A new semiclassical approach to ionization by an oscillating field is presented. For a delta-function atom, an asymptotic analysis is performed with respect to a quantity h, defined as the ratio of photon energy to ponderomotive energy. This h appears formally equivalent to Planck's constant in a suitably transformed Schroedinger equation and allows semiclassical methods to be applicable. Systematically, a picture of tunneling wave packets in complex time is developped, which by interference account for the typical ponderomotive features of ionization curves. These analytical results are then compared to numerical simulations and are shown to be in good agreement.
The relativistic theory of above-threshold ionization (ATI) of hydrogen-like atoms in ultrastrong radiation fields, taking into account the photoelectron induced rescattering in the continuum spectrum is developed. It is shown that the contribution of the latter in the multiphoton ionization probability even in the Born approximation by Coulomb field is of the order of ATI probability in the scope of Keldysh-Faisal-Reiss ansatz.
The Yudin-Ivanov formula [Phys. Rev. A 64, 013409 (2001)] is generalized such that the most general analytical expression for single-electron spectra, which includes the dependence on the instantaneous laser phase, is obtained within the strong field approximation. No assumptions on the momentum of the electron are made. Previously known formulas for single-electron spectra can be obtained as approximations to the general formula.
Multiphoton ionization of helium is investigated in the superintense field regime, with particular emphasis on the role of the electron-electron interaction in the ionization and stabilization dynamics. To accomplish this, we solve ab initio the time-dependent Schrödinger equation with the full electron-electron interaction included. By comparing the ionization yields obtained from the full calculations with corresponding results of an independent-electron model, we come to the somewhat counterintuitive conclusion that the single-particle picture breaks down at superstrong field strengths. We …
We address the concept of direct multiphoton multiple ionization in atoms exposed to intense, short wavelength radiation and explore the conditions under which such processes dominate over the sequential. Their contribution is shown to be quite robust, even under intensity fluctuations and interaction volume integration, and reasonable agreement with experimental data is also found.
In this paper, we extend the results of an earlier paper in which we had demonstrated the limitations of the notion of non-resonant multiphoton ionization, in the exploration of photon statistics effects in non-linear processes. Through the quantitative analysis of specific realistic processes, we provide the connection to conditions of intensity and pulse duration necessary in relevant experiments, including a recent seminal experiment demonstrating the effect of superbunching found in squeezed radiation.
A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A…
The measurement of the tunneling time in attosecond experiments, termed attoclock, triggered a hot debate about the tunneling time, the role of time in quantum mechanics, where the interaction with the laser pulse involves two regimes of a different character, the multiphoton and the tunneling (field-) ionization. In the adiabatic field calibration, one of us (O. K.) developed in earlier works a real tunneling time model and showed that the model fits well to the experimental data of Landsmann et al. (Optica {\bf 1}, 343 2014). In the present work, it is shown that the model explains the exper…
The intermediate domain of strong-field ionization between the tunneling and the multiphoton regimes is investigated using the strong field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit, a delayed appearance in the continuum as well …
We considered the multiphoton resonance in the periodically driven quantum oscillator with Kerr nonlinearity in the presence of weak high-order nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips in the dependence of the stationary occupations of the stable states on detuning. We demonstrated that due to high-order nonlinearities, these peaks and dips acquire additional fine structure and split into several closely spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling between the regions of the oscillator phase portrait, and the fine structure …
We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and atom-driving cases, and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blo…
The coherent control of electron beams and ultrafast electron wave packets dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Bot…
We present a multichannel photoelectron interferometry technique based on trichromatic pulse shaping for unambiguous determination of quantum phases in multiphoton ionization (MPI) of potassium atoms. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$-state resulting in a (2+1) resonance-enhanced MPI (REMPI), a (1+2) REMPI occurs via the non-resonant intermediate $4p$-state with an initial green or blue pulse. We show that ionization via a non-resonant intermed…
Canonical semiclassical methods can be used to develop an intuitive definition of tunneling time through potential barriers. An application to atomic ionization is given here, considering both static and time-dependent electric fields. The results allow one to analyze different theoretical constructions proposed recently to evaluate ionization experiments based on attoclocks. They also suggest new proposals of determining tunneling times, for instance through the behavior of fluctuations.
A perturbative study of the Schrödinger equation in a strong electromagnetic field with dipole approximation is accomplished in the Kramers-Henneberger frame. A prove that just odd harmonics appear in the spectrum for a linear polarized laser field is given, assuming that the atomic radius is much lesser than the free-electron quiver motion amplitude. Within this approximation a perturbation series is obtained in the Keldysh parameter giving a description of multiphoton processes in the tunneling regime. The theory is applied to the case of hydrogen-like atoms: The spectrum of higher order har…
It is known that the ponderomotive potential from the laser electron interaction behaves like a static potential that scatters off electrons. We have investigated the process of the electron tunneling the ponderomotive potential by using the nonperturbative quantum electrodynamic approach with a modified Gaussian quantized laser field. The results show that the ponderomotive tunneling is significantly larger than the tunneling of a static potential of the same profile. The tunneled electron is discrete in energy spectrum and spatial diffraction as the result of multiphoton processes. A resonan…
Nonlinear interactions between ultrashort optical waveforms and solids can be used to induce and steer electric current on a femtosecond (fs) timescale, holding promise for electronic signal processing at PHz frequencies [Nature 493, 70 (2013)]. So far, this approach has been limited to insulators, requiring extremely strong peak electric fields and intensities. Here, we show all-optical generation and control of directly measurable electric current in a semiconductor relevant for high-speed and high-power (opto)electronics, gallium nitride (GaN), within an optical cycle and on a timescale sho…
We show that interference phenomena plays a big role for the electron yield in ionization of atoms by an ultra-short laser pulse. Our theoretical study of single ionization of atoms driven by few-cycles pulses extends the photoelectron spectrum observed in the double-slit experiment by Lindner et al, Phys. Rev. Lett. \textbf{95}, 040401 (2005) to a complete three-dimensional momentum picture. We show that different wave packets corresponding to the same single electron released at different times interfere, forming interference fringes in the two-dimensional momentum distributions. These struc…
We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient and…
The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ioniza- tion experiments. The parameter status of time in the time dependent Schrödinger equation (TDSE) is supported by the well-known Pauli's ob- jection as well as by its interpretation as an emerging property of entangle- ment with a classical environment. On the other hand, the introduction of a self-adjoint dynamical time operator in Dirac's formulation of elec- tron's relativistic quantum mech…
Two-color multiphoton emission from polycrystalline tungsten nanotips has been demonstrated using two-color laser fields. The two-color photoemission is assisted by a three-photon multicolor quantum channel, which leads to a twofold increase in quantum efficiency. Weak-field control of two-color multiphoton emission was achieved by changing the efficiency of the quantum channel with pulse delay. The result of this study complements two-color tunneling photoemission in strong fields, and has potential applications for nanowire-based photonic devices. Moreover, the demonstrated two-color multiph…
The Salecker-Wigner-Peres quantum-clock approach is applied in order to determine the tunneling time of an electron in strong-field tunnel ionization via a time-dependent electric field. Our results show that the ionization of the electron takes a nonvanishing period of time. This tunneling time is of the order of the Keldysh time but strictly larger than the Keldysh time. Comparing the quantum-clock tunneling time to the mean tunneling time as obtained by the virtual-detector approach, one finds that these two complementary methods give very similar results. Due to the asymmetric distribution…
Tunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during the ionization process. With this theoretical approach, it becomes possible to define unique moments when the electron enters and leaves with highest probability the classically forbidden region from first principles and a tunneling time can be specified unambiguously. It is shown that neither the moment when the electron enters the tunneling barrier nor when …
Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of an one-dimensional problem. High-order Coulomb corrected strong-field approximation is applied, where the exact continuum state in the S-matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although, without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified pr…
Momentum-resolved photoelectron emission from xenon in colinearly polarized two-color laser fields at above-threshold ionization conditions is studied both experimentally and theoretically. We utilize phase-of-the-phase spectroscopy as recently introduced by Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015) to analyze the dependence of the yields on the relative phase $φ$ between the fundamental and second harmonic laser fields. The resulting phase-of-phase spectra feature a characteristic checkerboard pattern, which can analytically be described within the strong-field approximation.
We use a quantum trajectory-based semi-classical method to account for Coulomb interaction between the photoelectron and the parent ion in the classically forbidden, sub-barrier region during strong-field tunneling ionization processes. We show that---besides the well-known modification of the tunneling ionization probability---there is also an influence on the interference pattern in the photoelectron spectra. In the long-wavelength limit, the shift of the intra-cycle interference fringes caused by sub-barrier Coulomb effects in the laser polarization direction can be derived analytically. We…
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…
The electron dynamics in the classically forbidden region during relativistic tunnel-ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge invariant total energy operator. Introducing position dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel-ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagat…
We present a practical numerical technique for calculating tunneling ionization rates from arbitrary 1-D potential wells in the presence of a linear external potential by determining the widths of the resonances in the spectral density, rho(E), adiabatically connected to the field-free bound states. While this technique applies to more general external potentials, we focus on the ionization of electrons from atoms and molecules by DC electric fields, as this has an important and immediate impact on the understanding of the multiphoton ionization of molecules in strong laser fields.
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 tunneling model of ionization applies only to longitudinal fields: quasistatic electric fields that do not propagate. Laser fields are transverse: plane wave fields that possess the ability to propagate. Although there is an approximate connection between the effects of longitudinal and transverse fields in a useful range of frequencies, that equivalence fails completely at very low frequencies. Insight into this breakdown is given by an examination of radiation pressure, which is a unique transverse-field effect whose relative importance increases rapidly as the frequency declines. Radiat…
The tunneling ionization of an electron from a p-state in a highly charged ion in the relativistic regime is investigated in a linearly polarized strong laser field. In contrast to the case of an s-state, the tunneling ionization from the p-state is spin asymmetric. We have singled out two reasons for the spin asymmetry: first, the difference of the electron energy Zeeman splitting in the bound state and during tunneling, and second, the relativistic momentum shift along the laser propagation direction during the under-the barrier motion. Due to the latter, those states are predominantly ioniz…
Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wavefunction, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation metho…
The present tutorial provides an overview of the time-dependent configuration interaction singles (\acs{TDCIS}) scheme applied to nonlinear ionization over a broad photon-energy range. The efficient propagation of the wave function and the calculation of photoelectron spectra within this approach are described and demonstrated in various applications. Above-threshold ionization of argon and xenon in the extreme ultraviolet energy range is investigated as an example. A particular focus is put on the xenon $4d$ giant dipole resonance and the information that nonlinear ionization can provide abou…
Tunneling ionization of an atom in ultrashort laser pulses is considered. When the driving laser pulse is switched-on and -off with a steep slope, the photoelectron momentum distribution (PMD) shows an edge-effect because of the photoelectron diffraction by the time-slit of the pulse. The trivial diffraction pattern of the edge effect consisting of fast oscillations in the PMD disguises in the deep nonadiabatic regime the physically more interesting features in the spectrum which originate from the photoelectron dynamics. We point out the precise conditions how to avoid this scenario experimen…
Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. M…
We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and energy distribution in the instantaneous potential, we reveal the importance of quantum interference between tunneling and over-the-barrier pathways of escape. Tunneling is blurred both in space and time, and the contribution of tunneling at the mean energy is almost negligible. We suggest and justify improved initial conditions for a classical particle approximation of strong-field ionization, based…
The average dwell time of an electron in a potential barrier formed by an external electric field and the potential of a helium atom is evaluated within a semi classical one-dimensional tunneling approach. The tunneling electron is considered to interact with a nuclear charge screened by the electron in the helium ion. It is found that screening leads to smaller average dwell times of the tunneling electron. The dissipative effect of the environment on the tunneling electron is taken into account within a semiclassical model involving a velocity dependent frictional force and is found to chang…
The influence of inner electrons on the ionization dynamics in strong laser fields is investigated in a wavelength regime where the inner electron dynamics is usually assumed to be negligible. The role of inner electrons is of particular interest for the application of frozen-core approximations and pseudopotentials in time-dependent density functional theory (TDDFT) and the single-active-electron (SAE) approximation in strong-field laser physics. Results of TDDFT and SAE calculations are compared with exact ones obtained by the numerical ab initio solution of the three-electron time-dependent…
