By efficient nanoscale plasma etching, the nitrogen-vacancy (NV) centers in diamond were brought to the sample surface step by step successfully. At each depth, we measured the ratios of spin coherence times before and after applying external spins on the surface, which reflected the contribution of external spins to the decoherence, and then investigated the relationships between depth and ratios. The values of ratios declined and then rose with the decreasing depth, which was attributed to the decoherence influenced by external spins, surface spins, discrete surface spin effects, and electric field noise. Moreover, our work experimentally and theoretically revealed a characteristic depth at which the NV center would experience relatively the strongest decoherence caused by external spins in consideration of inevitable surface spins. And the characteristic depth was found depending on the local environments of NV centers and the density of surface spins.
We investigated the depth dependence of coherence times of nitrogen-vacancy (NV) centers through precise depth control using oxidative etching at 580 °C in air. By successive nanoscale etching, NV centers could be brought close to the diamond surface step by step, which enabled us to track the evolution of the number of NV centers remaining in the chip and to study the depth dependence of coherence times of NV centers with diamond etching. Our results showed that the coherence times of NV centers declined rapidly with the depth reduction in the last about 22 nm before they finally disappeared, which revealed a critical depth for the influence of a rapid fluctuating surface spin bath. Moreover, by using the slow etching method combined with low-energy nitrogen implantation, NV centers with depths shallower than the initially implanted depths can be generated, which are preferred for detecting external spins with higher sensitivity.
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.
Understanding the dynamics of a quantum bit's environment is essential for the realization of practical systems for quantum information processing and metrology. We use single nitrogen-vacancy (NV) centers in diamond to study the dynamics of a disordered spin ensemble at the diamond surface. Specifically, we tune the density of "dark" surface spins to interrogate their contribution to the decoherence of shallow NV center spin qubits. When the average surface spin spacing exceeds the NV center depth, we find that the surface spin contribution to the NV center free induction decay can be described by a stretched exponential with variable power n. We show that these observations are consistent with a model in which the spatial positions of the surface spins are fixed for each measurement, but some of them reconfigure between measurements. In particular, we observe a depth-dependent critical time associated with a dynamical transition from Gaussian (n=2) decay to n=2/3, and show that this transition arises from the competition between the small decay contributions of many distant spins and strong coupling to a few proximal spins at the surface. These observations demonstrate the potential of a local sensor for understanding complex systems and elucidate pathways for improving and controlling spin qubits at the surface.
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.
The nitrogen-vacancy (NV) center in diamond exhibits spin-dependent fluorescence and long spin coherence times under ambient conditions, enabling applications in quantum information processing and sensing.NV centers near the surface can have strong interactions with external materials and spins, enabling new forms of nanoscale spectroscopy.However, NV spin coherence degrades within 100 nm of the surface, suggesting that diamond surfaces are plagued with ubiquitous defects.Prior work on characterizing near-surface noise has primarily relied on using NV centers themselves as probes; while this has the advantage of exquisite sensitivity, it provides only indirect information about the origin of the noise.Here we demonstrate that surface spectroscopy methods and single-spin measurements can be used as complementary diagnostics to understand sources of noise.We find that surface morphology is crucial for realizing reproducible chemical termination, and use this insight to achieve a highly ordered, oxygenterminated surface with suppressed noise.We observe NV centers within 10 nm of the surface with coherence times extended by an order of magnitude.