Control of concerted back-to-back double ionization dynamics in helium

Abstract

To first order, a strong, external field doubly-ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion). Here, using a (1+1)-dimensional model, we optimize the field with the objective that the two electrons be ejected into opposite directions (back-to-back motion). The optimization is performed using four different control procedures: (1) Local control, (2) derivative-free optimization of basis expansions of the field, (3) the Krotov method and (4) control of the classical equations of motions. Superficially, all four procedures give different fields. However, upon a more careful analysis all the fields obtained exploit essentially the same two-step mechanism leading to back-to-back motion: First, the electrons are displaced by the field into the same direction. Second, after the field turns off, the nuclear attraction and the electronelectron repulsion combine to generate the final motion into opposite directions for each electron. By performing quasi-classical calculations, we confirm that this mechanism is essentially classical.