Investigation and comparison of measurement schemes in the low frequency biosensing regime using solid-state defect centers

Ensembles of solid state defects in diamond make promising quantum sensors with high sensitivity and spatiotemporal resolution. The inhomogeneous broadening and drive amplitude variations across such ensembles have differing impacts on the sensitivity depending on the sensing scheme used, adding to the challenge of choosing the optimal sensing scheme for a particular sensing regime. In this work, we numerically investigate and compare the predicted sensitivity of schemes based on continuous-wave (CW) optically detected magnetic resonance (ODMR) spectroscopy, pi-pulse ODMR and Ramsey interferometry for sensing using nitrogen-vacancy centers in the low-frequency (<10 kHz) range typical for signals from biological sources. We show that inhomogeneous broadening has the strongest impact on the sensitivity of Ramsey interferometry, and drive amplitude variations least impact the sensitivity of CW ODMR, with all methods constrained by the Rabi frequency. Based on our results, we can identify three different regions of interest. For inhomogeneous broadening less than 0.3 MHz, typical of diamonds used in state of the art sensing experiments, Ramsey interferometry yields the highest sensitivity. In the regime where inhomogeneous broadening is greater than 0.3 MHz, such as for standard optical grade diamonds or in miniaturized integrated devices, drive amplitude variations determine the optimal protocol to use. For low to medium drive amplitude variations, the highest sensitivity is reached using pi-pulse ODMR. For high drive amplitude variations, relevant for widefield microscopic imaging, CW ODMR can yield the best sensing performance.