Control of the evolution of Heisenberg spin systems

In this paper, we give an algorithm for the control of the for the system of two spin 1/2's unitary evolution operator ? interacting through Heisenberg interaction. This algorithm allows for arbitrarily bounded control. The results extend previous ones that only concerned the control of a pure state. A Lie group decomposition technique is used to this goal and the problem is reduced to a two level problem with constraints. We also show how the control result allows to obtain information on the initial state through a series of evolutions and measurements. The study of the Heisenberg spin model is motivated by applications in electron paramagnetic resonance and in molecular magnetism. For these systems, the drift which models the interaction between the spins is typically large and cannot be neglected in the control design but it has to be used to reach the objective.