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IEEE Transactions on Quantum Engineering

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

Chou-Wei Kiang, Jean‐Fu Kiang

Published Jan 1, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tqe.2025.3529868

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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 containN=108N = 10^{8}N=108uncorrelated NV centers. The application of a Berry sequence to each NVE can achieve the maximum detectable magnetic field of over460 μ460 \ \mu460 μT, 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-μ\muμs temporal resolution in the near future.
A quantum sensing protocol is proposed to apply continuous-wave microwave sequences modulated by Daubechies wavelets to control quantum sensors. The Daubechies wavelet coefficients thus extracted are used to reconstruct a fast time-varying magnetic field with higher smoothness, mitigating square-shaped artifacts as Haar wavelets or Walsh functions are used for modulation. The relations between the qubit readout, the accumulated phase of the quantum state, and the wavelet coefficients are derived based on an intuitive model represented on the Bloch sphere. The efficacy and accuracy of the proposed waveform reconstruction method under various conditions are evaluated by simulations.
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.
Nitrogen vacancy (NV) centers in diamond are atom-scale defects that can be used to sense magnetic fields with high sensitivity and spatial resolution. Typically, the magnetic field is measured by averaging sequential measurements of single NV centers, or by spatial averaging over ensembles of many NV centers, which provides mean values that contain no nonlocal information about the relationship between two points separated in space or time. Here, we propose and implement a sensing modality whereby two or more NV centers are measured simultaneously, and we extract temporal and spatial correlations in their signals that would otherwise be inaccessible. We demonstrate measurements of correlated applied noise using spin-to-charge readout of two NV centers and implement a spectral reconstruction protocol for disentangling local and nonlocal noise sources.
Nitrogen vacancy (NV) centers in diamond are widely deployed as local magnetic sensors, using coherent, single qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators, or using entangled states to improve measurement sensitivity. Here, we describe protocols to use optically unresolved NV center pairs and nuclear spins as multi-qubit sensors for measuring correlated noise, enabling covariance magnetometry at nanometer length scales. For NV centers that are optically unresolved but have spectrally resolved spin transitions, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations by alternating the relative spin orientations of the two NV centers. For NV centers that are both optically and spectrally unresolved, we leverage the presence of a third qubit, a 13C nucleus that is strongly coupled to one of the NV centers, to effect coherent single-NV spin flips and enable a similar phase-cycling protocol. For length scales around 10 nm, we create maximally entangled Bell states through dipole-dipole coupling between two NV centers, and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centers. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV center spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in a dramatic sensitivity improvement. Finally, we demonstrate methods for the detection of high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centers.
An ensemble of nitrogen-vacancy (NV) centers in diamond is a fascinating candidate for realizing a sensitive magnetic field sensor. In particular, since the axes of the NV centers are distributed along four directions, a collection of measurement data from NV centers with different axes provides information on the vector components of a magnetic field. However, in the conventional approach, the low measurement contrast of NV centers limits the sensitivity of vector magnetic field sensing. Recently, to overcome this problem, multi-frequency control of the NV centers has been proposed. The key idea is that four types of NV centers with different axes are simultaneously controlled by multi-frequency microwave pulses. Here, we demonstrate vector magnetic field sensing with an ensemble of NV centers in diamond via such multi-frequency control with pulsed-type measurements. We use Hahn echo pulses and extract information on the vector components of an applied AC magnetic field. We find that the sensitivity of the vector field sensing with multi-frequency control is better than that with single-frequency control for every vector component of a magnetic field.
Quantum sensing of low-frequency magnetic fields using nitrogen-vacancy (NV) center ensembles has been demonstrated in multiple experiments with sensitivities as low as $\sim1pT/1 pT/1pT/\sqrt{\text{Hz}}.Todate,however,demonstrationsofhigh−frequencymagnetometryintheGHzregimewithNVdiamondareordersofmagnitudelesssensitive,abovethenT/. To date, however, demonstrations of high-frequency magnetometry in the GHz regime with NV diamond are orders of magnitude less sensitive, above the nT/.Todate,however,demonstrationsofhigh−frequencymagnetometryintheGHzregimewithNVdiamondareordersofmagnitudelesssensitive,abovethenT/\sqrt{\text{Hz}}$ level. Here we adapt for microwave frequencies techniques that have enabled high-performance, low-frequency quantum sensors. Using a custom-grown NV-enriched diamond combined with a noise cancellation scheme designed for high-frequency sensing, we demonstrate a Rabi-sequence-based magnetometer able to detect microwave fields near 2.87 GHz with a record sensitivity of 3.4 pT/Hz\sqrt{\textrm{Hz}}Hz​. We demonstrate both amplitude and phase sensing and project tunability over a 300 MHz frequency range. This result increases the viability of NV ensembles to serve as microwave circuitry imagers and near-field probes of antennas.