Wavelet-Based Quantum Sensing of Geomagnetic Fluctuations With Multiple NV Ensembles

Nitrogen-vacancy (NV) ensembles are viable magnetometers to be implemented on nanosatellites for monitoring geomagnetic fluctuations, which are credible precursors for predicting earthquakes at short notice. In this work, a Haar wavelet-based quantum sensing method is proposed to reconstruct the time-varying waveform of geomagnetic fluctuations in the very low frequency band. To collect different frequency components of fluctuations waveform at once, we propose a schematic to employ multiple NV ensembles (NVEs), with each controlled by an independent microwave source. Berry sequences are applied on one set of NVEs to extract the scaling coefficients from accumulated geometric phases to reconstruct near-dc components of a waveform. Spin-echo sequences are applied to another set of NVEs to extract the Haar wavelet coefficients from the dynamic phases to reconstruct high-frequency components. The efficacy of the proposed sensing protocol implemented on multiple NVEs is validated by reconstructing a waveform of geomagnetic fluctuations from a DEMETER satellite dataset through simulations. Each NVE is assumed to contain $N = 10^{8}$ uncorrelated NV centers. The application of a Berry sequence to each NVE can achieve the maximum detectable magnetic field of over $460 \ \mu$T, resolving the issues of phase ambiguity and hyperfine-induced detuning if conventional Ramsey sequence were applied. The feasibility of the proposed simulation scenario considering spin-bath noise within an NVE is justified by simulations. The effects of wavelet scales, Rabi frequency in Berry sequence, and number of NV centers in each NVE are analyzed. The proposed NVE quantum sensors operated with the proposed sensing protocol can be installed on nanosatellites to monitor global geomagnetic fluctuations, with sub-$\mu$s temporal resolution in the near future.