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-envelope phase and ellipticity. Moreover, we show that the subcycle resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.
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…
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800~nm) 27~fs laser pulse. For intensities ranging from the tunneling to the over-the-barrier regime, we identify the double ionization pathways in a unified way as a function of total electron energy. For the tunneling regime, we discuss the differences in the interplay of double ionization (DI) pathways between strongly driven He and strongly driven $N_{2}$. For intermediate intensities in the over-the-barrier regime, we find that both the correlated momenta and the do…
Based on the strong-field approximation, we obtain analytical expressions for the initial momentum at the tunnel exit and instantaneous ionization rate of tunneling ionization in elliptically polarized laser fields with arbitrary ellipticity. The tunneling electron reveals a nonzero offset of the initial momentum at the tunnel exit in the elliptically polarized laser field. We find that the transverse and longitudinal components of this momentum offset with respect to the instantaneous field direction are directly related to the time derivatives of the instantaneous laser electric field along …
The geometry-dependent ionization behavior of the ammonia molecule is investigated. Different theoretical approaches for obtaining the ionization yield are compared, all of them showing a strong dependence of the ionization yield on the inversion coordinate at long wavelengths ($\geq$ 800 nm). It is shown how this effect can be exploited to create and probe nuclear wave packets in neutral ammonia using Lochfraß. Furthermore, imaging of a wave packet tunneling through the barrier of a double-well potential in real time is discussed.
We take advantage of the information provided by use of elliptical polarization in a recent two-electron release time experiment [A.N. Pfeiffer et al., Nature Physics 7, 428 (2011)]. This allows a comparative test of the currently dominant conjectures regarding independent-electron tunneling theory vs. fully electron-correlated classical release theory to describe electron release in strong-field double ionization.
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…
We propose a method to study the tunneling process by analyzing the time-dependent ionization yield in circularly polarized laser. A numerical calculation shows that for an atom exposed to a long laser pulse, if its initial electronic state wave function is non-spherical symmetric, the delayed phase shift of the ionization rate vs. the laser cycle period in real time in the region close to the peak intensity of the laser pulse can be used to probe the tunneling time. In this region, an obvious delay phase shift is observed, showing the tunneling time is in order of tens of attoseconds. Further…
Strong field photoelectron holography has been proposed as a means for interrogating the spatial and temporal information of electrons and ions in a dynamic system. After ionization, part of the electron wave packet may directly go to the detector (the reference wave), while another part may be driven back to the ion where it scatters off (the signal wave). The interference hologram of the two waves may be used to retrieve the target information. However, unlike conventional optical holography, the propagations of electron wave packets are affected by the Coulomb potential as well as by the la…
The tunneling ionization of exotic atoms such as muonic hydrogen, muonium and positronium in a strong laser field of circular polarization is investigated taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center of mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for comm…
A new pathway of strong laser field induced ionization of an atom is identified which is based on recollisions under the tunneling barrier. With an amended strong field approximation, the interference of the direct and the under-the-barrier recolliding quantum orbits are shown to induce a measurable shift of the peak of the photoelectron momentum distribution. The scaling of the momentum shift is derived relating the momentum shift to the tunneling delay time according to the Wigner concept. This allows to extend the Wigner concept for the quasistatic tunneling time delay into the nonadiabatic…
Recent attoclock experiments and theoretical studies regarding the strong-field ionization of atoms by few-cycle infrared pulses revealed new features that have attracted much attention. Here we investigate tunneling ionization and the dynamics of the electron probability using Bohmian Mechanics. We consider a one-dimensional problem to illustrate the underlying mechanisms of the ionization process. It is revealed that in the major part of the below-the-barrier ionization regime, in an intense and short infrared pulse, the electron does not tunnel \through" the entire barrier, but rather alrea…
The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although many efforts have been done within semiclassical models, there are few discussions describing multiphoton absorption process with quantum framework. In this letter, by comparing the results obtained with the time-dependent Schrodinger equation (TDSE) and Keldysh-Faisal-Reiss (KFR) theory, we have studied the nonperturbative effects of ionization dynamics beyond KFR theory. The difference in momentum spectra bet…
Pulsed field ionization of high-$n$ (90 $\leq n \leq$ 150) manifold states in Rb Rydberg atoms has been investigated in high slew-rate regime. Two peaks in the field ionization spectra were systematically observed for the investigated $n$ region, where the field values at the lower peak do not almost depend on the excitation energy in the manifold, while those at the higher peak increase with increasing excitation energy. The fraction of the higher peak component to the total ionization signals increases with increasing $n$, exceeding 80% at $n$ = 147. Characteristic behavior of the peak compo…
We study ionization of atoms in strong elliptically-polarized laser fields. We focus on the physical origin of the offset angle in the photoelectron momentum distribution and its possible relation to a specific time. By developing a model which is based on strong-field approximation and considers the classical Coulomb scattering, we are able to quantitatively explain recent attoclock experiments in a wide region of laser and atomic parameters. The offset angle can be understood as arising from the scattering of the electron by the ionic potential when the electron exits the laser-Coulomb-forme…
We study ionization of atoms in strong two-dimensional (2D) laser fields with various forms, numerically and analytically. We focus on the local most-probable tunneling routes (some specific electron trajectories) which are corresponding to the local maxima of photoelectron momentum distributions (PMDs). By making classic-quantum correspondence, we obtain a condition for these routes characterized by the electron position at the tunnel exit. With comparing the identified routes with the classical limit and the partial-decoupling approximation where it is assumed that tunneling is dominated by …
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.
We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees freedom. In the regime where the BO approximation is applicable imaging of the BO nucle…
We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneli…
Recently, in a strong Coulomb field regime of tunneling ionization an unexpected large enhancement of photoelectron spectra due to the Coulomb field of the atomic core has been identified by numerical solution of time-dependent Schrödinger equation [Phys. Rev. Lett. \textbf{117}, 243003 (2016)] in the upper energy range of the tunnel-ionized direct electrons. We investigate the origin of the enhancement employing a classical theory with Monte Carlo simulations of trajectories, and a quantum theory of Coulomb-corrected strong field approximation based on the generalized eikonal approximation fo…
Enhancing high harmonic generation in a short-pulse two-color laser field by controlling the atomic-electron subcycle detachment and acceleration dynamics
Ionization of an atom or molecule presents surprising richness beyond our current understanding: strong-field ionization with low-frequency fields recently revealed unexpected kinetic energy structures (1, 2). A solid grasp on electron dynamics is however pre-requisite for attosecond-resolution recollision imaging (3), orbital tomography (4), for coherent sources of keV light (5), or to produce zeptosecond-duration x-rays (6). We present a methodology that enables scrutinizing strong-field dynamics at an unprecedented level. Our method provides high-precision measurements only 1 meV above the …
Molecules show a much increased multiple ionization rate in a strong laser field as compared to atoms of similar ionization energy. A widely accepted model attributes this to the action of the joint fields of the adjacent ionic core and the laser on its neighbor inside the same molecule. The underlying physical picture for the enhanced ionization is that the up-field atom that gets ionized. However, this is still debated and remains unproven. Here we report an experimental verification of this long-standing prediction. This is accomplished by probing the two-site double ionization of ArXe, whe…
The photoelectron momentum distribution in the strong-field ionization has a variety of structures that reveal the complicated dynamics of this process. Recently, we identified a low-energy interference structure in the case of a super-intense extreme ultraviolet (XUV) laser pulse and attributed it to the laser-induced electron Fresnel diffraction. This structure is determined by the laser-induced electron displacement [Geng L et al. 2021 Phys. Rev. A 104(2) L021102]. In the present work, we find that the Fresnel diffraction picture is also present in the tunneling and over-barrier regime of i…
We study the double ionization of atoms subjected to circularly polarized (CP) laser pulses. We analyze two fundamental ionization processes: the sequential (SDI) and non-sequential (NSDI) double ionization in the light of the rotating frame (RF) which naturally embeds nonadiabatic effects in CP pulses. We use and compare two adiabatic approximations: The adiabatic approximation in the laboratory frame (LF) and the adiabatic approximation in the RF. The adiabatic approximation in the RF encapsulates the energy variations of the electrons on subcycle timescales happening in the LF and this, by …
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…
Vortex photoelectron holography in strong-field tunneling ionization
School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology（华中科技大学物理科学与技术学院与武汉光电国家研究中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Advanced Science, The University of Electro-Communications（电波大学高级科学研究所）；Hubei Fundamental Research Center for Physics（湖北物理基础研究中心）
When a strong laser pulse induces the ionization of an atom, momentum conservation dictates that the absorbed photons transfer their momentum $p_γ=E_γ/c$ to the electron and its parent ion. Even after 30 years of studying strong-field ionization, the sharing of the photon momentum between the two particles and its underlying mechanism are still under debate in theory. Corresponding experiments are very challenging due to the extremely small photon momentum ($~10^{-4}$ a.u.) and their precision has been too limited, so far, to ultimately resolve the debate. Here, by utilizing a novel experiment…
We perform a detailed analysis of the recollision-excitation-tunneling (RESI) mechanism in laser-induced nonsequential double ionization (NSDI), in which the first electron, upon return, promotes a second electron to an excited state, from which it subsequently tunnels, based on the strong-field approximation. We show that the shapes of the electron momentum distributions carry information about the bound-state with which the first electron collides, the bound state to which the second electron is excited, and the type of electron-electron interaction. Furthermore, one may define a driving-fie…
Statistical Characteristics of Tunneling States in Strong-Field Atomic Ionization
College of Physics and Information Technology and Quantum Materials and Devices Key Laboratory of Shaanxi Province’s High Education Institution, Shaanxi Normal University（陕西师范大学物理与信息工程学院、陕西省高校量子材料与器件重点实验室）；College of Physics and Hebei Key Laboratory of Photophysics Research and Application, Physics Postdoctoral Research Station, Hebei Normal University（河北师范大学物理学院、河北省光物理研究与应用重点实验室、物理学博士后科研流动站）；Hebei Key Laboratory of Optoelectronic Information and Geo-detection Technology, School of Mathematics and Science, Hebei GEO University（河北地质大学数理学院、河北省光电信息与地质探测技术重点实验室）；College of Physics, Henan Normal University（河南师范大学物理学院）
The orientation-dependent strong-field ionization of CO molecules is investigated using the fully propagated three-dimensional time-dependent Hartree-Fock theory. The full ionization results are in good agreement with recent experiments. The comparisons between the full method and single active orbital (SAO) method show that although the core electrons are generally more tightly bounded and contribute little to the total ionization yields, their dynamics cannot be ignored, which effectively modify the behaviors of electrons in the highest occupied molecular orbital. By incorporating it into th…
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…
We present a detailed comparison of strong-field ionization of diatomic molecules and their companion atoms with nearly equal ionization potentials. We perform calculations in the length and velocity gauge formulations of the molecular strong-field approximation and with the molecular tunneling theory, and in both cases we consider effects of nuclear motion. A comparison of our results with experimental data shows that the length gauge strong-field approximation gives the most reliable predictions.
In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wavefunction of the molecular orbital from which the electron is removed. The orbital wavefunctions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory (DFT). We show that the asymptotic wavefunction can be improved with an iteration method and after one iteration accurate asymptot…
If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-…
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 …
We revisit a recently proposed scheme [M.F. Ciappina et al 2019 Phys. Rev. A 99 043405] for accurate measurement of electromagnetic radiation intensities in a focus of high-power laser beams. The method is based on the observation of multiple sequential tunneling ionization of atoms and suggests the determination of the peak intensity value from the appearance in the focal area ions with a certain charge number. Here we study the sensitivity of the approach to two essential factors: the focal volume effect and the tunneling ionization model chosen to calculate ionization rates. We show, on the…
We coincidently measure the molecular frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionization of CO molecules by using circularly and elliptically polarized femtosecond laser pulses, respectively. The orientation dependent ionization rates for various kinetic energy releases allow us to individually identify the ionizations of multiple orbitals, ranging from the highest occupied to the next two lower-lying molecular orbitals for various channels observed in our experiments. Not only the emission of a single electron, but also the sequentia…
A theoretical derivation is given for the formula describing N-electron ionization of atom by a dc field and laser radiation in tunneling regime. Numerical examples are presented for noble gases atoms.
We provide detailed analysis of strong field ionization of degenerate valence p orbitals by circularly polarized fields. Our analytical approach is conceptually equivalent to the Perelomov, Popov, and Terent'ev (PPT) theory and is virtually exact for short range potentials. After benchmarking our results against the PPT theory for s orbitals, we obtain the results for p orbitals. We also show that, as long as the dipole approximation is valid, both the PPT method and our results are gauge invariant, in contrast with widely used strong field approximation (SFA). Our main result, which has alrea…
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 perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion, and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time $t^{\prime}$. The second electron then reaches the continuum at a later time $t$ by tunneling ionization. We show that, if $t^{\prime}$ and $t$ are co…
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 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 …
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…
National Research Nuclear University MEPhI（国立研究核大学MEPhI）；P.N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Prokhorov General Physics Institute of the Russian Academy of Sciences（俄罗斯科学院普罗霍罗夫普通物理研究所）
We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations present an excellent agreement with the result from time-dependent Schrödinger equation method. We show that the low-energy fan-shaped structure in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattering electron trajectories, which affects different momenta and scattering angles unequal…
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.
Using a three-dimensional semiclassical model, we study double ionization for strongly-driven He fully accounting for magnetic field effects. For linearly and slightly elliptically polarized laser fields, we show that recollisions and the magnetic field combined act as a gate. This gate favors more transverse - with respect to the electric field - initial momenta of the tunneling electron that are opposite to the propagation direction of the laser field. In the absence of non-dipole effects, the transverse initial momentum is symmetric with respect to zero. We find that this asymmetry in the t…
