Hydrogen atom in a strong laser field: Numerical simulation versus Keldysh-type theories

The dynamics of a 3D hydrogen atom in an intense laser pulse is investigated using the direct numerical integration of the nonstationary Schrödinger equation in the multiphoton regime of ionization. The results obtained are compared with the theoretical data of the strong-field approximation (SFA) method and the validity of the SFA and other Keldysh-type theories in the problem of the strong-field ionization of atoms is analyzed in a wide range of laser frequencies and intensities. The Reiss approximation (SFA) provides qualitative agreement with the numerical simulation for moderate laser intensities and reveals the channel closing phenomena during the multiphoton ionization. However, this approach is found to be inappropriate in the presence of strong fields where we numerically demonstrate the suppression of atomic ionization. The reason for the stabilization lies in the formation of a new system (dressed atom), which is not taken into account in the SFA and other Keldysh-type theories.     

Comparative analysis of the strong-field ionization of a quantum system with the Coulomb and short-range potentials

The dynamics of a hydrogen atom and a 3D model quantum system with a short-range potential is investigated using the direct numerical integration of the nonstationary Schrödinger equation in a wide range of laser intensities and frequencies. The simulation data are compared with the predictions of variants of the Keldysh-type theories. It is demonstrated that, in the low-frequency (tunnel) limit, the ionization rates of the systems with the Coulomb and short-range potentials and the same values of the ionization potential significantly differ from each other whereas, in the high-frequency (single-photon) limit, we do not observe a substantial difference between the ionization rates. Specific features of the angular distribution of the photoelectron emission and the photoelectron energy spectra are investigated in detail. In addition, the ionization suppression is studied for both Coulomb- and short-range-potential atoms. The stabilization is due to the dramatic reconstruction of the atom in the presence of a strong laser field and the formation of a new system (Kramers-Henneberger atom) that exhibits an increasing resistance to the ionization upon an increase in the laser intensity. In the two-photon ionization regime, the stabilization phenomenon is substantially more pronounced for the system with the Coulomb potential. This results from the effective excitation of the Rydberg states of the dressed atom in the strong-field limit.     

Stabilization of circular states of the hydrogen atom in a strong field

A solution of the three-dimensional time-dependent Schrödinger equation, describing the ionization dynamics of the hydrogen atom in a circular state in an electromagnetic field, is obtained by direct numerical integration. It is shown that the observed stabilization effect can be interpreted on the basis of the Kramers-Henneberger approach. A simple analytical model is proposed, which qualitatively describes the basic laws of the ionization process under the conditions of the reported calculations and laboratory experiments on ionization of the circular hydrogenlike 5g, m=4 state of the Ne atom.     

Strong-field approximation in photoionization

Abstract

The definition and characteristics of the strong-field environment for an atom in a laser field are specified in terms of the relevant intensity parameters. The limits of perturbation theory are set, and it is emphasized that this must be done in terms of laser field energy, not electric field strength. The formal basis and special features of the SFA (strong-field approximation) are reviewed, and it is pointed out that the three methods encompassed in the so-called KFR (Keldysh-Faisal-Reiss) technique are actually quite different. Validity conditions and some applications of the SFA are given.     

Bohmian trajectory perspective on strong field atomic processes

The interaction of an atom with an intense laser field provides an important approach to explore the ultrafast electron dynamics and extract the information of the atomic and molecular structures with unprecedented attosecond temporal and angstrom spatial resolution. To well understand the strong field atomic processes, numerous theoretical methods have been developed, including solving the time-dependent Schr ?dinger equation(TDSE), classical and semiclassical trajectory method, quantum S-matrix theory within the strong-field approximation, etc. Recently, an alternative and complementary quantum approach, called Bohmian trajectory theory, has been successfully used in the strong-field atomic physics and an exciting progress has been achieved in the study of strong-field phenomena. In this paper, we provide an overview of the Bohmian trajectory method and its perspective on two strong field atomic processes, i.e., atomic and molecular ionization and high-order harmonic generation, respectively.     

A gauge-covariant derivation of the strong-field approximation

A brief discussion of gauge invariance in nonrelativistic quantum mechanics is presented. The strong-field approximation for ionization of an atom by a laser field is rederived in such a way that the resulting ionization amplitude comes out identical in any gauge. This result agrees with the usual length-gauge form.     

Stabilization of an atom in a strong high-frequency field

The dynamics of a classical model two-electron atom in a strong high-frequency electromagnetic field is investigated by numerical integration. It is found that, with an increase in the field intensity, the system demonstrates enhanced stability with respect to ionization. It is shown that stabilization arises due to the formation of a new object—a Kramers-Henneberger atom.     

Single-photon double ionization of an atom in a strong radiation field

Double ionization is studied by direct numerical integration of the time-dependent Schrödinger equation for a model two-electron system in the field of an electromagnetic wave in the case when the photon energy exceeds the energy required for the removal of both electrons of the atom. The probabilities of single-electron and double ionization are obtained as functions of the radiation intensity. The energy spectra and double pulse distributions of photoelectrons are analyzed. It is shown that single-photon ionization plays a significant role only in the limiting cases of weak and strong fields. The obtained results are used in an analysis of the contributions from different channels to the double-ionization process (in particular, for clarifying the role of the electron-electron interaction). The results of numerical calculations are compared with the analytic model of the phenomenon.     

Shape of the amplification line corresponding to an adjacent transition in a strong field

An analysis is made of the effect of a strong field on the shape of the amplification line for monoenergetic atoms. There are three strong-field contributions, differing in their dependence on the set of relaxation parameters of the medium and on the differences among the populations corresponding to the Raman transitions. An analysis is made of the conditions under which each of the contributions is predominant. The change in the line shape by an intensified external field is found for each case. Neon atoms are discussed as an example. The results are compared with those corresponding to a Maxwellian velocity distribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 38–44, November, 1970.The authors thank S. G. Rautian for useful discussions and S. I. Mortsev for assistance in the numerical calculations.     

用强场近似方法研究强激光场中H原子的电离

利用传统的强场近似方法和考虑Coulomb修正的强场近似方法,计算了H原子在激光场中的总电离几率及H原子在不同波长激光场中电离的能量谱,并将得到的能量谱与直接数值求解含时Schrödinger方程的结果进行了比较,结果发现：当激光波长较长时,考虑Coulomb 修正的强场近似方法得到的结果与数值求解含时Schrödinger方程的结果符合得较好。     

Symmetry of carrier-envelope phase difference effects in strong-field, few-cycle ionization of atoms and molecules

In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that, for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules, this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or nongeometric. The observations are exemplified by strong-field calculations on hydrogen.     

The effect of the crystal structure of the field emitter on field ion energy distributions

The field ionization probability of an atom as a function of distance from the field emitter is discussed in terms of the atomic arrangement and the electron scattering properties of the ion cores of the emitter in the immediate neighborhood of the atom to be ionized, and the electron transmission properties of the potential barrier between the emitter and that atom. This approach to field ionization calculations is somewhat similar to field ionization calculations based on low energy electron diffraction (LEED) procedure in that it takes into account electron scattering from the first few atomic layers of the emitter. It differs from LEED type calculations, because it considers the highly localized nature of the ionization near a surface atom. This localization makes the ionization probability relatively insensitive to the two-dimensional periodicity of the emitter surface. A one-dimensional calculation, in which only the potential barrier and three ion core scatterers in line with the field are considered, shows secondary structure in the predicted field ion energy distributions near the critical energy deficit, as well as the well known, primary field induced resonance peaks. The surface orientation dependence of these distributions arises naturally from this model because the secondary structure depends strongly upon the crystal parameter along a line parallel to the field. This one-dimensional calculation can be no more than an approximation to a complete calculation. It is interesting, however, that such a simple physical model, in which scattering from the image potential and only two or three ion cores is considered, rather than scattering from a complete crystal, can give prodicted field ion onergy distributions which are similar to those experimentally observed.     

Peculiarities of the ionization of many-electron systems and generation of attosecond pulses in ultrashort laser fields

The ionization of a model two-electron atom in the field of a strong ultrashort laser pulse is studied by numerical integration of the nonstationary Schrödinger equation describing the dynamics of a quantum system in the field of an electromagnetic wave. Pecularities of the two-electron ionization are analyzed for pulses whose duration amounts to one to two periods of oscillation of the electric field of the wave at different frequencies of the incident radiation. For extremely short pulses, the double ionization is found to be suppressed. This effect is caused by the finiteness of the interelectron energy exchange time during the laser action. Peculiarities of the generation of high-order harmonics and single XUV attosecond pulses upon ionization of atoms by laser pulses, whose duration is within one to two optical cycles, are investigated.     

Influence of quantum transitions in the continuum on ionization of atoms in strong fields

The tight-binding method is used to analyze the ionization of a hydrogenlike atom by an intense monochromatic laser field. The orthogonal and normalized basis in which the solution of the time-dependent Schrödinger equation is expanded contains unperturbed wave functions of the discrete spectrum and generalized Coulomb wave functions of the continuum. In the solution of the coupled equations we make use of the fact that the bound-free and free-free transitions are efficient in different regions of complex time. Simplified equations are constructed and investigated. Results of calculations for ionization of a hydrogen atom from its ground state and of the energy distribution of the electrons in strong and superstrong linearly polarized fields are presented. It is shown that in this case the ground state decays completely, and free-free transitions play a defining role in the dynamics of the process. It is established that the total probability of population of the upper Rydberg states abutting the continuum does not exceed 0.05. The range of applicability of the approach is discussed. A comparison with numerical results obtained by other authors is given.     

Scaling of wave-packet dynamics in an intense midinfrared field

A theoretical investigation is presented that examines the wavelength scaling from near-visible (0.8 micro m) to midinfrared (2 micro m) of the photoelectron distribution and high harmonics generated by a "single" atom in an intense electromagnetic field. The calculations use a numerical solution of the time-dependent Schr?dinger equation (TDSE) in argon and the strong-field approximation in helium. The scaling of electron energies (lambda2), harmonic cutoff (lambda2), and attochirp (lambda -1) agree with classical mechanics, but it is found that, surprisingly, the harmonic yield follows a lambda -(5-6) scaling at constant intensity. In addition, the TDSE results reveal an unexpected contribution from higher-order returns of the rescattering electron wave packet.     

Manipulating Photoelectron Distributions for Rare Gas Atoms Ionized with Polarized Femtosecond Laser Pulses

Above-threshold ionizations of rare gas atoms excited by polarized femtosecond laser pulses are investigated. The photoelectron momentum spectra are obtained applying the strong-field approximation (SFA) theory. It is found that, distribution of the emitted photoelectrons varies with different polarizations of laser pulses. We have interpreted the relationship between the observed distribution and the laser polarization taking advantage of tunneling ionization theory and simple-man model. The polarization sensitivity indicates that one can easily manipulate the photoelectron distribution by controlling the polarization of the exciting pulse.     

Attosecond correlated dynamics of two electrons passing through a transition state

The strong-field induced decay of a doubly excited, transient Coulomb complex Ar**→Ar(2+)+2e(-) is explored by tracing correlated two-electron emission in nonsequential double ionization of Ar as a function of the carrier-envelope phase. Using <6 fs pulses, electron emission is essentially confined to one optical cycle. Classical model calculations support that the intermediate Coulomb complex has lost memory of its formation dynamics and allows for a consistent, though model-dependent definition of "emission time," empowering us to trace transition-state two-electron decay dynamics with sub-fs resolution. We find a most likely emission time difference of ～200±100 as.     

激光强度依赖的阈下谐波产生机制

利用广义伪谱方法精确数值求解了氢原子在强激光场中的三维含时薛定谔方程,获得了强激光中氢原子的含时波函数,利用时间依赖的偶极矩的傅里叶变换得到了高次谐波谱,研究了氢原子在强激光场中发射低于电离阈值的谐波谱对激光强度的依赖性.研究发现,激光强度在低于电离阈值的谐波产生的通道选择的过程中扮演着重要角色,主要有两种量子通道对阈下谐波的产生有贡献,即广义的短轨道和长轨道,其中长轨道对激光场强度比较敏感.结合小波时频变换、经典轨道分析、以及强度依赖的量子通道选择分析,本文阐明了其背后的物理机制.     

Transition from strong-field sequential to nonsequential double ionization at near-infrared wavelengths and low intensities

Within a quantum-mechanical model, we investigate strong-field double ionization of a model helium atom by near-infrared, linearly polarized laser pulses at intensities far below the recollision threshold. The quantum simulations show a clear mechanism change from sequential to nonsequential double ionization (NSDI) as the laser intensity increases. For NSDI, the two-electron correlated momentum distribution exhibits a strong final-state Coulomb repulsion effect for high-energy photoelectrons, but absent for low-energy photoelectrons. This repulsion effect is ascribed to field double ionization from doubly-excited states populated by recollision of the first ionized electron when it returns to the parent ion. Such recollision-induced excited states are absent at ultraviolet wavelengths due to the very low returning kinetic energies, resulting to the absence of final-state repulsion effect in NSDI.