A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Electron flux distributions in photodetachment of H<Superscript>-</Superscript> in parallel electric and magnetic fields

Photo-detached electrons of negative hydrogen ion in parallel electric and magnetic fields show quite complicated classical dynamical behavior, and a sequence of bifurcation and anti-bifurcation occurs. We investigate the effects of bifurcations on the flux distribution of photo-detached electrons by using position and momentum diagrams. Detached-electron flux distributions are calculated based on a uniform semi-classical theory. The flux distributions exhibit patterns with multiple rings. The bright rings correspond to special points in the diagrams. The flux distributions can be controlled by adjusting the magnetic field strength while fixing the electric field.     

Electron angular distributions in double photoionization: Use of effective Sommerfeld parameters

We present calculations of the fivefold differential cross-section (FDCS) for double photoionization of helium at excess energies of 6 and 20 eV above threshold. Our results are obtained using for the final double-continuum state a product of three Coulomb wave functions, with the Sommerfeld parameters modified to describe the strength of interaction of any two particles affected by the third particle. Our calculations are compared with recent absolute measurements by D?rner et al. (Phys. Rev. A 57, 1074 (1998)), both in coplanar and non-coplanar geometries. Very good agreement is obtained for the shape of the angular distributions, and differences in the absolute magnitude exist in comparison with the standard choice of Sommerfeld parameters. Received: 17 July 1998 / Received in final form and Accepted: 23 October 1998     

Classical Effects of Carrier--Envelope Phase on Nonsequential Double Ionization

A classical microcanonical 1＋1-dimensional model is used to investigate the ion momentum distributions in nonsequential double ionization with linearly polarized few-cycle pulses. We find that the ion momentum distribution has a strong dependence on the carrier-envelope phase of the few-cycle pulse, which is consistent with the experimental results qualitatively. Back analysis shows that the ionization probability of the first electron at different phases and its returning kinetic energy play the main role on the ion momentum distributions.     

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals,implementation, and nano-optical applications

In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli–Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann–Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.     

Vacuum ultraviolet photoionization of the 5d elements in the region of the 5p and 4f excitation

The results of recent VUV photoionization experiments of the 5d elements Ta, W, Re, Ir and Pt using atomic beam technique, excitation with monochromatized synchrotron radiation and detection of singly and doubly charged photoions are discussed. Special attention is given to the resonances caused by discrete transitions of the 5p and 4f electrons into the unfilled 5d subshells. As there is a crossover of the 5p and 4f levels along the series of the 5d elements the result is a complicated structure of the corresponding interacting resonances. The photoion spectra are compared with theoretical calculations carried out within the relativistic time dependent local density and the relativistic Hartree-Fock approximation. Received: 9 October 1997 / Accepted: 3 November 1997     

Four Electrons in a Coupled Three-Layer Quantum Dot

We investigate four electrons confined in a coupled three-layer quantum dot, by the exact diagonalization method. A vertical magnetic field to the confinement plane is considered. The ground-state electronic structures and angular momentum transitions are investigated. We find that for four-electron Q Ds, the Series of the magic numbers in three-layer QDs are different from those in one-, and two-layer Q Ds. These are connected to the exchange and rotational symmetries of the systems.     

Nondipole parameters of TDCS for electron impact ionization and drag current

A comprehensive study is undertaken of angular distributions of electron knock-out from atomic targets by fast electrons with a small transfer of momentum. The general expressions for the parameters of the triple differential cross-section of impact ionization in the optical limit are derived. The calculated parameters are compared with those of the angular distribution of electrons ejected from an atom in the process of photoionization. In these processes, when the multipole transitions are involved, the one-to-one correspondence between the photoionization and impact ionization parameters disappears. The nondipole transitions lead to the backward/forward asymmetry of the angular distribution of ejected electrons that is absent in the dipole approximation for ionization by both fast electrons and photons. Using the He atom as an example, the character of the asymmetry for these two processes is qualitatively different and the backward/forward asymmetry results in macroscopic directed motion of secondary electrons accompanying the passing of a fast electron beam through gas or plasma. The general formulas for this drag current are derived and applied to gaseous He.     

Effects of Spatial Nonlocality versus Nonlocal Causality for Bound Electrons in External Fields

Using numerically exact solution of the time-dependent Schrödinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations, here we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential in one spatial dimension. It was found that the spatial entanglement quantified by the linear quantum entropy is predicted with good accuracy using the spatial nonlocality, parameterized naturally within the TDQMC approach. At the same time, the nonlocal causality predicted by the exact solution leads to only small oscillations in the quantum trajectories which belong to the idler electron as the driven electron is subjected to a strong high frequency electric field, without interaction between the electrons.     

Gauge-invariant exact solution of a general separable potential model of a quantum system in a laser field

In this Letter we present the exact stationary solution in the length-gauge of the Schrödinger equation for interaction of a circularly polarized laser field with a quantum system possessing the continuous spectrum and any (finite) number of bound states of arbitrary angular momentum symmetry. This manifestly gauge-invariant solution complements the recently given velocity-gauge solution of the model. We also briefly consider the corresponding model with a quantum field in the number-state representation.     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

Laser-assisted positron-impact ionization of atomic hydrogen

We study the ionization of atomic hydrogen by a fast positron in the presence of an external linearly polarized laser field. We concentrate on the limit of a small momentum transfer and describe the fast positron's continuum states by Volkov wave functions. The ejected electron is described by a Coulomb-Volkov wave function. We are limited to small laser intensities such that the dressed state of the target is treatable within the time-dependent perturbation theory, even though the laser intensity is still quite high by laboratory standards. Numerical results for the triply differential cross sections and their dependencies on laser-field parameters are discussed and compared with the results of laser-assisted ionization by electron impact.     

Signatures of the Unruh effect from electrons accelerated by ultrastrong laser fields

We calculate the radiation resulting from the Unruh effect for strongly accelerated electrons and show that the photons are created in pairs whose polarizations are perfectly correlated. Apart from the photon statistics, this quantum radiation can further be discriminated from the classical (Larmor) radiation via the different spectral and angular distributions. The signatures of the Unruh effect become significant if the external electromagnetic field accelerating the electrons is not too far below the Schwinger limit and might be observable with future facilities. Finally, the corrections due to the birefringent nature of the QED vacuum at such ultrahigh fields are discussed.     

Polarisation effect of laser field in inelastic electron - hydrogen collisions

We study the influence of the laser polarization on the electron impact excitation of atomic hydrogen. Our method takes into account the “dressing” of the target states by including the laser-atom interaction to first order time-dependent perturbation theory, while the interaction of the laser field with the incident electron is treated to all orders by using the non relativist Volkov function. The interaction of the fast projectile with the target atom is treated in the first Born approximation. The calculations are performed via two distinct computations. The first one is based on a direct calculation, the second based on a Sturmian approach. Important differences appear between the angular distributions depending on the polarization chosen. Received : 17 february 1998 / Revised : 20 july 1998 / Accepted : 2 september 1998     

Ground-state energy of two-dimensional interacting electrons in strong magnetic fields

Summary The ground-state energy of two-dimensional interacting electrons in a strong magnetic field in the angular-momentum representation is studied using a modified Lanczos diagnonalization method. In the presence of a positive background density the ground-state energy increases with the total angular momentum, while a cusp-type behaviour appears. The problem of the electron-impurities interaction is formulated as well. The results are discussed in connection with the observed fractional quantum Hall states. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction. The author of this paper has agreed to not receive the proofs for correction.     

Spectrum of two quasiequal-energy electrons ejected by a high-energy photon

We present numerical results for the photoelectron spectrum in double ionization by keV photons in the quasiequal-energy sharing region. In this region of the spectrum, the relevant ionizing mechanism is due to a mutual sharing of the photon momentum by both electrons, with small momentum transferred to the atomic nucleus. Calculations were performed for photon energies of 25 and 50 keV, where retardation effects are fundamental, while final-state correlations are of minor importance. The spectra present a two-peak structure, with maxima located at the photoelectron energies , with the photon energy in atomic units. We discuss the general features of the spectrum in terms of the picture of the photoionization of two free electrons, and we propose a way of detecting the contribution by experiments. Received 24 January 2000     

Advanced adiabatic approximation for momentum distributions of ejected electrons in slow atomic collisions

The problem of determination of momentum distributions of ejected electrons in slow atomic collisions is studied within the impact-parameter method by using a dynamic adiabatic basis which takes into account the correct boundary conditions. An expression is obtained which relates the momentum distribution of the ejected electrons with a coherent sum of the delocalized dynamic adiabatic eigenstates (elementary wavepackets). The form of the momentum distribution exactly coincides with the form of the total wavepacket in configuration space. General formulas are applied to a model problem of electron detachment in the process in which the electron-atom interactions are described by the zero-range potentials. In the example considered, the momentum distribution of ejected electrons, in the center-of-mass frame, exhibits a maximum located in the scattering plane on the circle of radius (in atomic units), where v is the relative collision velocity and is the impact parameter. Received: 5 October 1998     

Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector - a complex combination of the electric and magnetic field vectors - that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.     

Photoelectron angular distributions from two-photon ionization of atoms near ionization threshold

Photoelectron angular distributions(PADs) from two-photon ionization of atoms in linearly polarized strong laser fields are obtained in accordance with the nonperturbative quantum scattering theory.We also study the influence of laser wavelength on PADs.For two-photon ionization very close to the ionization threshold,most of the ionized electrons are vertically ejected to the laser polarization.PADs from twophoton ionization of atoms are determined by the second order generalized phased Bessel function at which the ponderomotive parameter plays a key role.In terms of dependence of PADs on laser wavelength,corresponding variations for the ponderomotive parameter are demonstrated.