Full Qubit Control in the NV$^-$ Ground State for Low Field or High Frequency Sensing

Abstract: We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV$^-$) defect in diamond. The protocol is especially useful in the low-field regime and for high-frequency sensing applications. It constitutes an extension to the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis change for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast qubit transformations in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields.