High field magnetometry with hyperpolarized nuclear spins

Sub-micron scale NMR spectroscopy is a significant challenge in chemical analysis. Quantum sensing, particularly using nitrogen-vacancy (NV) centers in diamond, has shown promise. However, NV sensors typically operate at low magnetic fields (<0.3 T), limiting chemical shift discrimination. High magnetic fields are advantageous for NMR due to increased chemical shift dispersion and higher analyte polarization. The high electronic gyromagnetic ratio of NV centers makes high-field control difficult, and precise field alignment is crucial for spin readout. Nanodiamond magnetometers face similar challenges at high fields. This paper proposes using hyperpolarized ¹³C nuclei in diamond as the primary sensor, with NV centers for initialization. The low gyromagnetic ratio of ¹³C is advantageous for high-field operation, and their long transverse and longitudinal relaxation times (T₂* and T₁, respectively) enable minute-long sensing periods. The ¹³C nuclei's sensitivity to magnetic fields is not affected by crystal orientation, unlike NV centers, and RF readout is background-free and immune to optical scattering. Although low gyromagnetic ratios and strong dipolar coupling between ¹³C nuclei are normally detrimental to sensor sensitivity, the researchers show that hyperpolarization and spin-locking techniques mitigate these drawbacks.

The authors review existing literature on quantum sensing methods, focusing on the limitations of NV center-based sensors at high magnetic fields. They highlight the advantages of using ¹³C nuclei for high-field sensing, referencing prior work on optical hyperpolarization and long spin lifetimes of ¹³C in diamond. The challenges associated with using nuclear spins as quantum sensors due to their low gyromagnetic ratio and strong dipolar coupling are also discussed. The researchers contrast their approach with previous methods using nuclear spins and dynamical decoupling techniques.

The researchers employed a single-crystal diamond sample with approximately 1 ppm NV center concentration and natural abundance ¹³C. Hyperpolarization of the ¹³C nuclei was achieved using a previously described method at 38 mT (details in Supplementary Note 6). At 7 T, a pulsed spin-locking sequence was implemented to maintain the ¹³C spins along the transverse x-axis. A train of θ pulses was applied, with a high pulse duty cycle (19-54%) and short interpulse spacing (τ < 100 μs). Inductive interrogation of the ¹³C nuclei occurred during acquisition windows between pulses. The magnetometer signal was derived from the magnitude of the heterodyned Larmor precession, representing the transverse magnetization component. Experiments involved applying a large number of pulses (N ≥ 200k). The response to an applied AC magnetic field was analyzed by decomposing the signal into decaying (Sd) and oscillatory (So) components. The decay component's dependence on the AC field frequency was investigated, revealing a sharp decay response (dip) at resonance. The oscillatory component was analyzed using Fourier transforms to extract high-resolution peaks corresponding to harmonics of the AC field frequency. The frequency response of the sensor was characterized using a chirped AC field, revealing a narrow response near resonance and a Gaussian response outside the resonance region. The researchers used Average Hamiltonian Theory (AHT) to model the system's dynamics under the pulsed spin-locking sequence and the applied AC field. Two complementary perspectives were used: one equivalent to dynamical decoupling sensing and the other using a rotating-frame NMR experiment analogy. The theoretical analysis considered the Zeeman Hamiltonian, dipolar interactions between ¹³C nuclei, and the applied AC field.

The key findings include: a demonstration of a high-field magnetometer using hyperpolarized ¹³C nuclear spins in diamond; achieving a single-shot sensitivity of 410 pT/√Hz at 7 T; demonstrating a detection bandwidth up to 7 kHz and a spectral resolution <100 mHz; observing long transverse spin lifetimes exceeding 30 s despite the high pulsing rate; extracting high-resolution AC magnetometry linewidths (92 mHz and 96 mHz for primary and secondary harmonics, respectively) from the oscillatory component of the signal; showing that the sensor response is robust to pulse errors and can be operated with arbitrary flip angles (except π); identifying a resonance condition where the AC field periodicity matches the time to complete a 2π rotation; observing a linear and quadratic dependence of primary and secondary harmonic intensities on the AC field amplitude; demonstrating real-time tracking of a chirped AC magnetic field; and developing a theoretical model using Average Hamiltonian Theory to explain the observed behavior. The study successfully mitigated the challenges associated with the low gyromagnetic ratio of ¹³C nuclei and their strong dipolar coupling via hyperpolarization and spin-locking, achieving remarkable sensitivity and resolution at high magnetic fields.

The results demonstrate the feasibility of high-field quantum sensing using hyperpolarized nuclear spins, overcoming the limitations of traditional NV center-based sensors. The achieved sensitivity and resolution are comparable to or better than other competing technologies for high-field AC magnetometry in a specific niche. The robustness of the method to pulse errors and the ability to operate with arbitrary flip angles enhance its practicality. The theoretical analysis provides a good qualitative understanding of the system's behavior, but a more complete model is needed to account for the effects of dipolar interactions. The approach opens new avenues for microscale NMR chemical sensors and high-resolution magnetometry.

This work successfully demonstrated a high-field magnetometer using hyperpolarized ¹³C nuclear spins, achieving high sensitivity and resolution. The approach is robust, offering advantages over existing high-field sensing technologies. Future research should focus on optimizing the sensitivity through improvements in hyperpolarization, sample filling factor, and RF coil design. Further theoretical work is needed for a complete quantitative description of the system's behavior. This technology has the potential for applications in microscale NMR chemical sensing and high-resolution magnetometry in condensed matter systems.

The current sensitivity is lower than that of low-field NV quantum sensors. Although the authors provide estimates for sensitivity improvements, realizing these gains requires further technological advancements. The theoretical model is a qualitative description that does not fully account for dipolar interactions. The experiments were primarily conducted on single-crystal diamonds. Extending the methodology to nanodiamonds requires further investigation.