Magnetometry with broadband microwave fields in nitrogen-vacancy centers in diamond

Nitrogen-vacancy (NV) centers in diamond are optically addressable and versatile light-matter interfaces with practical application in magnetic field sensing, offering the ability to operate at room temperature and reach sensitivities below pT/$\sqrt{\mathrm{Hz}}$. We propose an approach to simultaneously probe all of the magnetically sensitive states using a broadband microwave field and demonstrate that it can be used to measure the external DC magnetic field strength with sensitivities on the order of 10~pT/$\sqrt{\mathrm{Hz}}$. We develop tools for analyzing the temporal signatures in the transmitted broadband microwaves to estimate the magnetic field, comparing maximum likelihood estimation based on minimizing the Kullback-Leibler divergence to various neural network models, and both methods independently reach practical sensitivities. These results are achieved without optimizing parameters such as the bandwidth, and shape of the probing microwave field such that further improvements in sensitivity can be envisioned. Our results motivate novel implementations of NV-based magnetic sensors with the potential for vectorial magnetic field detection at 1-10 kHz update rates and improved sensitivities without requiring a bias magnetic field.