Optimal control design strategies for pulsed dynamic nuclear polarization.

We present optimal control methods for the optimization of periodic pulsed dynamic nuclear polarization (DNP) sequences. Specifically, we address the challenge of the optimization of a basic and repeated pulse sequence element which, apart from being easily adaptable to spin systems with different coupling interaction sizes, also proves beneficial in terms of performance. It is demonstrated that matrix power and matrix logarithm functions combined with an auxiliary matrix formalism can be used to derive expressions for gradient ascent pulse engineering (GRAPE) optimization. We illustrate how different implementations provide effective and intuitive control of DNP experiments by tailoring the effective Hamiltonian governing polarization transfer and, in this manner, addressing some of the limitations of prevailing optimal control based pulse design strategies.