  Experiments in coherent spectroscopy correspond to control of quantum
mechanical ensembles guiding them from initial to final target states. The
control inputs (pulse sequences) that accomplish these transformations should
be designed to minimize the effects of relaxation and to optimize the
sensitivity of the experiments. For example in nuclear magnetic resonance (NMR)
spectroscopy, a question of fundamental importance is what is the maximum
efficiency of coherence or polarization transfer between two spins in the
presence of relaxation. Furthermore, what is the optimal pulse sequence which
achieves this efficiency? In this letter, we initiate the study of a class of
control systems, which leads to analytical answers to the above questions.
Unexpected gains in sensitivity are reported for the most commonly used
experiments in NMR spectroscopy.
