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AIP Advances

A statistical correlation investigation for the role of surface spins to the spin relaxation of nitrogen vacancy centers

Xuerui Song, Jian Zhang, Fupan Feng, Junfeng Wang, Wenlong Zhang, Liren Lou, Wei Zhu, Guanzhong Wang

Published Apr 1, 2014• 25 citations
Publisher

Abstract

We investigated the influence of spins on surface of nanodiamonds (NDs) to the longitudinal relaxation time (T1) and transverse relaxation time (T2) of nitrogen vacancy (NV) centers in ND. A spherical model of the NDs was suggested to account for the experimental results of T1 and T2, and the density of surface spins was roughly estimated based on the statistical analysis of experimental results of 72 NDs containing a single NV center. For NDs studied here, the T1 of NV center inside is highly dependent to the surface spins of the NDs. However, for the T2 of NV center, intrinsic contributions must be much pronounced than that by surface spins. In other words, T1 of an NV center in NDs is more sensitive to the change of the surface spin density than T2.

DOI
10.1063/1.4870938

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We investigated the influence of spins on surface of nanodiamonds (NDs) to the longitudinal relaxation time (T1) and transverse relaxation time (T2) of nitrogen vacancy (NV) centers in ND. A spherical model of the NDs was suggested to account for the experimental results of T1 and T2, and the density of surface spins was roughly estimated based on the statistical analysis of experimental results of 72 NDs containing a single NV center. For NDs studied here, the T1 of NV center inside is highly dependent to the surface spins of the NDs. However, for the T2 of NV center, intrinsic contributions must be much pronounced than that by surface spins. In other words, T1 of an NV center in NDs is more sensitive to the change of the surface spin density than T2.
Nanoscale quantum probes such as the nitrogen-vacancy (NV) center in diamonds have demonstrated remarkable sensing capabilities over the past decade as control over fabrication and manipulation of these systems has evolved. The biocompatibility and rich surface chemistry of diamonds has added to the utility of these probes but, as the size of these nanoscale systems is reduced, the surface chemistry of diamond begins to impact the quantum properties of the NV center. In this work, we systematically study the effect of the diamond surface chemistry on the quantum coherence of the NV center in nanodiamonds (NDs) 50 nm in size. Our results show that a borane-reduced diamond surface can on average double the spin relaxation time of individual NV centers in nanodiamonds when compared to thermally oxidized surfaces. Using a combination of infrared and X-ray absorption spectroscopy techniques, we correlate the changes in quantum relaxation rates with the conversion of sp 2 carbon to C–O and C–H bonds on the diamond surface. These findings implicate double-bonded carbon species as a dominant source of spin noise for near surface NV centers. The link between the surface chemistry and quantum coherence indicates that through tailored engineering of the surface, the quantum properties and magnetic sensitivity of these nanoscale systems may approach that observed in bulk diamond.
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.
Fluorescent nanodiamonds (NDs) are crystal defect-based light-emitting nanoparticles that can be applied to quantum information science and quantum sensing. Of particular interest are nitrogen vacancy (NV) centers that allow optical access to their coherently controllable electron spin systems, leading to spin-photon quantum devices and nanoscale sensing of various physical parameters. However, the NV spin coherence time (T2) in NDs has been limited to one or two orders of magnitude shorter than those in bulk diamonds owing to the complicated surface effect that decoheres the NV spin systems. Here, we study the relation between the surface properties and T2 of single NV centers in NDs by systematically analyzing the effect of surface oxidation. We apply aerobic and acidic oxidation methods with various heating temperatures and processing times and find that aerobic oxidation most effectively oxidizes the surface and extends T2 by a factor of 1.6 to the original NDs. The ND-size dependence of T2 clearly shows that the surface oxidation removes a constant decoherence contribution irrespective of the ND size and that a new surface derived decoherence source emerges when the ND size reduces below 50 nm. The present results provide quantitative information on the decoherence sources of NV spin systems of NDs and will enable a strategic surface modification for better spin manipulations of NV centers in the context of quantum information science and nanoscale quantum sensing.
This thesis focuses on the spin physics of nitrogen-vacancy (NV) centres in nanodiamonds (NDs) via their coupling to external fields. In the first part, we theoretically investigate the feasibility of coupling a ND with a high density of NV centres to a gap-tunable flux qubit. We calculate the optimum position including the tolerance for maximizing the coupling and calculate its dependence on the orientation of the ND. We demonstrate that the coherent coupling of a 150-nm ND containing many (10³) NV centres and a flux qubit with dephasing time of ~1 μs is feasible. In the second part, we investigate the spin-coherence properties of NV centres in NDs and discuss them in the context of the NVs-to-flux qubit coupling. In particular, we manipulate the NV spins via an external microwave field using two distinct methods. The first, more conventional method employs a thin wire in direct contact with the sample as the microwave antenna. The second method has been developed by our group. It uses a cavity to produce the microwave field at the position of the NV spins with the advantage over the wire architecture of addressing the NV centre spins, without sample heating and over macroscopic spatial distances (milli-meters versus micro-meters).
Thanks to their versatility, nitrogen-vacancy (N-VVV) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-VsV\mathrm{s}Vs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the ${m}_{s}=|\ifmmode\pm\else\textpm\fi{}1⟩$ states of the N-${V}^{\ensuremath{-}}$ electronic ground state in approximately 40-nm nanodiamonds under ambient conditions. For frequency splittings between these states of 20 MHz or less the maximum theoretically achievable coherence time of the N-VVV spin is approximately 2 orders of magnitude shorter than would be expected if the N-VVV spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with N-VsV\mathrm{s}Vs in nanodiamonds should be performed at moderate axial magnetic fields (>60>60>60 G). We also observe that the qutrit relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for N-VsV\mathrm{s}Vs in nanodiamonds.
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.