We apply correlation function analysis for a study of strong field ionization of atoms. We show that the study of the correlations of electron's coordinate and velocity reveals patterns which can be naturally interpreted as manifestations of the electron's barrier exit point (the spatial point where the electron exits the tunneling barrier). This analysis provides an unambiguous definition of the exit point in the tunneling ionization process. The location of the exit point thus determined agrees well with the estimates used in the semiclassical simulations.
In the framework of the standard semi-classical picture of ionization based on the Keldysh theory and its modifications, known as the two-step model, an electron emerges into the continuum with zero or near zero velocity at a certain point in space (the tunnel exit), setting up initial conditions for the subsequent electron motion. An initial value of the coordinate is defined either by the so-called Field Direction Model or (for Coulomb systems) by an estimate based on the use of the parabolic coordinate system, as a point at which the electron exits the barrier. Despite the great deal of success which had the trajectory based calculations employing these initial conditions defining the subsequent electron motion, the notions of the initial conditions are not easy to reconcile with quantum mechanics (QM). We cannot assign direct meaning to the initial electron's coordinates and velocity using the wave-function provided by the solution of the conventional TDSE, such a possibility being excluded by the very basic principles of the QM. What we can do, using the TDSE and the framework of the conventional QM, is to study correlations between different observables at different moments of time. We show that study of the correlation function $C(z,t;v,t_m)$, describing correlations between the probabilities to locate electron in particular regions of the coordinate and momentum spaces, reveals patterns which can be naturally interpreted as manifestations of the electron's ionization event, providing information about spatial location of the exit point, where electron exits the tunneling barrier.
|Presenter name||Igor Ivanov|