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npj Quantum Information

Decoherence of nitrogen-vacancy spin ensembles in a nitrogen electron-nuclear spin bath in diamond

Huijin Park, Jung‐Hyun Lee, Sang-Wook Han, Sangwon Oh, Hosung Seo

Published Aug 12, 2022• 46 citations
Publisher

Abstract

Abstract Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units for a wide range of solid-state-based quantum technology applications. While such applications require the long spin coherence times of the NV centers, they are often limited due to decoherence. In this study, we theoretically investigate the decoherence of NV-spin ensembles induced by nitrogen impurities (P1 centers), which are one of the most dominant and inevitable magnetic field noise sources in diamond. We combined cluster correlation expansion and density functional theory to compute the Hahn-echo spin-coherence time of the NV centers for a broad range of P1 concentrations. Results indicate a clear linear dependence of T2 on P1 concentrations on a log scale with a slope of −1.06, which is in excellent agreement with previous experimental results. The interplay between the Jahn–Teller effect and the hyperfine interaction in the P1 center plays a critical role in determining the bath dynamics and the resulting NV decoherence. Our results provide a theoretical upper bound for the NV-spin T2 over a wide range of P1 densities, serving as a key reference for materials optimization and spin bath characterization to develop highly coherent NV-based devices for quantum information technology.

DOI
10.1038/s41534-022-00605-4

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Abstract Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units for a wide range of solid-state-based quantum technology applications. While such applications require the long spin coherence times of the NV centers, they are often limited due to decoherence. In this study, we theoretically investigate the decoherence of NV-spin ensembles induced by nitrogen impurities (P1 centers), which are one of the most dominant and inevitable magnetic field noise sources in diamond. We combined cluster correlation expansion and density functional theory to compute the Hahn-echo spin-coherence time of the NV centers for a broad range of P1 concentrations. Results indicate a clear linear dependence of T2 on P1 concentrations on a log scale with a slope of −1.06, which is in excellent agreement with previous experimental results. The interplay between the Jahn–Teller effect and the hyperfine interaction in the P1 center plays a critical role in determining the bath dynamics and the resulting NV decoherence. Our results provide a theoretical upper bound for the NV-spin T2 over a wide range of P1 densities, serving as a key reference for materials optimization and spin bath characterization to develop highly coherent NV-based devices for quantum information technology.
We present the experimental results of nitrogen-vacancy (NV) electron spin decoherence, which are linked to the coexistence of electron spin bath of nitrogen impurity (P1 center) and 13 C nuclear spin bath. In previous works, only one dominant decoherence source is studied: P1 electron spin bath for type-Ib diamond; or 13 C nuclear spin bath for type-IIa diamond. In general, the thermal fluctuation from both spin baths can be eliminated by the Hahn echo sequence, resulting in a long coherence time ( T 2 ) of about 400 μs. However, in a high-purity type-IIa diamond where 13 C nuclear spin bath is the dominant decoherence source, dramatic decreases of NV electron spin T 2 time caused by P1 electron spin bath are observed under certain magnetic field. We further apply the engineered Hahn echo sequence to confirm the decoherence mechanism of multiple spin baths and quantitatively estimate the contribution of P1 electron spin bath. Our results are helpful to understand the NV decoherence mechanisms, which will benefit quantum computing and quantum metrology.
ABSTRACT The negatively charged nitrogen‐vacancy (NV) center in diamond has emerged as a leading qubit platform. One of the key challenges for NV‐based quantum applications is building an accurate model to predict their decoherence properties. In this study, a combination of theory and experiment is used to investigate NV decoherence dynamics in the presence of P1 center baths. A cluster‐correlation expansion method to compute the decoherence under the Hahn‐echo and CPMG pulse sequences at various P1 concentrations from 1 to 300 ppm is employed. Notably, we find that the coherence time ( T 2 ) scales quadratically as a function of the pulse number, on a logarithmic scale, as opposed to the linear scaling predicted by widely accepted semi‐classical theories. In this experiment, the CPMG signal for two diamond samples with high P1 concentrations of 0.8 and 13 ppm is measured. It is demonstrated that the T 2 scaling is indeed quadratic, thus confirming our theoretical predictions. These results show that the quantum bath model combined with the CCE method can accurately capture the quantum nature of the P1‐driven NV decoherence. This study opens a new avenue for developing a complete noise model that can be used to optimize the performance of NV‐based quantum devices.
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.
Abstract Nitrogen-vacancy (NV) center ensembles in diamond are one of the most promising solid-state quantum platforms for various sensing applications. Achieving ultimate sensitivity requires simultaneously long spin dephasing times ( T2∗{T}_{2}^{* }T2∗​ T 2 * ) and high NV center concentrations. In this work, we propose a systematic measurement approach to quantify the electron spin dephasing in NV center ensembles and analyze the contributions of various sources to the dephasing time, including NV-NV interactions, strain and electric field distributions, 13 C nuclear spins, and P1 electron spins. Our method is validated using a series of high-performance diamond samples, providing a comprehensive understanding of dephasing mechanisms and revealing correlations between NV concentration and different dephasing sources. Building on these insights, we outline strategies to further enhance the achievable sensitivity for DC magnetic field measurements.
Quantum decoherence induced by defects remains a major limitation for solid-state quantum technologies, yet predicting decoherence in realistic materials remains computationally challenging. Complex defect populations are often approximated as homogeneous spin baths, obscuring the role of defect-specific electronic structure and spin dynamics. Here, we develop a predictive framework for decoherence in diamond by combining first-principles electronic-structure calculations, quantum many-body spin-bath simulations, and experimental validation. The framework incorporates defect-resolved spin Hamiltonians and heterogeneous spin baths containing multiple paramagnetic defect species. Using diamond nitrogen-vacancy ensembles as a model platform, we investigate mixed nitrogen-, vacancy-, and hydrogen-related defect environments. We show that decoherence depends not only on defect density but also on defect identity and bath composition, whose distinct electronic structures, hyperfine interactions, and spin dynamics produce different coherence behavior. Heterogeneous defect populations can either suppress or enhance decoherence, producing trends unexplained by homogeneous-bath models. Magnetic-field-dependent Hahn-echo measurements on samples with different defect concentrations validate the framework. The calculations reproduce the observed coherence times and stretched-exponential decay behavior across a broad magnetic-field range and identify vacancy-related defects as critical contributors beyond the conventionally assumed P1 spin bath. By linking atomistic defect properties to quantum coherence, our framework provides a predictive route for identifying hidden defect environments and optimizing decoherence in defect-based quantum materials.
We investigate nitrogen-vacancy center (NV) ensembles in diamond under the influence of strongly correlated electron-spin baths. We thoroughly calculate the decoherence properties of the NV central spin for bath concentrations of 0.1–1000.1\text{--}1000.1–100 ppm using the cluster-correlation expansion (CCE) method. We systematically analyze possible origins of the significant deviations in the values of the T2{T}_{2}T2​ coherence time reported in the literature. We demonstrate that significant variations can originate from the choice of averaging and fitting procedures used for the ensemble average and we point out the respective aspects that need to be considered when comparing the various theoretical studies. Our study may inspire readers to perform reliable simulations on the central spin problem. It provides an understanding and interpretation of the outcome parameters describing the dynamics of the local bath spins.