Charged Nitrogen-vacancy Center In Diamond Research Articles

Spin-lattice relaxation of individual solid-state spins

Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nano systems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasi-localized phonons when appropriate. Our results, in addition to confirming a $T^5$ temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.

Optically detected magnetic resonance in negatively charged nitrogen-vacancy centers in diamond under resonant optical excitation at cryogenic temperatures

We study optically detected magnetic resonance (ODMR) in diamond ${\mathrm{NV}}^{\ensuremath{-}}$ centers at cryogenic temperatures. We find that when we use resonant optical excitation at zero phonon line wavelength, turning on microwave radiation leads to an increase in fluorescence. This is different from the conventional case of nonresonant optical pumping where microwave radiation instead leads to a decrease in fluorescence. In addition, we observe a significant increase in contrast compared to the nonresonant ODMR. To explain this effect, we propose a theoretical model based on the interaction of the resonant optical radiation with different groups from the inhomogeneously broadened ensemble of ${\mathrm{NV}}^{\ensuremath{-}}$ centers. We find that the effect is temperature dependant and can only be observed at temperatures below 35 K.

Electron-phonon processes of the nitrogen-vacancy center in diamond

Applications of negatively charged nitrogen-vacancy center in diamond exploit the center's unique optical and spin properties, which at ambient temperature, are predominately governed by electron-phonon interactions. Here, we investigate these interactions at ambient and elevated temperatures by observing the motional narrowing of the center's excited state spin resonances. We determine that the center's Jahn-Teller dynamics are much slower than currently believed and identify the vital role of symmetric phonon modes. Our results have pronounced implications for center's diverse applications (including quantum technology) and for understanding its fundamental properties.

Quantum optical master equation for solid-state quantum emitters

We provide an elementary description of the dynamics of defect centers in crystals in terms of a quantum optical master equation which includes spontaneous decay and a simplified vibronic interaction with lattice phonons. We present the general solution of the dynamical equation by means of the eigensystem of the Liouville operator and exemplify the usage of this damping basis to calculate the dynamics of the electronic and vibrational degrees of freedom and to provide an analysis of the spectra of scattered light. The dynamics and spectral features are discussed with respect to the applicability for color centers, especially for negatively charged nitrogen-vacancy centers in diamond.

A neutral oxygen-vacancy center in diamond: A plausible qubit candidate and its spintronic and electronic properties

Spintronic and electronic properties of a neutral oxygen-vacancy (O-V) center, an isoelectronic defect similar to the negatively charged nitrogen-vacancy center in diamond, were studied by combining first-principles calculations and a mean-field theory for spin hyperfine interaction. It is elucidated that the neutral O-V center is stable in the p-type diamond and possesses an S = 1 triplet ground state and four spin-conserved excited states with the spin coherence times in an order of second at T = 0 K. The results indicate that the neutral O-V center is another promising candidate for spin coherent manipulation and qubit operation.

Optically detected cross-relaxation spectroscopy of electron spins in diamond.

The application of magnetic resonance spectroscopy at progressively smaller length scales may eventually permit 'chemical imaging' of spins at the surfaces of materials and biological complexes. In particular, the negatively charged nitrogen-vacancy (NV(-)) centre in diamond has been exploited as an optical transducer for nanoscale nuclear magnetic resonance. However, the spectra of detected spins are generally broadened by their interaction with proximate paramagnetic NV(-) centres through coherent and incoherent mechanisms. Here we demonstrate a detection technique that can resolve the spectra of electron spins coupled to NV(-) centres, in this case, substitutional nitrogen and neutral nitrogen-vacancy centres in diamond, through optically detected cross-relaxation. The hyperfine spectra of these spins are a unique chemical identifier, suggesting the possibility, in combination with recent results in diamonds harbouring shallow NV(-) implants, that the spectra of spins external to the diamond can be similarly detected.

New insight into the spin-conserving excitation of the negatively charged nitrogen-vacancy center in diamond.

The negatively charged nitrogen-vacancy (N-V−) color center in diamond is an important solid-state single photon source for applications to quantum communication and distributed quantum computation. Its full usefulness relies on sufficient radiative emission of the optical photons which requires realizable control to enhance emission into the zero-phonon line (ZPL) but until now is still a challenge. Detailed understanding of the associated excitation process would be of essential importance for such objective. Here we report a theoretical work that probes the spin-conserving optical excitation of the N-V− center. Using density-functional-theory (DFT) calculations, we find that the ZPL and the phonon-side band (PSB) depend sensitively on the axial strain of the system. Besides, we find a relatively small PSB appearing at about 100 GPa in the emission spectrum at low temperatures, which provides a means to enhance the coherent emission of the N-V− center in quantum optical networks.

Strong magnetic coupling of an inhomogeneous nitrogen-vacancy ensemble to a cavity

We study experimentally and theoretically a dense ensemble of negatively charged nitrogen-vacancy centers in diamond coupled to a high-$Q$ superconducting coplanar waveguide cavity mode at low temperature. The nitrogen-vacancy centers are modeled as effective spin-one defects with inhomogeneous frequency distribution. For a large enough ensemble the effective magnetic coupling of the collective spin dominates the mode losses and inhomogeneous broadening of the ensemble and the system exhibits well-resolved normal-mode splitting in probe transmission spectra. We use several theoretical approaches to model the probe spectra and the number and frequency distribution of the spins. This analysis reveals an only slowly temperature-dependent $q$-Gaussian energy distribution of the defects with a yet unexplained decrease of effectively coupled spins at very low temperatures below $100\phantom{\rule{0.28em}{0ex}}\mathrm{m}\mathrm{K}$. Based on the system parameters we predict the possibility to implement an extremely stable maser by adding an external pump to the system.

Theory of the ground-state spin of the NV−center in diamond

The ground-state spin of the negatively charged nitrogen-vacancy center in diamond has been the platform for the recent rapid expansion of new frontiers in quantum metrology and solid-state quantum-information processing. However, in spite of its many outstanding demonstrations, the theory of the spin has not yet been fully developed, and there do not currently exist thorough explanations for many of its properties, such as the anisotropy of the electron $g$ factor and the existence of Stark effects and strain splittings. In this work, the theory of the ground-state spin is fully developed using the molecular orbital theory of the center in order to provide detailed explanations for the spin's fine and hyperfine structures and its interactions with electric, magnetic, and strain fields. Given these explanations, a general solution is obtained for the spin in any given electric-magnetic-strain field configuration, and the effects of the fields on the spin's coherent evolution, relaxation, and inhomogeneous dephasing are examined. Thus, this work provides the essential theoretical tools for the precise control and modeling of this remarkable spin in its current and future applications.

The negatively charged nitrogen-vacancy centre in diamond: the electronic solution

The negatively charged nitrogen-vacancy centre is a unique defect in diamond that possesses properties highly suited to many applications, including quantum information processing, quantum metrology and biolabelling. Although the unique properties of the centre have been extensively documented and utilized, a detailed understanding of the physics of the centre has not yet been achieved. Indeed, there persist a number of points of contention regarding the electronic structure of the centre, such as the ordering of the dark intermediate singlet states. Without a detailed model of the centre's electronic structure, the understanding of the system's unique dynamical properties cannot effectively progress. In this work, the molecular model of the defect centre is fully developed to provide a self-consistent model of the complete electronic structure of the centre. The application of the model to describe the effects of electric, magnetic and strain interactions, as well as the variation of the centre's fine structure with temperature, provides an invaluable tool to those studying the centre and a means of designing future empirical and ab initio studies of this important defect.

The foundations of the defect-molecule model of the N–V center in diamond

The negatively charged nitrogen-vacancy center in diamond is highly suited to many quantum information processing applications. Although the center has been comprehensively observed experimentally, there still remains contention regarding some of the key aspects of the current theoretical model of the center. In this article, the explicit development of the defect-molecule model of the center and the implications of the accumulated ab initio results are discussed. The aspects of the model that require further ab initio investigation are clearly identified and a possible Hartree-Fock extension is motivated.

Symmetric Double-Well Potential Model and Its Application to Vibronic Spectra: Studies of Inversion Modes of Ammonia and Nitrogen-Vacancy Defect Centers in Diamond

In this paper, we have studied the vibronic transitions between two symmetric double-well potentials by proposing a model Hamiltonian consisting of a harmonic oscillator and a parturition described by a Gaussian function that leads to a double minima potential with a barrier between the two energy minima. Making use of the contour integral form of Hermite polynomials, we present a new formula that can calculate Franck-Condon factors of the system rigorously. The simulated vibronic spectra of ammonia and the negatively charged nitrogen-vacancy center in diamond are presented as an application of the formula.