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arXiv:2505.05825

Frequency Range Boosted Magnetometry Beyond the Spin Coherence Limit via Compressive Sensing

Ruiqi Wang, Peiyu Yang, Huang, Ding, Guzhi Bao, Weiping Zhang

Published May 9, 2025• 0 citations
arXivHTMLPDF

Abstract

Free induction decay (FID) of spin precession serves as an essential tool for quantum sensing across diverse platforms. While extending spin coherence time remains critical for sensitivity enhancement, the requisite long single-shot acquisitions narrow the resolvable frequency range, establishing a fundamental ``spin coherence limit (SCL)'', according to the Nyquist Sampling Theorem. Besides, conventional spectral analysis for FID measurement suffers from frequency alias, causing signal attenuation and positional errors that compromise the measurement validity. Here, we demonstrate a general frequency-range-extended technique that overcomes SCL by leveraging compressive sensing. By applying this method to the FID magnetometer, we expand the resolvable frequency range significantly from the Nyquist-limited range of 251\,Hz to 3000\,Hz, effectively avoiding frequency alias. Our work paves the way for implementing long-coherence-time spin systems in high-sensitivity, broad-bandwidth, and alias-free magnetic field sensing.

DOI
10.48550/arxiv.2505.05825

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Free induction decay (FID) of spin precession serves as an essential tool for quantum sensing across diverse platforms. While extending spin coherence time remains critical for sensitivity enhancement, the requisite long single-shot acquisitions narrow the resolvable frequency range, establishing a fundamental ``spin coherence limit (SCL)'', according to the Nyquist Sampling Theorem. Besides, conventional spectral analysis for FID measurement suffers from frequency alias, causing signal attenuation and positional errors that compromise the measurement validity. Here, we demonstrate a general frequency-range-extended technique that overcomes SCL by leveraging compressive sensing. By applying this method to the FID magnetometer, we expand the resolvable frequency range significantly from the Nyquist-limited range of 251,Hz to 3000,Hz, effectively avoiding frequency alias. Our work paves the way for implementing long-coherence-time spin systems in high-sensitivity, broad-bandwidth, and alias-free magnetic field sensing.
We demonstrate an optically pumped magnetometer (OPM) operated in a free-induction-decay (FID) configuration that is capable of tracking oscillating magnetic signals in the presence of a 50 μT static field. Excellent waveform reconstruction is demonstrated for low frequency modulations with respect to the Nyquist limited bandwidth. A 100 pT oscillation was successfully reconstructed using signal averaging, and an optimum sensitivity of 3.9 pT/Hz was measured from the spectrum of the residuals relative to the sinusoidal fit. The impact of the pump-probe repetition rate and spin depolarization on the frequency response of the sensor is investigated in detail using miniaturized vapor cell technology, with the (-3 dB) bandwidths residing beyond the Nyquist limit in each case. We also discuss technical limitations associated with the magnetometer when exposed to oscillating fields of sufficiently high amplitude or frequency. This is discussed in the context of potential distortions arising in the reproduced signals, induced by frequency modulation (FM) and aliasing artefacts.
Optically pumped magnetometers (OPMs) based on the free-induction-decay (FID) configuration have recently attracted interest owing to their advantages, such as being calibration-free, easy to operate, and showing reduced light shifts induced by the pump light. Currently, alkali-metal vapor cells have been employed in most of the FID magnetometers. However, the relatively narrow linewidth of the magnetic resonance signal and nonlinear Zeeman (NLZ) effects generate bandwidth limitation and heading errors of these magnetometers in the Earth's field, respectively. In this work, we propose a 4He{}^{4}\mathrm{He}4He-based FID magnetometer, which not only has the advantages of being NLZ-free and showing a high bandwidth, but also maintains an enhanced sensitivity assisted by a multipass cell. This magnetometer demonstrates a magnetic field noise floor of 0.34pT/Hz1/20.34\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/{\mathrm{Hz}}^{1/2}0.34pT/Hz1/2 with a Nyquist-limited bandwidth of 555 kHz, which opens another route for atomic magnetometry using FID signals, and exhibits potential for applications in high-frequency magnetic field detection, such as biomagnetic measurements and magnetic communications in the geomagnetic field.
Nitrogen-vacancy (NV) center in diamond is a promising quantum metrology tool finding applications across disciplines. The spin sensor measures magnetic fields, electric fields and temperature with nano-scale precision and is fully operable under ambient conditions. Moreover, it achieves precision scaling inversely with total measurement time σB ∝ 1/T (Heisenberg scaling) rather than as the inverse of the square root of T, with σB = √T the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs), in combination with single-shot read-out. Despite their accuracy, the range of applicability of PEAs is limited to sensing single frequencies with negligible temporal fluctuations. Nuclear Magnetic Resonance (NMR) signals from molecules often contain multifrequency components and sensing them using PEA is ruled out. Here we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques focusing on nanoscale NMR. We show that CS can provide for precision scaling approximately as σB ≈ 1/T, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required. We illustrate our method by taking model solid-state spectra of Glycine acquired under Magic Angle Spinning conditions.
Alkali-metal optically-pumped magnetometers are prone to inaccuracies arising from the overlap of the average F = I + 1/2 and F = I - 1/2 ground-state Zeeman resonances. We employ density-matrix simulations and experiments to investigate how this hyperfine systematic error varies with spin polarization in a 87^{87}87Rb free-induction-decay (FID) magnetometer. At low spin polarizations, (P≤0.5P \leq 0.5P≤0.5), this effect causes single-frequency magnetic-field extraction techniques to exhibit inaccuracies up to approximately 3.5 nT. Density-matrix simulations reveal that this bias can be traced to the relative amplitude and phase between the F = I ±\pm± 1/2 hyperfine ground-state manifolds in the FID spin precession signal. We show that this systematic error can be mitigated using either a double-frequency fitting model that accounts for the relative amplitude and phase or synchronous-pulse pumping, that minimizes the F = 1 contribution to the FID signal. Theoretical simulations predict accuracies within 0.5 nT for both techniques across a wide range of spin polarizations, suggesting a sevenfold enhancement over single-frequency extraction methods. Our experiments validate this, showcasing a variation in the extracted field below 1 nT, a 3.5-fold improvement compared to single-frequency extraction methods. Furthermore, the mitigation techniques demonstrate agreement of the extracted magnetic field within 1.5 nT.
Free induction decay (FID) optically pumped magnetometers are among the most sensitive quantum sensors available for high-precision magnetic field measurements. This review summarizes recent advances in FID magnetometers, which represent a critical technological route that suppresses systematic errors by temporally separating atomic polarization from magnetic field detection. This review covers light-modulated optical pumping schemes (such as the Bell-Bloom mode), radio-frequency excitation schemes, and magnetic-field-enhanced pumping schemes. Key technological developments, including chip-scale MEMS fabrication, optical multipass architectures, advanced frequency estimation algorithms, and error suppression methods, are also discussed. Finally, emerging trends toward higher integration, environmental robustness, and intelligent signal demodulation are highlighted. These trends provide insights into the development of next-generation high-performance quantum sensors and their growing role in biomedical and geophysical applications, as well as in fundamental scientific research.
Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time σB∝1/Tσ_{B} \propto 1/TσB​∝1/T (Heisenberg scaling) rather than as the inverse of the square root of TTT, with σB=1/Tσ_{B} =1/\sqrt{T}σB​=1/T​ the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs) using adaptive or non-adaptive feedback, in combination with single-shot readout techniques. Despite their accuracy, the range of applicability of PEAs is limited to periodic signals involving single frequencies with negligible temporal fluctuations. In this Letter, we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques. We show that CS can provide for precision scaling approximately as σB≈1/Tσ_{B} \approx 1/TσB​≈1/T, both in the case of single frequency and frequency multiplexed signals, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required.