Piecewise time-independent procedure to control two-level systems

We present a general and mathematically simple method to control two-level systems. It is based on a piecewise time-independent procedure. We assume that some parameters of an external interaction potential can be rapidly switched at specified time instants, and then kept constant during small time intervals Δt. By properly setting the parameter values, obtained from algebraic, instead of differential or integral, equations, we can drive the time evolution of arbitrary observables. We illustrate the approach with some examples and discuss important technical aspects, relevant in real concrete situations, such as the robustness of the method to errors in the control parameter values, the influence of the switching mechanism transient times, the appropriate choice for the Δt's, and so on.