Optimal control of homonuclear spin dynamics subject to relaxation

In this manuscript, we investigate an optimal control problem that arises in connection with the manipulation of open quantum system dynamics. Specifically, we examine a system arising in homonuclear spectroscopy experiments, and show an optimal control can be found by first relaxing the constraint imposed on the control, and then using the solution to the relaxed control problem to solve the original problem. In the context of coherent spectroscopy, this solution translates into the maximum signal to noise ratio that can be obtained in an experiment.