Controllability, observability, and parameter identification of two coupled spin 1's

In this note, we study the control theoretic properties of a couple of interacting spin 1's driven by an electromagnetic field. In particular, we assume that it is possible to observe the expectation value of the total magnetization and we study controllability, observability, and parameter identification of these systems. We give conditions for controllability and observability and characterize the classes of equivalent models which have the same input-output behavior. The analysis is motivated by the recent interest in three level systems in quantum information theory and quantum cryptography as well as by the problem of modeling molecular magnets as spin networks.