Entanglement Generation on the Double Quantum Transition of NV Ground State Via Globally Addressing Microwave Pulse

Entanglement is a key quantum feature that enables quantum sensors to improve their sensitivity up to the Heisenberg limit. In the NV center platform, the Heisenberg limit can only be achieved when the axes of the NV centers are parallel. Nevertheless, parallel NV centers are spectrally indistinguishable and no mechanisms to directly prepare Heisenberg--limit--grade entanglement in such configurations are known to date. In this work we propose for the first time a viable mechanism to prepare entangled states in the double quantum transition of two dipolarly coupled NV centers whose axes are parallel without populating intermediate states, so as to reach the Heisenberg limit in sensing. Our approach is based on the NV effective Raman coupling (NV-ERC) protocol and makes use of global addressing of both NV centers with a single monochromatic microwave pulse. Supported by an adiabatic elimination analysis, several mechanisms for the preparation of different entangled states are identified, all of which avoid the involvement of intermediate states. This not only minimizes the impact of additional noise sources, but also enables the state generation process itself to serve as effective sensing time--an advantage over conventional approaches where such preparation typically constitutes a separate, non--contributory stage. We consider the generation of different entangled states belonging to the double quantum transition, sensitive to either transverse electric fields or longitudinal magnetic fields, all with a fourfold improved sensitivity compared to conventional single NV settings.