Optimal Control of Spin Dynamics in the Presence of Relaxation

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.