NV-ERC: a robust protocol for control of double quantum transitions in diamond NV centers

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 for sensing in two regimes: on the one hand, in the low-field limit where the Zeeman splitting of the NV center is smaller than the MW Rabi frequency; on the other hand, for the detection of high-frequency signals comparable to the Zeeman splitting of the NV center. It constitutes an extension of 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 with the approach and, more specifically, the relevant basis transformation for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast single-qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors and demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields, testing its effectiveness in a Hahn-echo sequence.