MULTIPHOTON PROCESSES: ICOMP VIII: 8th International Conference

Transition matrix elements in the closed form for freefree transitions and ATI of atomic hydrogen in Rydberg states
View Description Hide DescriptionTwophoton freefree transitions take place in such processes as the ionization with excess photons and bremsstralung. In nonrelativistic dipole approximation it is convenient to use the Green’s function formalism. Up to now in the configuration space freefree transition amplitudes have not been written in the closed form [1]. The modified Coulomb Green’s function (CGF) Sturmian expansion is derived and analytic expressions for twophoton boundfree and freefree transition amplitudes are obtained.

Quantum paths in abovethreshold ionization for elliptical polarization
View Description Hide DescriptionCalculations of highorder abovethresholdionization (ATI) spectra for a zerorange model potential are interpreted in terms of quantum orbits as they formally result from a saddlepoint evaluation of the Smatrix element. The spectrum is built up by the superposition of these orbits and exhibits distinctive interference patterns. For a laser with elliptical polarization, the ATI plateau becomes a stair whose individual steps can be attributed to particular quantum orbits. The real parts of the orbits are depicted. They are closely related to electronic spacetime orbits. For parameters around an ATI channel closing, the spectrum shows resonant behavior.

Quantum effects in above threshold ionization
View Description Hide DescriptionWe report on the relevance of quantum effects in above threshold ionization for low and high energy photoelectrons. High repetition rate lasers are used to study energy resolved electron yields as a function of ellipticity as well as the angular distribution of the photoelectrons. In comparison with theory it is possible to identify quantum effects.

Calculations of multiphoton ionization of inert gases: Gauge comparisons using a new Rmatrix Floquet code
View Description Hide DescriptionWe present calculations of multiphoton ionization of inert gases using an improved version of the Rmatrix Floquet method. We use a new radial basis for the R–matrix internal region which avoids the use of nonvariational corrections to the calculated Rmatrix. This provides the freedom to choose either the length or velocity gauge to describe the laser–atom interaction in this region. Differences between results calculated using length and velocity gauges are discussed. We present new results for argon at 248 nm, the fundamental mode of the KrF laser.

Calculations of strong field multiphoton processes in alkali metal atoms
View Description Hide DescriptionThe development of a new class of laser systems, capable of producing intense radiation in the midinfrared (MIR) regime (photon energies between 0.3 and 0.4 eV), opens the possibility of observing multiphoton processes in a new class of systems with lower ionization potentials than those previously studied. Of particular interest are the alkali metal atoms, which are true one(valence)electron systems. We present theoretical calculations of above threshold ionization (ATI) and high harmonic generation (HHG) from alkali metal atoms subject to 34 μm laser irradiation. The ATI calculations, which use a multiple gauge propagation method, show a striking dependence in the production of highorder photoelectrons on the electronion potential. The HHG calculations illustrate the importance of the strong groundtofirst excited state coupling in multiphoton processes in the alkali metals.

Strong field atomic physics in the midinfrared
View Description Hide DescriptionWe examine strong field atomic physics in a wavelength region (34 microns) where very little work has previously been done. The soft photon energy allows the exploration of oneelectron atoms with low binding energies (alkali metals). We find that photoionization spectra differ from rare gas studies at shorter wavelengths due to more complex ion core potentials. Harmonic generation is studied, and we find that harmonic bandwidths are consistent with theory and the possibility of compression to pulse widths much shorter than that of the driving pulse. Harmonic yields in the visible and UV are sufficient for a complete study of their amplitude and phase characteristics.

On the absence of multielectron effects in ATI photoelectron spectra of argon
View Description Hide DescriptionWe present a detailed comparison of experiment and calculation for photoelectron kinetic energy spectra in argon using high intensity 800 nm, 120 fs laser light. The calculation utilizes only single electron physics and matches the experimental data very well. For a wide range of laser intensities and electron kinetic energies we find that multielectron effects are absent.

Multiphoton detachment of by the Rmatrix floquet approach
View Description Hide DescriptionMultiphoton detachment rates have been obtained for using the Rmatrix Floquet (RMF) approach. In the low intensity limit agreement has been found with recent theoretical calculations of the total photodetachment cross section. At intensities of twophoton above threshold detachment rates are presented and similarities with earlier calculations in are discussed. Also at this intensity, threephoton rates are investigated for energies ranging from below the threshold to the threshold.

Excessphoton ionization spectra and atomic structure in intense laser fields
View Description Hide DescriptionFloquet states represent intrinsic modes of ionization of an atom in a monochromatic field of constant intensity. To describe atomic wave packets evolving in realistic laser pulses, linear superpositions of Floquet states are required (“multistate Floquet theory”). This gives the possibility of following the evolution of wave packets in terms of the Floquet states that are populated during the pulse. We study here the way in which the Floquet states present in the representation of the wave packet manifest themselves in the excessphoton ionization spectra (EPI/ATI). For the purpose of illustration we choose a 1D atomic model with a softcore Coulomb potential. We calculate the totality of the Floquet states, at all intensities needed, and generate the corresponding “Floquet map”. We then calculate the EPI spectra for wave packets evolving from the ground state under different types of pulses. By analyzing the location of the lines in the spectrum, and their shapes, we show that they can be associated, in a clear cut and predictable way, to Floquet states responsible for the emission. The understanding of the underlying physics can lead to tailoring laser pulses, such as to obtain EPI signals in a controlled way. Whereas our analysis is applied to theoretical spectra, it would apply, just as well, to experimental ones.

Stabilization of atoms in ultrastrong laser fields, a decade later
View Description Hide DescriptionThis overview presents basic notions on atomic stabilization, some new illustrative results, as well as the recent controversy it has stirred. We start with quasistationary (adiabatic) stabilization (QS), the original form in which the concept has emerged from highfrequency Floquet theory (HFFT). QS designates the property of the highfrequency ionization rates to decrease with intensity beyond some critical high value of the latter. Other forms of Floquet theory (Sturmian basis diagonalization, close coupling in the angular momentum basis, Rmatrix) have confirmed the existence of QS, and obtained concordant numerical values for the rates of H. The experimental manifestation of QS can be obtained with adiabatically varying pulses. Dynamic stabilization (DS), on the other hand, is the general form of the phenomenon, covering also the case of rapidly turnedon pulses. It designates the fact that, for wavepacket solutions of the timedependent Schrödinger equation, the ionization probability of an atomic electron at the end of a laser pulse of given shape and length, starts decreasing (albeit in an oscillatory manner) beyond a certain critical value of the peak intensity. At still higher intensities, a “destabilization” regime was found, in which the ionization probability increases slowly to 1. We illustrate this behavior with recent results. Further, we give an interpretation of DS based on the expansion of Schrödinger wave packets in terms of Floquet eigenstates (“multistate Floquet theory”). The interpretation relies on the fact that the Floquet states involved manifest QS, that several of them may be populated during the turnon of the pulse (“shakeup”), and that, if the turnon is very rapid, the initial population can be projected directed directly into the continuum (“shakeoff”). We also comment on the controversy around DS in recent years, originating, on the one hand, in numerical results disagreeing with mainstream calculations, and, on the other, in results from mathematical physics. The experimental evidence on stabilization is presented subsequently: two state of the of the art experiments have been performed on lowlying Rydberg states. Finally, perspectives are considered, and the advent of VUVFEL light sources is signalled as a crucial step towards the experimental study of the ground state stabilization of H. The message of the overview is that, on the basis of existing information, (nonrelativistic) atomic stabilization is in good shape, and further research is desirable to reveal its potential.

Dynamic stabilization and the numerical evidence
View Description Hide DescriptionWe define dynamic stabilization and offer a direct comparision between the ionization probability computed from numerical wave function solutions of the time dependent Schrödinger equation and the analytical bounds proposed by Schrader et al. The comparision presents convincing evidence that dynamic stabilization occurs within the analytical bounds.

Comments on atomic stabilization in intense fields and relativity
View Description Hide DescriptionWe comment on the problem of atomic stabilization for nonrelativistic intensities, and discuss how it might be affected at relativistic intensities, Two concepts of stabilization, type I and type II, are distinguished in the present discussion. It is pointed out that in the relativistic case investigations in 3D become unavoidable for any reliable information on the problem. We also point out that for ponderomotive energies greater than the threshold of real pairs production, both the frameworks of classical relativistic simulation, as well as of oneparticle Dirac wavefunction, break down. New thinking is needed to develop nonperturbative QED methods in that situation.

Mechanisms of stabilization of Rydberg atoms in a strong light field
View Description Hide DescriptionThe main ideas and features of strongfield interference stabilization of Rydberg atoms are described. Both analytical and model calculations, as well as exact numerical solutions of the Schördinger equation are discussed and compared with each other. Experiments of the FOM Institute groups (The Netherlands) on stabilization of Ba and Ne atoms excited initially, correspondingly, to 27d and 5g levels are discussed. In both cases mechanisms of stabilization are argued in favor of different kinds of interference phenomena rather than adiabatic stabilization.

Stabilization not for certain and the usefulness of bounds
View Description Hide DescriptionStabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no computational method exists which is entirely agreed upon. It is therefore very useful to provide various consistency criteria which have to be satisfied by this quantity, whose discussion is the main objective of this contribution. We show how the scaling behavior of the space leads to a symmetry in the ionization probability, which can be exploited in the mentioned sense. Furthermore, we discuss how upper and lower bounds may be used for the same purpose. Rather than concentrating on particular analytical expressions we obtained elsewhere for these bounds, we focus in our discussion on the general principles of this method. We illustrate the precise working of this procedure, its advantages, shortcomings and range of applicability. We show that besides constraining possible values for the ionization probability these bounds, like the scaling behavior, also lead to definite statements concerning the physical outcome. The pulse shape properties which have to be satisfied for the existence of asymptotical stabilization is the vanishing of the total classical momentum transfer and the total classical displacement and not smoothly switched on and off pulses. Alternatively we support our results by general considerations in the GordonVolkov perturbation theory and explicit studies of various pulse shapes and potentials including in particular the Coulomb and the delta potential.

Breakdown of the dipole approximation in atomic ionization by intense laser fields
View Description Hide DescriptionIt is widely accepted that the dipole approximation (i.e., ellimination of magnetic field effects) fails when the interaction with very strong fields is studied. There are, however, many publications particularly related to atomic stabilization that study the dipole limit. It is shown in this note that the breakdown of the dipole approximation already appears for laser parameters generally regarded as a clear region to find atomic stabilization. Our simulations show the influence of the drift that is due to the magnetic field in situations in which a strong dichotomy of the wave function would otherwise have been expected.

A comment on nonsequential multiple ionization
View Description Hide DescriptionBased on the findings of recent experimental and theoretical investigations of nonsequential double and multiple ionization of atoms in an intense laser field we comment on a qualitative picture of the physical process.

Double ionization of a twoelectron model atom in a singlecycle laser pulse
View Description Hide DescriptionWe present theoretical results from the solution of a widely used model atom containing two interacting electrons in one dimension bound to a softCoulomb potential and ionized by an intense, short laser pulse. A halfcycle pulse leads to strong single but no double ionization (down to a probability density of ). A fullcycle laser pulse at low frequency leads to double ionization which begins precisely at the classical return time for the first ejected electron. At weak field, double ionization occurs at the time of maximum return kinetic energy. When the excursion range for the first electron is truncated, the double ionization at later times, corresponding to longer excursions, disappears. When the field near the nucleus is turned off during the return of the first electron, double ionization persists.

The role of correlation in nonsequential double ionization
View Description Hide DescriptionWe present the results of recent numerical studies of double ionization and correlation in a twoelectron model atom. We briefly review basic features of our model and describe the invariant measure of correlation that we find convenient. Our results help to illuminate the dynamics of the doubleionization process. We focus on the wellknown “knee” sone. We show that the spatial probability distribution of the twoelectron system exhibits jets of double ionization which occur each half cycle. We note a competing process of rapid sequential ionization. We also examine the dependence of these processes on the strength of the electronelectron repulsion, and we find that the size of the jets is particularly sensitive to it in the vicinity of the knee.

Collective multielectron tunneling ionization in strong fields
View Description Hide DescriptionThe process of multielectron tunneling in strong fields has, to the authors’ knowledge, never been considered in detail. In principle, it is one possible mechanism for multielectron ionization in strong laser fields. We have carried out first analytical and numerical studies of this novel process, that prove the existence of collective tunneling but fail to explain the laser experiments. As a second result, we present an empirical modification of the multielectron tunneling formula that leads to an astonishing agreement with laser experiments over a wide range of parameters, even if only for linear laser polarization.

Resonances in multiphoton ionization of helium at 248 nm
View Description Hide DescriptionMultiphoton ionization rates have been calculated for He at the KrF laser wavelength of 248 nm and for intensities up to using the Rmatrix Floquet method. For intensities above that at which channel closing takes place it is found that intermediate fivephoton resonances with bound states strongly influence the total rate. In particular the resonance between the ground state and the 1s2p state is found to occur at an intensity of This resonance is investigated at several neighboring wavelengths and its prominent nature, which is discussed in terms of a proposed nearby laserinduced degenerate state (LIDS), should enable it to be observed experimentally.