The Use of the Time Correlation Function in Floquet Theory

Abstract

In the description of the interaction of short and strong laser pulses with atoms or molecules the Floquet picture [1] provides in general the best basis for an analysis even down to pulse lengths of the order of 10 or 20 laser cycles. This is so because the Floquet states are the equivalents of the stationary states for the case of a constant laser amplitude and make it possible to separate the effects of the laser frequency from the effects of the time variation of the laser amplitude. The diagonalization of the Floquet Hamiltonian, however, is very difficult if the system contains a continuum and there is essentially only one method to do this, the complex dilatation method [2]. On the other hand, the direct, numerical solution of the time dependent Schrödinger equation is much easier and there are a number of efficient approaches, mostly based on real coordinates and energies [3,4]. Therefore the complex dilatation method can not be directly used to analyse a wavefunction calculated with such a real algorithm. It is the purpose of this contribution to describe an alternative method introduced into Roquet theory recently [5] to obtain informations about the Floquet content of a given wavefunction. This method is based on the calculation of the (local) time correlation function which can be calculated by solving the time dependent Schrödinger equation and which uses real energies and coordinates. It can therefore very easily incorporated into a given solution algorithm of the time dependent Schrödinger equation.