  Double ionization (DI) is a fundamental process that despite its apparent
simplicity provides rich opportunities for probing and controlling the
electronic motion. Even for the simplest multielectron atom, helium, new DI
mechanisms are still being found. To first order in the field strength, a
strong external field doubly ionizes the electrons in helium such that they are
ejected into the same direction (front-to-back motion). The ejection into
opposite directions (back-to-back motion) cannot be described to first order,
making it a challenging target for control. Here, we address this challenge and
optimize the field with the objective of back-to-back double ionization using a
(1 + 1)-dimensional model. The optimization is performed using four different
control procedures: (1) short-time control, (2) derivative-free optimization of
basis expansions of the field, (3) the Krotov method, and (4) control of the
classical equations of motion. All four procedures lead to fields with dominant
back-to-back motion. 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 electron-electron 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.
