Atomic Physics

The other area in which I take an active interest is high intensity laser physics. The understanding of the interaction of light and matter was up to recently essentially based on perturbative treatments, that is assuming that the atomic potential is large in absolute value compared with the intensity of the light. Fermi's golden rule, as one of the central elements in quantum mechanics, could be used successfully for many years in the prediction of photoionization rates of atoms in weak radiation fields. However, meanwhile laser intensities larger than the atomic potential (10 ¹⁶ W/cm² for typical frequencies) are experimentally feasible, such that standard perturbation theory in the electric field strength around the solution for a time independent set up breaks down. It is therefore important to understand the physics of this new intensity regime and develop entirely new approaches. Essentially one should reconsider the entire physics previously studied once more in this new domain. Amongst the phenomena occurring in the high intensity regime, in particular the so-called stabilization (see [ 43 ] for a general introduction) has caused some controversy with regard to its very existence. In general (also this is not always agreed upon) stabilization means that atomic bound states become resistant to ionization in ultra intense laser fields. Our initial goal was to understand this phenomenon. The large majority of results is based on numerical treatments. We aimed in our investigations at rigorous analytical descriptions. The main outcome of our studies [74 ,75 ,54 ,55 ,56 ,57 ] so far is that the governing parameters of the stabilization phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish stabilization exists asymptotically, i.e. the ionization probability as a function of the laser field intensity tends to a finite value. So far we did not find any evidence for the existence of stabilization under different circumstances. The main obstacle in tackling these issues in the high intensity regime is the time dependence of the Schrödinger equation leading to the Dyson series which incorporates the time ordering. Remarkably, for the delta potential one can turn the whole problem into a Volterra differential equation [ 109 ] and then study its properties. In [ 58 ] we investigated this equation with regard to the above mentioned questions, hence obtaining some exact results in this context. This will help to settle many issues which have only been addressed numerically so far.