Posts Tagged ‘strong fields’

STSM by Sandra Gomez,  Complutense University of Madrid (ES) with Volker Engel Institut für Physikalische und Theoretische Chemie der Universität Würzburg (DE)
On November 23rd, 2014 (5 days)logo

Strong field decoupling of nuclear dynamics

The interaction of molecules with strong laser fields produces molecular dynamics much more complicated than in the presence of weak fields. The solution for structureless two-level systems in a single frequency field is known as Rabi solution and the population of states oscillates at the Rabi frequency, known as Rabi oscillations or Rabi floppings.
When this system is replaced by two electronic states with dependance on nuclear coordinates, the Rabi oscillations decay on time while the nuclei are moving due to a dephasing that damps electronic coherences.
The goal of our collaboration is to minimize these effects by decoupling as much as possible the nuclear motion.

During the short visit we discussed possible models where these effects could be observed, we generated the potential energy curves of some diatomic molecules (Na2 and NaI) and we started to study how to analyze the dynamics using hamiltonians of coupled electron-nuclear motion (beyond Born-Oppenheimer approximation).
Due to the short time availiable, only the transition between ground and first excited state of Na2 molecule was studied at different amplitudes of the laser field (continuous wave laser).
We plan to extend these results to systems with other decoherence processes, as the NaI predissociation and to control of coupled nuclear and electronic degrees of freedom.

STSM by Patrick O`Mahony, Royal Holloway, University of London with Bernard Piraux, Universitè Catholique de Louvain, Louvain-la-Neuve
On August 22th, 2013 (9 days)

Time Scaling and Momentum Space Models in Intense Fields

The Time Dependent Schrödinger Equation (TDSE) in momentum space provides a very useful alternative to the coordinate representation to describe atomic and molecular processes in an intense laser field.  We wish to solve this equation in the very low frequency limit.

Taking a model in which the kernel of the nonlocal Coulomb potential in momentum space is replaced by a finite sum of separable potentials each supporting one bound state of atomic hydrogen, we have cast the kernel for the resultant integral equation in a form which is a sum of a pole term and an integral with has a rapidly decaying integrand which is smooth and doesn’t oscillate making it easy to evaluate numerically. We showed that in the limit of the frequency going to zero the pole term doesn’t contribute and we expect the integral to be strongly peaked making it possible to easily solve the integral equation.

We are now in a position to study semi-analytically the limit as the frequency of the laser goes to zero which would be impossible to do by solving the TDSE as the pulse length becomes extremely long. In this way we should be able to obtain new insights into the low energy structure (LES) found in both atoms and molecules in intense fields.

STSM by  Francisca Mota-Furtado,Royal Holloway, University of London with Bernard Piraux, Universitè Catholique de Louvain, Louvain-la-Neuve
On August 22th, 2013 (9 days)

Time-dependent methods for strong laser fields

Robust time propagators are required to solve the Time Dependent Schrödinger Equation (TDSE) for atomic, molecular and solid state systems as for example when matter interacts with an intense low frequency laser field.

The direct numerical ab initio solution of the TDSE using spectral methods leads to large systems of first order equations with a high degree of stiffness. We focussed on two explicit methods, Fatunla’s method and the Arnoldi algorithm.  Both of these methods have optimum stability properties but they differ in the degree of accuracy they are able to reproduce. We identified strategies to use them both successfully.

During the short visit we finished a joint paper with our hosts on this topic which has been submitted to Physical Review A.