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arXiv:cond-mat/0601360 · Physical Review B

Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics

Neil B. Manson, J. P. Harrison, Matthew J. Sellars

Published Sep 21, 2006• 649 citations
arXivHTMLPDF

Abstract

Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the change of emission level with spin polarization and for new experimental measurements of transient emission. The rate constants given are in variance to those reported previously.

DOI
10.1103/physrevb.74.104303

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The nitrogen-vacancy (N-V⁻) colour centre in diamond has potential applications in quantum information processing and single photon generation. It is currently the only known defect in a solid detected at a single site level that has a non-zero spin in the electronic ground state. For the proposed applications it is desirable to have a good understanding of the electronic structure and photodynamics of the centre, however this is currently not the case. Various models have been proposed to explain the fluorescence characteristics observed in single site experiments. The challenge has been to also account for the properties of the centre well-known from observations of the fluorescence from large ensembles of N-V⁻ in diamond. Firstly, that a non-Boltzmann population distribution between the. ground state spin levels is induced by optical excitation. Secondly, that the fluorescence intensity exhibits a strong dependence on the spin orientation. The models proposed to date either cannot account for these properties, or do so only by invoking optical processes that are arbitrary or, in some cases, not physical. In this thesis an alternative model is presented. The derivation of the model, from group theoretical considerations, does not form part of this thesis. This thesis is concerned primarily with a series of independent measurements to determine the transition rates which govern the photodynamics of the centre. When these transition rates are known, there will be no free parameters in the model and the N-V⁻ emission can be simulated for an arbitrary optical field by solving the classical rate equations. To conclude the first part of this thesis, a two-pulse optical excitation is considered and the results of experiment are compared to the predictions of the model. The latter part of t his thesis is concerned with optically detecting single N-V⁻ centres. A confocal microscope system, to enable single site detection, was developed as part of this work. The photon statistics from a single N-V⁻ centre is compared to the statistics predicted by the model. The implications for the modelling of individual N-V⁻ photon statistics are discussed.

•Jan 1, 2006•0 citations
Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the change of emission level with spin polarization and for new experimental measurements of transient emission. The rate constants given are in variance to those reported previously.
The nitrogen-vacancy (NV) center in diamond is of high importance in quantum information processing applications. The operation of the NV center relies on the efficient optical polarization of its electron spin. However, the full optical spin-polarization process, which involves the intersystem crossing between the shelving singlet state and the ground-state triplet, is not understood. Here we develop a detailed theory of this process which involves a combination of pseudo- and dynamic Jahn-Teller interactions together with spin-orbit interaction. Our theory provides an explanation for the asymmetry between the observed emission and absorption spectra of the singlet states. We apply density functional theory to calculate the intersystem crossing rates and the optical spectra of the singlets, and we obtain a good agreement with the experimental data. Since the NV center serves as a template for other solid-state-defect quantum bit systems, our theory provides a toolkit to study them that might help optimize their quantum bit operation.
Optical and microwave double resonance techniques are used to obtain the excited state structure of single nitrogen-vacancy centers in diamond. The excited state is an orbital doublet and it is shown that it can be split and associated transition strengths varied by external electric fields and by strain. A group theoretical model is developed. It gives a good account of the observations and contributes to an improved understanding of the electronic structure of the center. The findings are important for quantum information processing and other applications of the center.
The nitrogen - vacancy (N-V) center is a point defect found in diamonds containing substitutional nitrogen impurities. It arises after exposure to ionizing radiation and subsequent thermal annealing. The physical structure of the center has previously been identified as a substitutional nitrogen atom located adjacent to a neutral carbon vacancy, but prior to this work knowledge of its electronic structure was very incomplete. The results presented here are intended to establish the energy level structure of the N-V center unambiguously, using nonlinear laser spectroscopy in concert with paramagnetic resonance experiments. A new technique which achieves sub-Hertz resolution in nearly degenerate four-wave mixing (NDFWM) and optical two-beam coupling experiments was applied to determine the decay rates of excited states in the N-V center. Laser-enhanced EPR experiments were performed to assign spin character to the ground state. Fluorescent emission of the center was used to determine excited state energies. In particular, these results resolve earlier conflicting reports of the N-V ground state structure and offer a picture of state energies and dynamics consistent with all observations to date. The principal results of this thesis may be summarized as follows. We show that the ground state of the center consists of a spin triplet ground state with a zero-field splitting of 2.88 GHz and a spin-lattice relaxation time of 1.170 ±\pm± 0.003 ms. The first parity-allowed transition occurs to a triplet excited state at 1.944 eV with a lifetime of 13.3 ±\pm± 0.2 ns. The first metastable singlet excited state is shown to have a lifetime of 265.3 ±\pm± 0.6 ms at room temperature and its temperature dependence measured between 77 and 295 K. Through low temperature studies the mechanism for ground state spin-lattice relaxation is determined to be a two-phonon process involving 63 meV optical phonons. Finally, the origin of satellite lines in the persistent hole-burning spectrum is tentatively explained using our picture of the energy level structure and used to infer a zero-field spin splitting in the excited triplet state of 0.6 GHz.
The nitrogen-vacancy (N-V⁻) colour centre in diamond has potential applications in quantum information processing and single photon generation. It is currently the only known defect in a solid detected at a single site level that has a non-zero spin in the electronic ground state. For the proposed applications it is desirable to have a good understanding of the electronic structure and photodynamics of the centre, however this is currently not the case. Various models have been proposed to explain the fluorescence characteristics observed in single site experiments. The challenge has been to also account for the properties of the centre well-known from observations of the fluorescence from large ensembles of N-V⁻ in diamond. Firstly, that a non-Boltzmann population distribution between the. ground state spin levels is induced by optical excitation. Secondly, that the fluorescence intensity exhibits a strong dependence on the spin orientation. The models proposed to date either cannot account for these properties, or do so only by invoking optical processes that are arbitrary or, in some cases, not physical. In this thesis an alternative model is presented. The derivation of the model, from group theoretical considerations, does not form part of this thesis. This thesis is concerned primarily with a series of independent measurements to determine the transition rates which govern the photodynamics of the centre. When these transition rates are known, there will be no free parameters in the model and the N-V⁻ emission can be simulated for an arbitrary optical field by solving the classical rate equations. To conclude the first part of this thesis, a two-pulse optical excitation is considered and the results of experiment are compared to the predictions of the model. The latter part of t his thesis is concerned with optically detecting single N-V⁻ centres. A confocal microscope system, to enable single site detection, was developed as part of this work. The photon statistics from a single N-V⁻ centre is compared to the statistics predicted by the model. The implications for the modelling of individual N-V⁻ photon statistics are discussed.