Wavelet-based fast time-resolved magnetic sensing with electronic spins in diamond

Time-resolved magnetic sensing is of great importance from fundamental studies to applications in physical and biological sciences. Recently, the nitrogen-vacancy defect center in diamond has been developed as a promising sensor of magnetic fields under ambient conditions. However, methods to reconstruct time-resolved magnetic fields with high sensitivity are not yet fully developed. Here, we propose and demonstrate a sensing method based on spin echo and Haar wavelet transformation. Our method is exponentially faster in reconstructing time-resolved magnetic fields with comparable sensitivity than existing methods. It is also easier to implement in experiments. Furthermore, the wavelet's unique features enable our method to extract information from the whole signal with only part of the measuring sequences. We then explore this feature for a fast detection of simulated nerve impulses. These results will be useful to time-resolved magnetic sensing with quantum probes at nanoscale.