How University of Basel Researchers Resolve NV-Center Depth with NMR

University of Basel researchers have developed a new method for pinpointing the depth of shallow nitrogen-vacancy (NV) centers in diamond, utilizing the 1H nuclear magnetic resonance (NMR) signal of immersion oil. The team’s approach addresses limitations inherent in the commonly used XY8 dynamical decoupling sequence, which is vulnerable to inaccuracies stemming from interference from nearby spins due to its reliance on finite-width pulses. Instead, the researchers employ Spin-Lock NMR, leveraging the Hartmann, Hahn resonance to probe the 1H NMR signal and achieve substantially higher instrument-limited spectral resolution. The researchers derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination.

Nitrogen-Vacancy Centers as Quantum Sensors

Shallow nitrogen-vacancy (NV) centers in diamond are increasingly vital for quantum sensing, yet accurately determining their depth below the diamond surface has presented a persistent challenge for researchers. The team discovered that finite-width pulses used in XY8 make it susceptible to “subharmonic responses, including unwanted contributions from nearby spins,” meaning current depth readings may be less precise than previously assumed. The XY8 method also suffers from a low instrument-limited frequency resolution, typically in the range of 5 to 10 kHz, potentially leading to incomplete sampling of the NMR signal and reduced precision in depth calculations. Strategies like using isotopically purified diamond or operating at lower magnetic fields can mitigate these issues, but they introduce other experimental constraints. Daniel et al. sought a fundamentally different approach, introducing Spin-Lock NMR as an alternative for single-NV depth determination.

Critically, the team demonstrated that Spin-Lock NMR avoids the spurious harmonics that plague XY8, and can achieve a spectral resolution exceeding 5 kHz. To validate their approach, they applied it to investigate the 1H nuclear spin signal consistently observed on diamond surfaces, even without immersion oil. The results yielded NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers, establishing Spin-Lock NMR as a robust and reliable alternative for quantitative single-NV depth determination, and enabling more accurate quantum sensing applications.

Researchers at the University of Basel have developed Spin-Lock NMR as an alternative, addressing these limitations with a fundamentally different approach to signal acquisition. This improvement stems from tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, allowing the NV center to directly probe the NMR signal without the interference experienced by the XY8 sequence. The experimental arrangement, as detailed in their work, involves detecting magnetic fluctuations produced by the 1H spins with a gold wire loop, enabling the NV center to sense the signal. The researchers explain the precision and quantitative nature of their technique.

XY8 Sequence Limitations in Depth Measurement

Researchers at the University of Basel are refining techniques for precisely locating shallow nitrogen-vacancy (NV) centers within diamond, critical for advancing quantum sensing applications. The established protocol, detailed in recent work, infers NV center depth by modeling the interaction between the NV spin and the magnetic signal produced by the 1H spins. A key limitation of the XY8 sequence stems from the use of finite-width pulses, rendering it susceptible to “subharmonics of the target frequency as well as other spurious magnetic signals,” according to the research. This means that the XY8 method isn’t solely detecting the desired 1H signal; it also picks up interference from the fourth harmonic of 13C spins within the diamond lattice, potentially leading to an underestimation of the NV center’s depth when employing the standard analytical model.

The instrument-limited frequency resolution of XY8, typically in the range of 5 to 10 kHz, can lead to “undersampling of the NMR line and thereby reduce the precision of the resulting depth fit,” given typical 1H NMR linewidths of 10 to 20 kHz. While strategies like using isotopically purified diamond or operating at lower magnetic fields can mitigate these issues, they introduce other experimental constraints. Modifications to the XY8 sequence itself, like XY8 correlation spectroscopy or adaptive XY sequences, have also been explored, but these increase pulse complexity and sequence duration, ultimately reducing the signal-to-noise ratio. The team highlights that instead of refining XY8, they have introduced Spin-Lock NMR as a fundamentally different approach, aiming to overcome these limitations without compromise.

The prevailing technique, while widely used, is susceptible to interference. This equation directly correlates the measured spectrum with the NV center’s depth, providing a robust and accurate means of calculation. By accurately describing this interaction, the model can extract the NV depth from the observed NMR spectrum with greater precision than previously possible.

1H NMR Signal Detection with Spin-Lock Resonance

Shallow NV-center depth measurements, crucial for quantum sensing applications, have long relied on a technique now revealed to be less precise than previously understood. This discovery challenges the accuracy of depth readings obtained through established protocols, particularly in scanning NV magnetometry where precise depth knowledge is paramount for accurate magnetic field reconstruction. The widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape.

By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann, Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. The researchers derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ the method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.