Detection of diamond surface electric-field noise is of importance for studying the coherence properties of shallow nitrogen-vacancy (NV) centers. Using the double quantum relaxation method, we demonstrated that the noise has a power-law frequency dependence, and it increases slowly from 295 K to 420 K but reduces quickly at higher temperatures. As the Dutta-Horn model described, the noise is created by ensembles of two-level systems with activation energies ranging from 0.3 eV to 0.6 eV. For diamond surface passivation, we found that the solid covering material (PMMA) outperforms the liquid one (glycerol) in reducing the electric-field noise, which was attributed to the presence of surface-modified phononic coupling noise. We anticipate that our findings will contribute to a better understanding of the origins of surface 1/f electric-field noise, as well as identify optimal covering materials for enhancing the coherence time of near-surface NV centers.
Shallow nitrogen-vacancy (NV) centers in diamond are promising nanoscale quantum sensors, yet their coherence is strongly limited by surface-induced noise. Surface adsorbates are widely believed to be a major source of decoherence. Here, we test this assumption by characterizing shallow single NV centers under ultrahigh vacuum (UHV) conditions, where the diamond surface is kept free of adsorbates, and comparing their behavior to ambient conditions. Surprisingly, we observe a ~4x reduction in the Hahn echo coherence time T2 in UHV. By combining Hahn echo measurements in the single-quantum (SQ) and double-quantum (DQ) bases, we separate contributions from different noise sources and find that both electric and magnetic noise are enhanced in UHV. In contrast, T1 measurements reveal an increased DQ T1 in UHV, indicating suppressed electric field noise in the ~100 MHz frequency regime. These results point to a modification of the surface noise spectrum upon adsorbate removal, with different frequency regimes arising from distinct microscopic mechanisms. Specifically, we find that the low frequency noise is consistent with increased surface charge in UHV that can be compensated by surface adsorbates in ambient conditions. Our findings highlight a complex and previously underappreciated role of surface adsorbates in shaping the noise environment of shallow NV centers, with important implications for nanoscale quantum sensing.
Characterizing electric field noise in diamond is crucial for utilizing nitrogen-vacancy (NV) centers as probes and qubits. However, NV centers under axial magnetic fields are sensitive to magnetic fields and thus are limited in their ability to characterize electric fields directly. In this study, we engineered NV centers exhibiting strong intrinsic effective electric fields through ion implantation into CVD-grown diamond. We selected seven NV centers with splittings in the range of 18–66 MHz as the focus of our research. By virtue of the suppression effect of the strong effective field on the magnetic field, the energy level shift caused by the magnetic field was reduced by two orders of magnitude. Combining spectral decomposition techniques, we extracted the electric noise spectrum in the low-frequency range from the environmental noise. Our results indicate that the near-surface electrical noise of the diamond deviates from the 1/f noise model, and two characteristic correlation times were observed within the measured frequency range (1–10 MHz).
We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.
Nitrogen vacancy centers (NV) in proximity to diamond surfaces are promising nanoscale quantum sensors. However, their coherence properties are negatively affected by magnetic and electric surface noise, whose origin and detailed impact have remained elusive. Using atomistic models of diamond surfaces derived with density functional theory, together with decoherence time calculations with cluster correlation expansion methods, we quantify the effects of surface crystallographic orientation and functionalization, and of the density of unpaired electrons on the NV Hahn-echo time
T2. We determine a crossover depth at which
T2 ceases to be limited by surface nuclear spins and recovers the bulk-limited value. We find that for static surface-electron baths, the ratio between the NV depth and the separation between surface electron spins determines a transition from fast-fluctuating to quasi-static noise, leading to a dependence of
T2 on orientation for specific surfaces. We also find that the modulation of
T2 by spin-phonon relaxations leads to motional-narrowing at sub-microsecond relaxation times. Importantly, our calculations show that it is only when accounting for surface-spin in-sequence hopping that measured
T2 values as a function of depth can be reproduced, thus highlighting the importance of hopping-mediated models to describe the surface spin noise affecting NV sensors. Overall, our work provides clear guidelines for engineering diamond surfaces to achieve enhanced NV coherence for quantum sensing and information processing applications.
Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond, causing line broadening and decreasing the coherence time
(T2). Following our previous electric and magnetic field noise work, we investigate noise caused by the diamond surface roughness, which is a source for charge density fluctuations and incoherent photon scattering. We find that the varying surface charge density noise source is prevalent throughout the entire NV dynamical decoupling frequency range, while the photon scattering noise is almost negligible. Next, we combine the results from various noise sources to perform comprehensive analyses on
T2 and how it varies with NV depth. At a given NV depth of 5
nm below a hydrogen- or fluorine-terminated surface, we find that these magnetic nuclei reduce the NV coherence time the most, followed by the surface electric field noise sources. The photon scattering and bulk magnetic field noise effects on
T2 are weak compared to the varying charge density, electric dipole, and surface impurity noise. However, with oxygen surface termination, the surface electric field noise sources are comparable to the surface magnetic field noise. Our calculated values of
T2,Hahn (few $\ensuremath{\mu}\mathrm{s}$ to 10 $\ensuremath{\mu}\mathrm{s}$) are in good agreement with the experimental values reported elsewhere. Finally, we calculate an anticipated signal-to-noise ratio (SNR) for NV AC magnetometry of external nuclear spins. In our simplified assessment, where some depth-dependent parameters (e.g., NV conversion efficiency) are held constant, we find that shallower NV layers should yield the best SNR, which is consistent with experimental findings.
High spatial resolution quantum sensing of near-surface nitrogen vacancy (NV) centers in diamond has enabled detection of magnetic, electrical, and thermal signals at the nanoscale. At depths of just a few nanometers, NV centers serve as localized quantum probes for external spins or low-dimensional materials, but their proximity to the surface also enhances decoherence caused by fluctuating nuclear spins. While advances in surface engineering have stabilized the charge state of NV centers at depths of tens of nanometers, achieving both ultra-shallow implantation (0.5-2 nm) and long-term spin coherence remains a central challenge. In this work, we show using first-principles modeling that, by exploiting the interaction of surface-induced strain and weak dc magnetic fields, the spin coherence times of 1-nm-deep NV centers can be greatly improved near the spin-phonon-confined regime at room temperature in 12C-rich diamonds. We also demonstrate that this protocol benefits ~ 10-nm-deep NV centers in natural diamond, enabling vector magnetometry at the nanoscale. Shallow NV centers in diamond are advantageous for quantum sensing but suffer from surface magnetic noise. Using first-principles simulations supported by experiments, the authors show that a combination of small magnetic fields and surface strain can significantly enhance spin coherence of 1 nm-deep NV centers.