Reverse engineering approach for controlling the spin dynamics

In a reverse engineering protocol, one sets the evolution of the spin variables and infer the time evolution of the magnetic components. The solution is not unique, and therefore there are many classes of solutions depending on the analytical formulation of the problem that has been considered. I will illustrate this feature using three different formulations of the same problem.

In practice, we first setup a reverse protocol procedure to manipulate a single spin and two spins with different gyromagnetic factors in short amount of times. Finally, we expand the parameter space of those solutions to fulfill extra requirements such as the robustness of a given spin manipulation or the application of the transformation to two interacting spins. We consider isotropic or anisotropic interactions. In this latter situation, we study the production of entangled states.