Optimal Control of Coupled Spin Dynamics under Cross-Correlated Relaxation

Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this paper, we solve a new class of optimal control problems, which helps establish physical limits on how closely a quantum mechanical system can be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum coherence or polarization that can be transferred between coupled nuclear spins in the presence of very general decoherence mechanisms that include cross-correlated relaxation. We give analytical expressions for the optimal control laws (pulse sequences). Exploitation of cross-correlation effects has recently led to the development of powerful methods in NMR spectroscopy to study very large biomolecules in solution. We demonstrate that the optimal pulse sequences provide significant gains over these state of the art methods, opening new avenues for spectroscopy of much larger proteins. It is shown that in spite of very large relaxation rates, optimal control can transfer coherence without any loss when cross-correlated relaxation rates are tuned to auto-correlated relaxation rates.