Simulation of ODMR Spectra from Nitrogen-Vacancy Ensembles in Diamond for Electric Field Sensing

Solid state spins in diamond, in particular negatively charged nitrogen-vacancy centers (NV), are leading contenders in the field of quantum sensing. While addressing of single NVs offers nanoscale spatial resolution, many implementations benefit from using large ensembles to increase signal magnitude and therefore sensitivity. However, sensing with ensembles brings its own challenges given the random orientation of the spin quantization axis within the diamond crystal lattice. Here, we present an open source simulation tool that models the influence of arbitrary electric and magnetic fields on the electronic and nuclear spin states of NV ensembles, and can be extended to other color centers. Specifically, the code computes the transition strengths and predicts the sensitivity under shot-noise-limited optically-detected magnetic resonance. We illustrate the use of the code in the context of electric field sensing, a promising emerging functionality of NV centers with applications in biosensing and electronics, and bring several subtle features to light that are due to the interplay between different NV orientations and the external electric and microwave fields. Moreover, we show that our code can be used to optimize sensitivity in situations where usual arguments based on neglecting terms in the full Hamiltonian would give sub-optimal results. Finally, we propose a novel sensing scheme which allows to perform full vector electrometry without the need for precise bias magnetic field alignment, thus reducing the experimental complexity and speeding up the measurement procedure.