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arXiv:1309.5921

Analytic solutions to the central spin problem for Nitrogen Vacancy centres in diamond

Liam T. Hall, Jared H. Cole, Lloyd C. L. Hollenberg

Published Sep 19, 2013• 1 citation
arXivHTMLPDF

Abstract

Due to interest in both solid state based quantum computing architectures and the application of quantum mechanical systems to nanomagnetometry, there has been considerable recent attention focused on understanding the microscopic dynamics of solid state spin baths and their effects on the coherence of a controllable, coupled central electronic spin. Many analytic approaches are based on simplified phenomenological models in which it is difficult to capture much of the complex physics associated with this system. Conversely, numerical approaches reproduce this complex behaviour, but are limited in the amount of theoretical insight they can provide. Using a systematic approach based on the spatial statistics of spin bath constituents, we develop a purely analytic theory for the central spin decoherence problem of Nitrogen Vacancy centres in diamond that reproduces the experimental and numerical results found in the literature, whilst correcting a number of limitations and inaccuracies associated with existing analytical approaches.

DOI
10.48550/arxiv.1309.5921

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Due to interest in both solid state based quantum computing architectures and the application of quantum mechanical systems to nanomagnetometry, there has been considerable recent attention focused on understanding the microscopic dynamics of solid state spin baths and their effects on the coherence of a controllable, coupled central electronic spin. Many analytic approaches are based on simplified phenomenological models in which it is difficult to capture much of the complex physics associated with this system. Conversely, numerical approaches reproduce this complex behaviour, but are limited in the amount of theoretical insight they can provide. Using a systematic approach based on the spatial statistics of spin bath constituents, we develop a purely analytic theory for the central spin decoherence problem of Nitrogen Vacancy centres in diamond that reproduces the experimental and numerical results found in the literature, whilst correcting a number of limitations and inaccuracies associated with existing analytical approaches.
The field of quantum science and technology has generated many ideas for new revolutionary devices that exploit the quantum mechanical properties of small-scale systems. Isolated solid state spins play a large role in quantum technologies. They can be used as basic building blocks for a quantum computer or as ultra-sensitive magnetic-field probes which can detect the extremely weak magnetic field generated by a single proton. A major hurdle for realizing these applications is the loss of quantum coherence resulting from uncontrolled interactions with spins in the environment. In the experiments described in my thesis we studied spins associated with defect centers in diamond and used new strategies for mitigating decoherence involving advanced quantum control techniques and for fundamental studies of decoherence. We show that we can prolong the coherence time of a single spin associated with a Nitrogen-Vacancy (NV) defect center in diamond with dynamical decoupling techniques. Our experiments are accurately reproduced theoretically and from this theory we conclude that, with dynamically decoupling, the spin environment can in principle be made irrelevant for the decoherence of a single spin. This removes a major obstacle for using solid-state spins in quantum science and technology. Furthermore, the dynamics in the spin environment and its influence on the NV spin is thoroughly experimentally studied. By better understanding the mechanisms behind decoherence we may one day find the answer to unresolved fundamental issues in quantum physics such as the quantum measurement problem.
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.
Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.
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.
Phase coherence is a fundamental concept in quantum mechanics. Understanding the loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen-vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into the loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.
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.