in the simplest frame of reference, the charge moves along the well-known "figure-8" path. We have numerically calculated the Lorentz force acting on the charge as a function of time. In virtue of this, for the low frequency ionization (or detachment) rate, we discuss a manifestation of nondipole and relativistic effects.
The generation of electron vortex states in ionization by intense and short laser pulses is analyzed under the scope of the lowest-order Born approximation. For near infrared laser fields and nonrelativistic intensities of the order of $10^{16}$~W/cm$^2$, we show that one has to modify the nonrelativistic treatment of ionization by accounting for recoil and mass relativistic corrections. By using the corrected quasi-relativistic theory, the requirements for the observation of electron vortex states with non-negligible probability and large topological charge are determined.
Classically allowed transport is shown to compete with quantum tunneling during the ionization of atoms by ultrashort and intense laser pulses, despite Keldysh parameters smaller than unity. This is done by comparing exact probability densities with the ones obtained from purely classical propagation using the Truncated Wigner Approximation. Not only is classical transport capable of moving trajectories away from the core, but it can also furnish ionization probabilities of the same order as the quantum ones for intensities currently employed in experiments. Our results have implications rangi…
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 continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the fir…
When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first order beyond-dipole correction to the H…
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…
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…
A simple model for sequential multiphoton ionization by ultra-intense x-rays is presented. The derived scaling of the ion yield with pulse energy quantitatively reproduces the experimental data, which shows that the ion yield increases according to the "power law" behavior typical of multiphoton ionization, followed by saturation at high pulse energies. The calculated average time interval between ionizations for producing ions at a certain charge state is found to be proportional to the pulse duration and independent of all other x-ray pulse parameters. This agrees with previous studies where…
Ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong-field quantum electrodynamics. Our main focus is on the formation of ionization supercontinua. More specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. These supercontinua extend over hundreds of driving photon energies, thus corresponding to high-order nonlinear processes. The corresponding polar-angle distributions show asymmetries which are at…
Application of a parallel-projection inversion technique to z-scan spectra of multiply charged xenon and krypton ions, obtained by non-resonant field ionization of neutral targets, has for the first time permitted the direct observation of intensity-dependent ionization probabilities. These ionization efficiency curves have highlighted the presence of structure in the tunnelling regime, previously unobserved under full-volume techniques.
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…
The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules the photoelectron energy does not depend on the electron's emission direction but theoretical studies have questioned this since 1990. Here we provide experimental evidence, that the energies of photoelectrons emitt…
The alignment- and internuclear-distance dependent ionization of H$_2$ exposed to intense, ultrashort laser fields is studied by solving the time-dependent two-electron Schrödinger equation. In the regime of perturbative few-photon ionization, a strong dependence of the ionization yield on the internuclear distance is found. While this finding confirms a previously reported breakdown of the fixed-nuclei approximation for parallel alignment, a simpler explanation is provided and it is demonstrated that this breakdown is not due to vibrational dynamics during the laser pulse. The persistence of …
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.
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 present three dimensional time-dependent calculations of ionization of arbitrarily spatially oriented H$_2^+$ by attosecond, intense, high-frequency laser fields. The ionization probability shows a strong dependence on both the internuclear distance and the relative orientation between the laser field and the internuclear axis.
We examine correlated electron and doubly charged ion momentum spectra from strong field double ionization of Neon employing intense elliptically polarized laser pulses. An ellipticity-dependent asymmetry of correlated electron and ion momentum distributions has been observed. Using a 3D semiclassical model, we demonstrate that our observations reflect the sub-cycle dynamics of the recollision process. Our work reveals a general physical picture for recollision-impact double ionization with elliptical polarization, and demonstrates the possibility of ultrafast control of the recollision dynami…
Intense-field ionization of the hydrogen molecular ion by linearly-polarized light is modelled by direct solution of the fixed-nuclei time-dependent Schrödinger equation and compared with recent experiments. Parallel transitions are calculated using algorithms which exploit massively parallel computers. We identify and calculate dynamic tunnelling ionization resonances that depend on laser wavelength and intensity, and molecular bond length. Results for $λ\sim 1064$ nm are consistent with static tunnelling ionization. At shorter wavelengths $λ\sim 790 $ nm large dynamic corrections are observe…
We discuss the possibility of non-exponential tunneling ionization of atoms irradiated by intense laser field. This effect can occur at times, which are greater than the lifetime of a system under consideration. The mechanism for non-exponential depletion of an initial quasi-stationary state is the cutting of the energy spectrum of final continuous states at long times. We first consider the known examples of cold emission of electrons from metal, tunneling alpha-decay of atomic nuclei, spontaneous decay in two-level systems and the single-photon atomic ionization by a weak electromagnetic fie…
The ionization probability of N$_2$, O$_2$, and CO$_2$ in intense laser fields is studied theoretically as a function of the alignment angle by solving the time-dependent Schrödinger equation numerically assuming only the single-active-electron approximation. The results are compared to recent experimental data [D.~Pavi{č}i{ć} et al., Phys.\,Rev.\,Lett.\ {\bf 98}, 243001 (2007)] and good agreement is found for N$_2$ and O$_2$. For CO$_2$ a possible explanation is provided for the failure of simplified single-active-electron models to reproduce the experimentally observed narrow ionization dist…
We investigate the dynamics of electron-electron recollisions in the double ionization of atoms in strong laser fields. The statistics of recollisions can be reformulated in terms of an area-preserving map from the observation that the outer electron is driven by the laser field to kick the remaining core electrons periodically. The phase portraits of this map reveals the dynamics of these recollisions in terms of their probability and efficiency.
In this paper a 4-component Dirac theory of ionization of hydrogen molecular ion in a super-intense laser field is developed. Simple analytic expressions for the spin specific as well as the total ionization currents emitted from the ground state of the ion are derived. The results are given for all polarization and finite propagation vectors of the field. They apply for inner-shell ionization of analogous heavier molecular ions as well. The presence of molecular two-slit interference effect, first found in the non-relativistic case, and the spin-flip ionization current, and an asymmetry of th…
We revisit the stabilization of ionization of atoms subjected to a superintense laser pulse using nonlinear dynamics. We provide an explanation for the lack of complete ionization at high intensity and for the decrease of the ionization probability as intensity is increased. We investigate the role of each part of the laser pulse (ramp-up, plateau, ramp-down) in this process. We emphasize the role of the choice for the ionization criterion, energy versus distance criterion.
Diatomic molecules (e.g., O$_2$) in intense laser field exhibit a peculiar suppressed ionization behavior compared to their companion atoms. Several physical models have been proposed to account for this suppression while no consensus has been achieved. In this letter, we aim to clarify the underlying mechanisms behind this molecular ionization suppression. Experimental data recorded at midinfrared laser wavelength and its comparison with that at near-infrared wavelength revealed a peculiar wavelength and intensity dependence of the suppressed ionization of O$_2$ with respect to its companion …
Visualizing intense laser field driven electron dynamics in a multielectron molecule: dynamic electron localization, bonding properties and multiple ionization bursts
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…
We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schrödinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of c…
Ionization, excitation, and de-excitation to the ground state is studied theoretically for the first excited singlet state B $^1Σ_u^+$ of H$_2$ exposed to intense laser fields with photon energies in between about 3 eV and 13 eV. A parallel orientation of a linear polarized laser and the molecular axis is considered. Within the dipole and the fixed-nuclei approximations the time-dependent Schrödinger equation describing the electronic motion is solved in full dimensionality and compared to simpler models. A dramatic break-down of the single-active-electron approximation is found and explained …
We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
We solve the hydrodynamic-ballistic equations of motion for a one-dimensional time-dependent Thomas-Fermi model of Cl_2 exposed to an intense subpicosecond laser field, and observe simultaneous multielectron ionization and molecular dissociation. The fragment kinetic energy defect with respect to the simple Coulomb explosion picture is found to originate in ejected-electron screening of the escaping fragments; its magnitude agrees with that observed in recent experiments.
We formulate a three-dimensional semi-classical model to treat three-electron escape dynamics in a strongly-driven linear triatomic molecule, HeH$_{2}^{+}$. Our model includes the Coulomb singularities. Hence, to avoid unphysical autoionization, we employ two criteria to switch off the Coulomb repulsive force between two bound electrons and switch it on when the motion of one electron is mostly determined by the laser field. We investigate triple and "frustrated" triple ionization. In the latter process two electrons escape while one electron remains bound in a Rydberg state. We find that two …
We report a novel experimental technique for the comparison of ionization processes in ultrafast laser pulses irrespective of pulse ellipticity. Multiple ionization of xenon by 50 fs 790 nm, linearly and circularly polarized laser pulses is observed over the intensity range 10 TW/cm^2 to 10 PW/cm^2 using Effective Intensity Matching (EIM), which is coupled with Intensity Selective Scanning (ISS) to recover the geometry-independent probability of ionization. Such measurements, made possible by quantifying diffraction effects in the laser focus, are compared directly to theoretical predictions o…
