Processes In Intense Laser Fields Research Articles

Nondipole strong-field approximation for above-threshold ionization in a few-cycle pulse

The ionization of atoms and molecules by strong laser fields has been studied extensively, both theoretically and experimentally. The strong-field approximation (SFA) allows for the analytical solution of the Schr\"odinger equation and accurately predicts the behavior of ionization processes in intense laser fields. Over the past decade, there has been a growing interest in the study of nondipole effects in these processes. However, such predictions have so far been limited to monochromatic driving laser fields, while experiments often employ quite short pulses. In this paper, we therefore present an extension of the SFA that also allows incorporating the more complicated temporal structure of a few-cycle pulse. By this extension, the prediction of so-called peak shifts is significantly improved, and the ability to control the laser pulse inducing above-threshold ionization is greatly enhanced. The enhanced control over the characteristics of the laser pulse results in more accurate predictions of peak shifts. Our results show better agreement with experimental investigations compared to previous theoretical studies.

Wavelength scaling of strong-field Rydberg-state excitation: Toward an effective S -matrix theory

$S$-matrix theory and the Born expansion, the lowest-order term of which is known as the ``strong-field approximation'' (SFA), play an indispensable role in our understanding of atomic and molecular processes in intense laser fields. Most phenomena in this field are reproduced by the first two terms of the Born series. However, for a long-range potential such as the Coulomb potential, the second-order term may be larger than the SFA term, raising the problem of the convergence of the Born series. By simultaneously measuring and simulating ionization and Rydberg-state excitation of an argon atom subject to a strong laser field for various wavelengths, we demonstrate that the wavelength scaling law of the measured ratio of ${\mathrm{Ar}}^{*}$ over ${\mathrm{Ar}}^{+}$ and the period of its oscillation with respect to the laser intensity can be well reproduced by the second-order term of the $S$-matrix expansion in terms of the Coulomb potential, but not by the lowest-order (SFA) term. We conjecture that the second-order term of the $S$-matrix expansion may provide an effective theory for the intense-laser--atom interaction.

Direct Visualization of Deforming Atomic Wavefunction in Ultraintense High-Frequency Laser Pulses

Interaction of intense laser fields with atoms distorts the bound-state electron cloud. Tracing the temporal response of the electron cloud to the laser field is of fundamental importance for understanding the ultrafast dynamics of various nonlinear phenomena of matter, but it is particularly challenging. Here, we show that the ultrafast response of the atomic electron cloud to the intense high-frequency laser pulses can be probed with the attosecond time-resolved photoelectron holography. In this method, an infrared laser pulse is employed to trigger tunneling ionization of the deforming atom. The shape of the deforming electron cloud is encoded in the hologram of the photoelectron momentum distribution. As a demonstration, by solving the time-dependent Schrödinger equation, we show that the adiabatic deforming of the bound-state electron cloud, as well as the nonadiabatic transition among the distorted states, is successfully tracked with attosecond resolution. Our work films the formation process of the metastable Kramers-Henneberger states in the intense high-frequency laser pulses. This establishes a novel approach for time-resolved imaging of the ultrafast bound-state electron processes in intense laser fields.

Ultrafast Reaction Imaging and Control by Ultrashort Intense Laser Pulses

Abstract Molecules irradiated with intense laser pulses (field intensity ∼1015 W/cm2) exhibit a variety of characteristic processes, such as tunneling ionization, electron rescattering, high-order harmonics generation and Coulomb explosion, that cannot be seen in a weak light field. These features have attracted attention in the last decades as they provide unique approaches to visualize and manipulate ultrafast dynamics of atoms and molecules. Here we discuss molecular processes in intense laser fields, with focuses on the applications to ultrafast imaging and control of reaction dynamics.

Strong-fieldS-matrix theory with final-state Coulomb interaction in all orders

Despite its long standing usefulness for the analysis of various processes in intense laser fields, it is well-known that the so-called strong-field KFR or SFA ansatz does not account for the final-state Coulomb interaction. Due to its importance for the ubiquitous ionisation process, numerous heuristic attempts have been made during the last several decades to account for the final state Coulomb interaction with in the SFA. Also to this end an ad hoc model with the so-called Coulomb-Volkov final state was introduced a long time ago. However, till now, no systematic strong-field S-matrix expansion using the Coulomb-Volkov final state could be found. Here we solve this long standing problem by determining the Coulomb-Volkov Hamiltonian, identifying the rest-interaction in the final state, and explicitly constructng the Coulomb-Volkov propagator (or Green's function). We employ them to derive the complete S-matrix series for the ionisation amplitude governed by the Coulomb-Volkov final state in all orders. The results are given in both "velocity" and "length" gauges. We also present a gauge independent version of the Coulomb-Volkov S-matrix series.

High-order optical processes in intense laser field: Towards nonperturbative nonlinear optics

We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schr\"odinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields we derive and analytically solve propagation equations describing high-order (HO) wave-mixing, HO parametric amplification and HO stimulated scattering. These processes provide a way of efficient coherent XUV generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the super-exponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.

Simple, accurate, and efficient implementation of 1-electron atomic time-dependent Schrödinger equation in spherical coordinates

Modelling atomic processes in intense laser fields often relies on solving the time-dependent Schrödinger equation (TDSE). For processes involving ionisation, such as above-threshold ionisation (ATI) and high-harmonic generation (HHG), this is a formidable task even if only one electron is active. Several powerful ideas for efficient implementation of atomic TDSE were introduced by H.G. Muller some time ago (Muller, 1999), including: separation of Hamiltonian terms into tri-diagonal parts; implicit representation of the spatial derivatives; and use of a rotating reference frame. Here, we extend these techniques to allow for non-uniform radial grids, arbitrary laser field polarisation, and non-Hermitian terms in the Hamiltonian due to the implicit form of the derivatives (previously neglected). We implement the resulting propagator in a parallel Fortran program, adapted for multi-core execution. Cost of TDSE propagation scales linearly with the problem size, enabling full-dimensional calculations of strong-field ATI and HHG spectra for arbitrary field polarisations on a standard desktop PC. Program summaryProgram title: SCID-TDSE: Time-dependent solution of 1-electron atomic Schrödinger equation in strong laser fields.Catalogue identifier: AEYM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 334254No. of bytes in distributed program, including test data, etc.: 20005596Distribution format: tar.gzProgramming language: Fortran-2003 with OpenMP extensions.Computer: Portable code. Tested on x86_64 Linux.Operating system: Portable code. Tested on x86_64 Linux.RAM: Memory requirements depend on the input parameters. Time propagation of a given initial state requires O(32∗NR∗(LMAX+1)∗(MMAX−MMIN+1)) bytes of memory (double precision), where NR is the number of the radial grid points; LMAX is the maximum desired angular momentum; MMIN and MMAX are respectively the smallest and largest desired angular momentum projections. Preparation of the initial atomic states and analysis of the final wavefunction in terms of the field-free atomic states may require O(64∗NR2∗NCPU) bytes of RAM (double precision), where NCPU is the number of processing threads used.Classification: 2.5, 4.3.External routines: BLAS and LAPACK (required); libhugetlbfs (optional), DGEFA and DGEDI (LINPACK); routines included with the code.Nature of problem: Time propagation of non-relativistic 1-electron Schrödinger equation for a central potential, under the influence of a long-wavelength laser field treated in the velocity-gauge dipole approximation.Solution method: The propagator is constructed by separating the Hamiltonian into a large number of non-commuting terms, where each term can be handled simply and computationally efficiently (linear scaling). Time-reversibility of the propagator is ensured by combining the individual terms symmetrically around time midpoint (See ref. [1] and the text). The numerical accuracy is achieved through implicit representation of derivatives (accurate to O(d4) for a uniform grid), combined with variable grid spacing.Restrictions: Ill-conditioned Hamiltonians can occur for some choices or radial grids. The propagator is only approximately norm-conserving; small time steps may be necessary to achieve stable propagation.Unusual features: Due to the implicit representation of the spatial derivative operators, the overall Hamiltonian is not Hermitian. As the result, the left wavefunction is no longer given by a complex conjugate of the right wavefunction, and must be propagated explicitly.The code makes no assumptions on the accuracy of numerical types, and can be built for any real or integer kinds supported by the compiler. Detailed instructions for building the code in single, double, and quadruple precision are included.Running time: Running time is input dependent. Time propagation of the Schrödinger equation scales as O(NR∗(LMAX+1)∗(MMAX−MMIN+1)) per time step. Preparation of the initial atomic state and analysis of the results in terms of the field-free atomic states may require O(NR3) and O(NR3∗(LMAX+1)) work, respectively. On a 3.6 GHz core i7 desktop with 4 CPU cores available, run times are from 2 s (probability of a perturbative bound- to-bound transition in hydrogen atom) to 1 h (high-harmonic spectrum of a hydrogen atom driven by intense elliptically-polarised IR field).

Ultrarelativistic electron states in a general background electromagnetic field.

The feasibility of obtaining exact analytical results in the realm of QED in the presence of a background electromagnetic field is almost exclusively limited to a few tractable cases, where the Dirac equation in the corresponding background field can be solved analytically. This circumstance has restricted, in particular, the theoretical analysis of QED processes in intense laser fields to within the plane wave approximation even at those high intensities, achievable experimentally only by tightly focusing the laser energy in space. Here, within the Wentzel-Kramers-Brillouin approximation, we construct analytically single-particle electron states in the presence of a background electromagnetic field of general space-time structure in the realistic assumption that the initial energy of the electron is the largest dynamical energy scale in the problem. The relatively compact expression of these states opens, in particular, the possibility of investigating analytically strong-field QED processes in the presence of spatially focused laser beams, which is of particular relevance in view of the upcoming experimental campaigns in this field.

Time-dependent multiconfiguration theory for describing molecular dynamics in diatomic-like molecules

We extend the multiconfiguration time-dependent Hartree-Fock (MCTDHF) theory, which is originally developed for the investigation of electronic dynamics in atoms and molecules within the clamped nuclear model, for describing molecular dynamics in diatomic-like molecular systems which are composed of electrons, protons, and two heavy nuclei such as CH(3)OH, C(2)H(2), C(2)H(4), and H(5)O(2) (+). A novel representation of the molecular (electrons and nuclei) wave function to describe the electronic and nuclear quantal dynamics of molecules in an intense laser field is proposed, and the explicit coupled equations of motion (EOMs) for electron spin-orbitals, proton spin-orbitals, and CI-vectors are formulated. The CI-vectors are introduced to describe the quantal motion of the internuclear distance between two heavy nuclei. The derivation of the EOMs is done in two steps. First, the distance between the two heavy nuclei R is treated classically, i.e., electro-protonic dynamics within the clamped nuclear model, and then, the distance R is treated quantum mechanically to describe non-Born-Oppenheimer molecular dynamics. The properties of the EOMs are discussed for the application of the present theory to clarify the mechanism of intramolecular hydrogen (proton) migration processes within hydrocarbon molecules competing with the ionization and the fragmentation processes in intense laser fields.

Toward ab-initio simulations of multiple ionization processes in intense laser field

A non-variational Time-Dependent Multi-Configuration Self-Consistent Field (TDMCSCF) scheme has been developed [16] to describe, by an ab-initio approach, the time-resolved electron dynamics of a laser-driven many-electron atomic or molecular system. Its implementation within a typical quantum chemical package is discussed and its use demonstrated on the laser-driven electron dynamics of LiH. As an L 2 method, this approach faces severe challenges when ionization and large-amplitude electronic motions are addressed. We present here an extension of this TDMCSCF scheme to include multiple ionization processes, using a Feschbach state-partitioning formalism, allowing the bound electrons’ dynamics to be treated by the L 2 -TDMCSCF method, while the ionized electrons can be treated separately by an alternative approach. We present results of proof-of-principle calculations on the strong field ionization of H 2 and discuss the effect of the carrier-envelope phase (CEP) on electron localization and ionization processes in this model system.

Analysis of femtosecond laser ionization/dissociation of polyatomic molecule C6H10O from one-colour pump–probe measurement

This paper reports that a one-colour fs pump–probe measurement has been carried out for studying photoionization/photodissociation of cyclohexanone (C6H10O) in intense laser field. Two of the fragments from cyclohexanone, C2H3+ and C3H3+, are studied under 800 nm laser pump-probe and the results obtained show similar time evolutions. It proposes a feasible model for analysing the experimental observations of the one-colour fs pump-probe measurement. The results demonstrate that as an intermediate product, the excited molecular parent ions play a very important role in photionization/photodissociation processes in intense laser field.

New results in above-threshold ionization and high-order harmonic generation of atomic and molecular systems

Numerical results obtained applying the strong-field approximation to atomic and molecular processes in intense laser fields are presented. In particular, the forward-backward asymmetry in high-order above-threshold ionization (HATI) of Ar atoms by a few-cycle laser pulse is considered. It is shown that the resonantlike enhancements observed in the focal-averaged spectra disappear with the decreasing laser pulse duration. For HATI and high-order harmonic generation (HHG) by molecular systems, we present new results for diatomic molecules. The choice of gauge and the problem of dressing of the initial bound state are discussed. The appearance of the interference minima in molecular HATI and HHG spectra and their role in the characterization of the molecular structure are considered using the example of the Ar2 molecule.

Gauge-equivalent intense-field approximations in velocity and length gauges to all orders

A gauge invariant formulation of the so-called intense-field Keldysh-Faisal-Reiss (KFR) approximations in the ``velocity'' and ``length'' gauges is given and their equivalence is demonstrated term by term to all orders of the theory. It overcomes a long standing discrepancy between the velocity and the length gauge strong-field KFR amplitudes for nonperturbative processes in intense laser fields.

Quantum-orbit theory of high-order atomic processes in intense laser fields

The quantum-orbit formalism of high-order atomic processes in a strong laser field is presented starting from the strong-field approximation generalized to include higher-order effects. It is shown how to apply the quantum-orbit theory to various processes such as high-order above-threshold ionization and detachment, high-order harmonic generation, laser-assisted X-ray–atom scattering, laser-assisted electron–ion recombination, laser-assisted electron–atom scattering and non-sequential double ionization. Particular attention is devoted to high-order above-threshold ionization by few-cycle laser pulses. The results obtained using the strong-field approximation and the theory of quantum orbits are compared with the ab initio solution of the time-dependent Schrödinger equation. It is shown that Coulomb effects are important for low-energy electron spectra.

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

Floquet-liouville super-matrix approach for multiphoton non-linear optical processes in intense laser fields

A practical non-perturbative approach is presented for the treatment of multiphoton non-linear optical processes in intense monochromatic or polychromatic field. By extending the many-mode Floquet theory recently developed by the authors, the time-dependent Liouville equation for the density matrix of atoms or molecules undergoing radiative and/or collisional relaxations can be transformed into an equivalent time-independent Floquet-Liouville super-matrix eigenvalue problem. The method is illustrated by a study of the multiphoton resonance fluorescence spectra of two-level systems.

Uniform asymptotic expansion of a class of generalized Bessel functions occurring in the study of fundamental scattering processes in intense laser fields

Using the method of Bleistein and of Ursell, a uniform asymptotic expansion for an important class of so-called generalized Bessel functions is derived, which permits a fast and efficient evaluation of these functions in the interesting domain of large values of their parameters where conventional methods fail. With the help of this asymptotic representation, a whole number of cross sections that have been given in the literature in terms of generalized Bessel functions for a variety of fundamental scattering processes in intense linearly polarized plane-wave laser fields can now be converted into actual numbers, thus permitting a quantitative assessment of the investigated effects at a given intensity of the applied laser field.