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arXiv:2208.07954 · Physical review. B./Physical review. B

Surface roughness noise analysis and comprehensive noise effects on depth-dependent coherence time of NV centers in diamond

Philip Chrostoski, Pauli Kehayias, D. H. Santamore

Published Dec 14, 2022• 17 citations
arXivHTMLPDF

Abstract

Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond, causing line broadening and decreasing the coherence time $({T}_{2})$. 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 ${T}_{2}$ and how it varies with NV depth. At a given NV depth of 5 $\mathrm{nm}$ 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 ${T}_{2}$ 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 ${T}_{2,\text{Hahn}}$ (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.

DOI
10.1103/physrevb.106.235311

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Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond, causing line broadening and decreasing the coherence time (T2)({T}_{2})(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{T}_{2}T2​ and how it varies with NV depth. At a given NV depth of 5 nm\mathrm{nm}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{T}_{2}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{T}_{2,\text{Hahn}}T2,Hahn​ (few \ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs to 10 \ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs) 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.
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 T2T_2T2​. We determine a crossover depth at which T2T_2T2​ 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 T2T_2T2​ on orientation for specific surfaces. We also find that the modulation of T2T_2T2​ 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 T2T_2T2​ 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.
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.
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.
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.
Nitrogen vacancy (NV) color centers in diamond have shown great potential for various applications in quantum technology due to their long coherence times, high sensitivity to magnetic fields and atomic scale resolution. However, one major challenge in utilizing near surface NV centers is the decoherence caused by spins and charges fluctuating on the surface, which affects the spin properties of the sensors. To reduce the induced noise, various oxygen surface treatments such as low power oxygen plasma treatment and annealing under oxygen atmosphere have been explored to terminate the diamond surface and reduce its impact on NV coherence. We showed that the NV center’s coherence time can be enhanced up to a factor of 3 over a large spectral range of noise. Double electron–electron resonance measurements revealed an extra source of decoherence, scaling similarly as the P1 spin bath. The improvement in coherence times is accompanied with an increase in measured ketone/ether content and reduction of sp2 signal in x-ray photoelectron spectroscopy measurements. Finally we compared the performance of different NV ensembles and surface treatments for sensing external proton spins. The oxygen annealing is an effective procedure of enhancing the spin coherence times and reducing broad band spin noise experienced by shallow implanted ensemble NV centers in diamond.
Abstract Nitrogen vacancy (NV) color centers in diamond have shown great potential for various applications in quantum technology due to their long coherence times, high sensitivity to magnetic fields and atomic scale resolution. However, one major challenge in utilizing near surface NV centers is the decoherence caused by spins and charges fluctuating on the surface, which affects the spin properties of the sensors. To reduce the induced noise, various oxygen surface treatments such as low power oxygen plasma treatment and annealing under oxygen atmosphere have been explored to terminate the diamond surface and reduce its impact on NV coherence. We showed that the NV center’s coherence time can be enhanced up to a factor of 3 over a large spectral range of noise. Double electron–electron resonance measurements revealed an extra source of decoherence, scaling similarly as the P1 spin bath. The improvement in coherence times is accompanied with an increase in measured ketone/ether content and reduction of sp 2 signal in x-ray photoelectron spectroscopy measurements. Finally we compared the performance of different NV ensembles and surface treatments for sensing external proton spins. The oxygen annealing is an effective procedure of enhancing the spin coherence times and reducing broad band spin noise experienced by shallow implanted ensemble NV centers in diamond.