F. Mota-Furtado

(e,2e) triple differential cross sections for the simultaneous ionization and excitation of helium

The authors present absolute triple differential cross sections (TDCS) measurements for ionization of helium leaving the ion in both n=1 and n=2 final states, obtained under asymmetric geometry at an incident energy approximately 5.5 keV and ejected electron energies of 5, 10 and 75 eV. The kinematics are chosen to correspond either to a constant ejection energy, or to a constant energy transfer to the target. Angular distributions are measured at both constant ejection angle ( theta a mode) and at constant scattering angle ( theta b mode). In the theta a mode experiments, the momentum transfer dependence of the n=2 triple differential generalized oscillator strength is investigated for the first time. In both modes, the n=2 angular distributions show several new features which are not present for the n=1 ones, and which tend to vanish as the ejected energy is increased. They are attributed to final state interactions between the ejected electron and the excited ion. Comparison with first-order theoretical models shows the inadequacy of a Coulomb wave representation of the ejected electron, while in the R-matrix formalism it is found that a five-state multichannel calculation qualitatively describes the shape (but not the amplitude) of the TDCS measured in the theta b mode. Comparison is also made with the photoionization in the dipolar limit where the momentum transfer approaches zero. When integrated over the ejection direction, the double differential generalized oscillator strength ratio for ionization to the n=1 and n=2 states is found to agree with an earlier first Born close coupling prediction.

Quantum-state diffusion model and the driven damped nonlinear oscillator

We consider a driven damped anharmonic oscillator which classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state which does not display any bistability or hysteresis. We use quantum state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.

CONTINUOUS STOCHASTIC SCHRODINGER EQUATIONS AND LOCALIZATION

The set of continuous norm-preserving stochastic Schrodinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the environment operator. Particular focus is placed on determining the stochastic equation which exhibits the highest rate of localization for wide open systems. An equation having such a property is proposed in the case of a single non-Hermitian environment operator. This result is relevant to numerical simulations of quantum trajectories where localization properties are used to reduce the number of basis states needed to represent the system state, and thereby increase the speed of calculation.

Explicit schemes for time propagating many-body wave functions

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrodinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunlas or Arnoldis algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.

Modelling laser-atom interactions in the strong field regime

Abstract We consider the ionisation of atomic hydrogen by a strong infrared field. We extend and study in more depth an existing semi-analytical model. Starting from the time-dependent Schrödinger equation in momentum space and in the velocity gauge we substitute the kernel of the non-local Coulomb potential by a sum of N separable potentials, each of them supporting one hydrogen bound state. This leads to a set of N coupled one-dimensional linear Volterra integral equations to solve. We analyze the gauge problem for the model, the different ways of generating the separable potentials and establish a clear link with the strong field approximation which turns out to be a limiting case of the present model. We calculate electron energy spectra as well as the time evolution of electron wave packets in momentum space. We compare and discuss the results obtained with the model and with the strong field approximation and examine in this context the role of excited states. Graphical abstract

Ionization and excitation of the excited hydrogen atom in strong circularly polarized laser fields

In the recent work of Herath et al. [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.043004] the first experimental observation of a dependence of strong-field ionization rate on the sign of the magnetic quantum number m [of the initial bound state (n,l,m)] was reported. The experiment with nearly circularly polarized light could not distinguish which sign of m favors faster ionization. We perform ab initio calculations for the hydrogen atom initially in one of the four bound substates with the principal quantum number n=2, and irradiated by a short circularly polarized laser pulse of 800nm. In the intensity range of 1012-1013W/cm2 excited bound states play a very important role, but also up to some 1015W/cm2 they cannot be neglected in a full description of the laser-atom interaction. We explore the region that with increasing intensity switches from multiphoton to over-the-barrier ionization and we find, unlike in tunneling-type theories, that the ratio of ionization rates for electrons initially counter-rotating and corotating (with respect to the laser field) may be higher or lower than 1.

Strong field approximation within a Faddeev-like formalism for laser-matter interactions

Abstract We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation. By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schrödinger equation. Graphical abstract

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an

Distribution of Fano parameters in a mesoscopic system with broken time-reversal symmetry

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