Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters. Here we study the dependence of the lock-in spectral slope on the modulation of the spin-driving microwave field. Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is ≳1/4, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation. We formulate a model for calculating lock-in spectra which shows excellent agreement with our experiments, and which shows that an optimum slope is achieved when the linewidth/separation ratio is ≲1/4 and the modulation depth is less then the resonance linewidth, irrespective of the modulation function used.
@article{arxiv.1707.00916,
title = {Optimised frequency modulation for continuous-wave optical magnetic resonance sensing using nitrogen-vacancy ensembles},
author = {Haitham A. R. El-Ella and Sepehr Ahmadi and Adam M. Wojciechowski and Alexander Huck and Ulrik L. Andersen},
journal= {arXiv preprint arXiv:1707.00916},
year = {2017}
}