Optimal Microwave Control Pulse for Nuclear Spin Polarization and Readout in Dense Nitrogen-Vacancy Ensembles in Diamond

Nitrogen-vacancy (NV) centers possessing nuclear spins are promising candidates for a novel nuclear spin gyroscope. Preparation of a nuclear spin state is a crucial step to implement a sensor that utilizes a nuclear spin. In a low magnetic field, such a preparation utilizes population transfer, from polarized electronic spin to nuclear spin, using microwave pulses. The use of the narrowband microwave pulse proposed earlier is inefficient when magnetic transitions are not well resolved, particularly when applied to diamond with a natural abundance of carbon atoms or dense ensembles of NV centers. Herein, the optimization of the pulse shape for 3 relatively easily accessible pulse shapes is performed. The optimization is done for a range of magnetic transition linewidths, corresponding to the practically important range of nitrogen concentrations (5-50 ppm). It is found that, while at low nitrogen concentrations the optimized pulse adds very little to simple square shape pulse, in the case of dense NV ensembles, with a rather wide magnetic transition width of 1.5 MHz optimal pulses, a 15% improvement in the population of the target state is observed, potentially leading to 41% improvement in the NV-based gyroscope sensitivity.