Nonsequential Double Recombination in Intense Laser Fields
P. Koval, F. Wilken, D. Bauer, C. H. Keitel
备注：
4 pages, RevTeX, v2 with an extended strong field approximation treatment of the process; instead, v1 describes an attosecond control scheme to enhance the process
A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cut-off are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cut-off is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.
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…
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…
Consensus has been reached that recollision, as the most important post-tunneling process, is responsible for nonsequential double ionization process in intense infrared laser field, however, its effect has been restricted to interaction between the first ionized electron and the residual univalent ion so far. Here we identify the key role of recollision between the second ionized electron and the divalent ion in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method, which enables us to well reproduce the experimentally obser…
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.
With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we find a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides profound understandings of ele…
We perform a systematic analysis of how nonsequential double ionization in intense, linearly polarized laser fields is influenced by the initial states in which both electrons are bound, and by the residual ionic potential. We assume that the second electron is released by electron-impact ionization of the first electron with its parent ion, using an S-Matrix approach. We work within the Strong-Field Approximation, and compute differential electron momentum distributions using saddle-point methods. Specifically, we consider electrons in $1s$, $2p$, $3p$ and localized states, which are released…
We show that a family of key periodic orbits drive the recollision process in a strong circulary polarized laser field. These orbits, coined recolliding periodic orbits, exist for a wide range of parameters and their relative influence changes as the laser and atomic parameters are varied. We find the necessary conditions for recollision-driven nonsequential double ionization to occur. The outlined mechanism is universal in that it applies equally well beyond atoms: The internal structure of the target species plays a minor role in the recollision process.
Radiative recombination of a relativistic electron with a highly charged ion in the presence of an intense laser field is considered. Various relativistic effects, caused by the high energy of the incoming electron and its strong coupling to the intense laser field, are found to clearly manifest themselves in the spectra of the emitted $γ$-photons.
We consider the classical dynamics of a two-electron system subjected to an intense bichromatic linearly polarized laser pulse. By varying the parameters of the field, such as the phase lag and the relative amplitude between the two colors of the field, we observe several trends from the statistical analysis of a large ensemble of trajectories initially in the ground state energy of the helium atom: High sensitivity of the sequential double ionization component, low sensitivity of the intensities where nonsequential double ionization occurs while the corresponding yields can vary drastically. …
Nonsequential multiple ionization of atoms in intense laser fields is initiated by a recollision between an electron, freed by tunneling, and its parent ion. Following recollision, the initial electron shares its energy with several bound electrons. We use a classical model based on rapid electron thermalization to interpret recent experiments. For neon, good agreement with the available data is obtained with an upper bound of 460 attoseconds for the thermalization time.
We describe first-principles in-plane calculations of non-sequential triple ionization (NSTI) of atoms in a linearly polarized intense laser pulse. In a fully classically correlated description, all three electrons respond dynamically to the nuclear attraction, the pairwise e-e repulsions and the laser force throughout the duration of a 780nm laser pulse. Nonsequential ejection is shown to occur in a multi-electron, possibly multi-cycle and multi-dimensional, rescattering sequence that is coordinated by a number of sharp transverse recollimation impacts.
We theoretically study frustrated double ionization (FDI) of atoms subjected to intense circularly polarized laser pulses using a three-dimensional classical model. We find a novel "knee" structure of FDI probability as a function of intensity, which is similar to the intensity dependence of nonsequential double ionization probability. The observation of FDI is more favourable when using targets with low ionization potentials and short driving laser wavelengths. This is attributed to the crucial role of recollision therein, which can be experimentally inferred from the photoelectron momentum d…
We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted parallel and perpendicular to the direction of the {\em same} returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmoni…
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the previously proposed time-dependent extended Hartree-Fock (TD-EHF) method [Phys. Rev. A 51, 3999 (1995)] is equivalent to the multiconfiguration time-dependent Hartree-Fock method with two occupied orbitals. The latter wavefunction is further transformed into the natural expansion form, enabling the direct propagation of the natural orbitals (NOs). These methods, …
We show that high-order harmonics generated from molecules by intense laser pulses can be expressed as the product of a returning electron wave packet and the photo-recombination cross section (PRCS) where the electron wave packet can be obtained from simple strong-field approximation (SFA) or from a companion atomic target. Using these wave packets but replacing the PRCS obtained from SFA or from the atomic target by the accurate PRCS from molecules, the resulting HHG spectra are shown to agree well with the benchmark results from direct numerical solution of the time-dependent Schrödinger eq…
Contributions of the pre-ionized H$_2$ (PI-H$_2$) and ionized H$_2^+$ subsystems of the two-electron H$_2$ system to its high-order harmonic generation in 8-cycle $\sin^{2}$-like ultrafast intense laser pulses are calculated and analyzed based on the solution of the time-dependent Schrödinger equation (TDSE) for the one-dimensional two-electronic H$_2$ system with fixed nuclei. The laser pulses have $λ =\ 390\ \&\ 532$ nm wavelengths and $I=1\times 10^{14}$, 5$\times 10^{14}$, 1$\times 10^{15}$ \&\ 5$\times 10^{15}$ Wcm$^{-2}$ intensities. It is found that at the two lower intensities, the PI-…
We show that a dense spectrum of chaotic multiply-excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of the low-energy electron recombination of Au$^{25+}$ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht {\em et al.} [J. Phys. B {\bf 31}, 24…
The interaction of atomic clusters with short, intense pulses of laser light to form extremely hot, dense plasmas has attracted extensive experimental and theoretical interest. The high density of atoms within the cluster greatly enhances the atom--laser interaction, while the finite size of the cluster prevents energy from escaping the interaction region. Recent technological advances have allowed experiments to probe the laser--cluster interaction at very high photon energies, with interactions much stronger than suggested by theories for lower photon energies. We present a model of the lase…
We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.
High-order harmonic generation (HHG) in simultaneous intense near-infrared (NIR) laser light and brilliant x rays above an inner-shell absorption edge is examined. A tightly bound inner-shell electron is transferred into the continuum. Then, NIR light takes over and drives the liberated electron through the continuum until it eventually returns to the cation leading in some cases to recombination and emission of a high-order harmonic (HH) photon that is upshifted by the x-ray photon energy. We develop a theory of this scenario and apply it to $1s$ electrons of neon atoms. The boosted HH light …
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…
The time evolution of the electron density and the resulting time dependence of X-ray diffraction peak intensity in a crystal irradiated by highly intense femtosecond pulses of an XFEL is investigated theoretically on the basis of rate equations for bound electrons and the Boltzmann equation for the kinetics of the unbound electron gas that plays an essential role in the time evolution of the electron density of a crystal. The photoionization, Auger process, electron-impact ionization, electron--electron scattering, and three-body recombination have been implemented in the system of rate equat…
Asymmetric molecules look different when viewed from one side or the other. This difference influences the electronic structure of the valence electrons, thereby giving stereo sensitivity to chemistry and biology. We show that attosecond and re-collision science provides a detailed and sensitive probe of electronic asymmetry. On each 1/2 cycle of an intense light pulse, laser-induced tunnelling extracts an electron wave packet from the molecule. When the electron wave packet recombines, alternately from one side of the molecule or the other, its amplitude and phase asymmetry determines the eve…
The Quantitative Rescattering Theory (QRS) for high-order harmonic generation (HHG) by intense laser pulses is presented. According to the QRS, HHG spectra can be expressed as a product of a returning electron wave packet and the photo-recombination differential cross section of the {\em laser-free} continuum electron back to the initial bound state. We show that the shape of the returning electron wave packet is determined mostly by the laser only. The returning electron wave packets can be obtained from the strong-field approximation or from the solution of the time-dependent Schrödinger equ…
Solid-state materials have recently emerged as a new stage of strong-field physics and attosecond science. The mechanism of the electron dynamics driven by an ultrashort intense laser pulse is under intensive discussion. Here we theoretically discuss momentum-space strong-field electron dynamics in graphene and crystalline dielectrics and semiconductors. First, within massless Dirac fermion and tight-binding models for graphene, we rigorously derive intraband displacement and interband transition, which form the basis for understanding solid-state strong-field physics including high-harmonic g…
We calculate high-harmonic generation (HHG) by intense infrared lasers in atoms and molecules with the inclusion of macroscopic propagation of the harmonics in the gas medium. We show that the observed experimental spectra can be accurately reproduced theoretically despite that HHG spectra are sensitive to the experimental conditions. We further demonstrate that the simulated (or experimental) HHG spectra can be factored out as a product of a \macroscopic wave packet" and the photo-recombination transition dipole moment where the former depends on the laser properties and the experimental cond…
Real-space picture of electron recollision with the parent ion guides our understanding of the highly nonlinear response of atoms and molecules to intense low-frequency laser fields. It is also among several leading contestants for the dominant mechanism of high harmonic generation (HHG) in solids, where it is typically viewed in the momentum space, as the recombination of the conduction band electron with the valence band hole, competing with another HHG mechanism, the strong-field driven Bloch oscillations. In this work, we use numerical simulations to directly test and confirm the real-spac…
