Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximation, in upper and lower bound estimates and fully numerical solutions of the time dependent Schroedinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterium for the existence of atomic bound state stabilization.Comment: 12 pages of Latex, one figur

Stabilization not for certain and the usefulness of bounds

Stabilization 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 behaviour 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 behaviour, also lead to definite statements concerning the physical outcome. The pulse shape properties which have to be satitisfied 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 Gordon-Volkov perturbation theory and explicit studies of various pulse shapes and potentials including in particular the Coulomb- and the delta potential.Comment: 12 pages Late

Multielectron corrections in molecular high-order harmonic generation for different formulations of the strong-field approximation

We make a detailed assessment of which form of the dipole operator to use in calculating high order harmonic generation within the framework of the strong field approximation, and look specifically at the role the form plays in the inclusion of multielectron effects perturbatively with regard to the contributions of the highest occupied molecular orbital. We focus on how these corrections affect the high-order harmonic spectra from aligned homonuclear and heteronuclear molecules, exemplified by $\mathrm{N}_2$ and CO, respectively, which are isoelectronic. We find that the velocity form incorrectly finds zero static dipole moment in heteronuclear molecules. In contrast, the length form of the dipole operator leads to the physically expected non-vanishing expectation value for the dipole operator in this case. Furthermore, the so called "overlap" integrals, in which the dipole matrix element is computed using wavefunctions at different centers in the molecule, are prominent in the first-order multielectron corrections for the velocity form, and should not be ignored. Finally, inclusion of the multielectron corrections has very little effect on the spectrum. This suggests that relaxation, excitation and the dynamic motion of the core are important in order to describe multielectron effects in molecular high-order high harmonic generation.Comment: Figures 2 and 4 have been simplified in order to fulfil the size requirements of arXiv; in the new version references have been adde

Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules

The relation between high-harmonic spectra and the geometry of the molecular orbitals in position and momentum space is investigated. In particular we choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such that the highest occupied molecular orbital of the former exhibit at least one nodal plane. The imprint of such planes is a strong suppression in the harmonic spectra, for particular alignment angles. We are able to identify two distinct types of nodal planes. If the nodal planes are determined by the atomic wavefunctions only, the angle for which the yield is suppressed will remain the same for both types of molecules. In contrast, if they are determined by the linear combination of atomic orbitals at different centers in the molecule, there will be a shift in the angle at which the suppression occurs for the heteronuclear molecules, with regard to their homonuclear counterpart. This shows that, in principle, molecular imaging, which uses the homonuclear molecule as a reference and enables one to observe the wavefunction distortions in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order to comply with the arXiv size requirement