Time-optimal polarization transfer from an electron spin to a nuclear spin

Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum information processing on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches, and we thereby establish an important class of faster controls. We highlight how time-optimal polarization transfers and their optimality are related to the time optimality of unitary transformations. Moreover, our work develops generally applicable analytic methods for analyzing the limits in controlling quantum systems.